*Article* **Magnetoimpedance E**ff**ect in the Ribbon-Based Patterned Soft Ferromagnetic Meander-Shaped Elements for Sensor Application**

**Zhen Yang 1,2, Anna A. Chlenova 1,3, Elizaveta V. Golubeva 1, Stanislav O. Volchkov 1, Pengfei Guo 2, Sergei V. Shcherbinin 1,4 and Galina V. Kurlyandskaya 1,5,\***


Received: 7 May 2019; Accepted: 27 May 2019; Published: 29 May 2019

**Abstract:** Amorphous and nanocrystalline soft magnetic materials have attracted much attention in the area of sensor applications. In this work, the magnetoimpedance (MI) effect of patterned soft ferromagnetic meander-shaped sensor elements has been investigated. They were fabricated starting from the cobalt-based amorphous ribbon using the lithography technique and chemical etching. Three-turn (S1: spacing s = 50 μm, width w = 300 μm, length l = 5 mm; S2: spacing s = 50 μm, width w = 400 μm, length l = 5 mm) and six-turn (S3: s = 40 μm, w = 250 μm, length l = 5 mm; S4: s = 40 μm, w = 250 μm and l = 8 mm) meanders were designed. The 'n' shaped meander part was denominated as "one turn". The S4 meander possesses a maximum MI ratio calculated for the total impedance ΔZ/Z ≈ 250% with a sensitivity of about 36%/Oe (for the frequency of about 45 MHz), and an MI ratio calculated for the real part of the total impedance ΔR/R ≈ 250% with the sensitivity of about 32%/Oe (for the frequency of 50 MHz). Chemical etching and the length of the samples had a strong impact on the surface magnetic properties and the magnetoimpedance. A comparative analysis of the surface magnetic properties obtained by the magneto-optical Kerr technique and MI data shows that the designed ferromagnetic meander-shaped sensor elements can be recommended for high frequency sensor applications focused on the large drop analysis. Here we understand a single large drop as the water-based sample to analyze, placed onto the surface of the MI sensor element either by microsyringe (volue range 0.5–500 μL) or automatic dispenser (volume range 0.1–50 mL).

**Keywords:** Magnetoimpedance effect; amorphous ribbons; patterned ribbons; meander sensitive element; magnetic field sensor

#### **1. Introduction**

The magnetoimpedance (MI) effect is a classic electromagnetic phenomenon which can be described as a significant change of the total impedance of a ferromagnetic conducting sensor element applied to an external magnetic field when a high frequency alternating current flows through it [1–3]. The first magnetic field sensors working on the principle of the change of alternating current resistance applied to an external magnetic field were reported by Makhotkin et al. [4] even before the MI phenomenon was given its proper name [2,3].

In recent years, MI sensors have attracted special attention for their promising technological applications in different fields [5–8]. Cobalt-based amorphous ribbons show good MI characteristics with high sensitivity with respect to applied magnetic fields, sufficient even for biosensor applications [9,10]. Cobalt-based rapidly quenched materials have reasonably high saturation magnetization and nearly zero magnetostriction constant value, characteristics that make them good candidates for very different applications [11–13]. One of the shortcomings of the rapidly quenched ribbon-based materials is their relatively large size. It was shown previously that the shape anisotropy plays a crucial role and the MI ratio decreases significantly in the ribbons with a length of less than a few centimeters [14,15]. One of the solutions to such a problem was to create patterned elements in the shape of the meander [16–18] when the flat surface of the sensor element is required. Although meander geometry was previously applied with success for the case of MI multilayered structures [19–21], the proposed solution was shown to be useful in selected applications as the ribbon patterning technology is cheaper in comparison with the thin films case, despite the disadvantage of a lower degree of compatibility with semiconductor electronics, and the interaction effect resulting in a decrease of the overall sensitivity. The effective length in a meander-shaped MI sensor element is increased in comparison with the overall maximum dimension, providing the MI meander element a special advantage. At the same time, possible interactions between the fields created by the different parts of a meander can be complicated, and this geometry requires additional investigation.

Low working frequency is usually preferred for sensor applications as it makes the electronics circuit cheaper and insures easier processing of the electronic signals. At the same time, the frequency of the exciting current is an important parameter for determining the MI value [1,12]. Further development of electronic circuits and measurement techniques have possibly extended the frequency range of MI-based sensor applications [22–24] to higher frequencies where the signal-to-noise ratio can be improved [12].

Despite the fact that MI materials with a very high MI ratio and sensitivity, combined with a small size, have already been reported [25,26], there are particular biomedical applications for which flat biosensors are required to measure liquids with a relatively large bioanalyte drop. Such applications can be found in the environmental control and technological control of reservoirs. It is worth mentioning the existence of similar solutions found earlier for giant magnetoresistance-based elements for magnetic label detection [27]. In these cases, the resulting sensor elements consisted of wound lines forming the spiral structures. They were assembled into the element consisting of tens of the elements incorporated into the area of few squared millimeters. The signal for detection was collected from a number of elements after appropriate biochemical treatment. Therefore, we proposed to design a relatively large sensor element for the evaluation of the signal from one element. In future it might be useful for testing the composition with four elements in a bridge configuration.

In this work, the magnetic properties and magnetoimpedance of patterned Co-based amorphous ribbons were comparatively analyzed. We made the first step to work out the protocol of evaluation of magnetic properties of such complex subjects. MI was measured in the extended frequency range of 1–200 MHz. The patterning was done by lithography and chemical etching in the shape of meander sensor elements with three- or six-turns, with design focused on large drop analysis.

#### **2. Materials and Methods**

#### *2.1. Fabrication of Ribbon-Based Patterned Soft Ferromagnetic Multi-Turn Sensitive Elements*

First of all, we designed and developed small sensor elements in the geometry of the meander shape close to a square, aiming to develop a particular type of detector focused on the single large drop analysis of bioanalytes. Water droplet size is very important for different areas of analysis. Here, we understand a single large drop as the water-based sample to analyze, laced onto the surface of the MI sensor element either by microsyringe (volue range 0.5–500 μL) or automatic dispenser (volume range 0.1–50 mL). The fabrication process of patterned ribbons constitutes a series of steps. Initially the as-cast ribbon was produced by the rapid quenching technique [24,25] followed by cutting, field annealing, mechanical polishing and micromachining. Amorphous ribbons in the as-cast state were obtained with Co75Fe10Ni2Si8B5 nominal composition and a thickness of about 20 μm. Afterward, ribbons were cut in 4 × 3 cm pieces via the SPF-7100 die sawing system, and the subjected to transverse magnetic field annealing treatment in order to induce transverse magnetic anisotropy. The magnetic field during field annealing was applied perpendicular to the ribbon axis (perpendicular to the direction of the ribbon movement during the solidification). The details of the annealing process can be found elsewhere [23]. Mechanical polishing was performed by diamond sand-paper with a gradual reduction of the grain size in order to reduce the surface roughness having a negative impact on the value of MI sensitivity [28]. After polishing, the thickness of the ribbons was close to 15 μm. In order to reduce the etching error, chemical etching was carried out in a thermostatic water bath. Micromachining was done by micro electro-mechanical system (MEMS) technology, including bonding, lithography, and chemical etching. After etching, all patterned ribbons in the meander shape were polished again to ensure a smooth surface. The last request is especially important in biosensor applications for magnetic label detection.

Although different geometries obtained by the employed technique were tested, we selected just a few of them with reasonable quality (Figure 1). With the amorphous ribbons it is impossible to ensure a flat cross-section of the samples for the individual line width below 0.1 mm. Planning the creation of the magnetic marker sensor for the in-liquid detection, one must keep the surface geometry as flat as possible. Meanders with a larger number of turns are difficult to fabricate by etching; therefore we selected some simple options for testing. Figure 1a,b shows the surface features of the amorphous ribbon after both chemical etching and polishing.

**Figure 1.** Surface micrograph of the Co75Fe10Ni2Si8B5 ribbon after chemical etching (**a**). Surface micrograph of the chemical etched Co75Fe10Ni2Si8B5 ribbon after polishing (**b**). The description of the selected types of the patterned MI meanders (**c**,**d**). General view of the fabricated patterned MI meanders S1 and S4 (**e**,**f**). Part (**c**) shows three-turn and part (**d**) shows six-turn meanders.

The micropatterned ribbon sensor elements were designed as compact n-shaped meander structures. Figure 1c,d shows selected examples of the meander geometry. The 'n' shaped meander part was denominated as a "one turn" sample.

Three-turn meanders were denominated as S1 and S2, and six-turn meanders were denominated as S3 and S4. Details of the geometries of all samples are given in Table 1. The length close to 8 mm was previously described in the literature as a critical length for non-patterned amorphous ribbon [13,14]. The spacing of 50 μm and length of 5 mm were used for S1 and S2 meanders and the same spacing of 40 μm and width of 250 μm were used for S3 and S4 meanders. Figure 1e,f shows a general view of the fabricated S1 and S4 meanders. High magnification allows an estimation of the quality of the fabricated sensitive elements.


**Table 1.** Selected parameters of Co75Fe10Ni2Si8B5 meanders.

#### *2.2. Measurement of Surface Magnetic Properties of the Samples*

Surface magnetic properties of the samples were investigated by the magneto-optical Kerr effect (MOKE) using a Kerr microscope (Evico magnetics GmbH, Dresden, Germany). MOKE measurements were performed by collecting the signal in the longitudinal mode, i.e., the component of magnetization lying in the sample plane and parallel to the direction of incidence of light was analyzed. Figure 1c,d shows some selected positions—A, B, C, D, E, F, G, H for MOKE measurement (white squares) according to the symmetric structure of the meander patterning. The signal was obtained from the plot area of 0.5 <sup>×</sup> 0.5 mm2. Some characteristic positions named by the same letter were picked up for the same location for different samples. The magnetic field up to 270 Oe was applied along the ribbon axis coinciding with longer part of the "n"- shaped direction. Meanwhile the magnetic field was also applied perpendicular to the ribbon axis for comparative analysis.

MOKE is a surface sensitive method that probes the surface magnetization. The origin of the high frequency alternating current impedance is connected to the change of the dynamic magnetic permeability and skin effect [1–3]. As the high frequency alternating current flows close to the surface, it is the surface anisotropy that makes a significant contribution to the MI effect value.

We made the first step to work out the protocol of evaluation of the magnetic properties of such complex subjects. On one hand, the bulk measurements with vibrating sample magnetometer (VSM) could provide more complete information because the VSM signal comes not only from the surface but also from the volume of the massive sample. On the other hand, the information obtained from the whole meander is quite mixed as the shape anisotropy and interactions between different parts of the meanders are crucial. There is no detailed evaluation of local magnetic properties of such structures in the literature and we made a step in this direction. As will be shown below, the proposed methodology seems to be working.

#### *2.3. Measurement of MI*

In order to ensure high-quality MI measurements and to minimize the "microstripe line" holder parasite signal contribution, special sample holders were prepared in accordance with the size of each sample (Figure 2b). The total effective impedance of the sample installed in a measuring circuit ("microstrip" line in this particular case) consisted of two different parts. The first one was the intrinsic impedance of the sample. It changes under the application of the external magnetic field. The second one is the external impedance attributed to the circuit itself. The last contribution does not change in the course of the external magnetic field application. This means that the measured effect is lower than the one corresponding to the intrinsic impedance of the MI sensor element.

**Figure 2.** Schematic view of the MI measuring system for meander samples (**a**) and and "microstrype line" type sample holder with incorporated meander sample (**b**).

The impedance was measured as a function of alternating current frequency in the frequency range of 1 to 200 MHz using an automatic system based on a precision Agilent HP E4991A impedance analyzer. The calibration of the system and mathematical subtraction of the contributions of the test fixture were in accordance with a previously established procedure [29]. Total impedance (Z) was measured as a function of the external magnetic field for the exciting current amplitude of 10 mA in all measurements. The external quasi-static magnetic field (H) generated by Helmholtz coils was changed in the interval +110 to −110 Oe and aligned with the long parts of the meander.

Measurements in the decreasing field were denominated as the "down" branch; measurements in the increasing field were denominated as the "up" branch. The MI ratio for total impedance variation and its real part in the external magnetic field were calculated as follows:

$$
\Delta\text{Z/Z} = 100 \times (\text{Z(H)} - \text{Z(H\_{max})}) / \text{Z(H\_{max})}\tag{1}
$$

$$\text{AR} \text{/R} = 100 \times (\text{R}(\text{H}) - \text{R}(\text{H}\_{\text{max}})) / \text{R}(\text{H}\_{\text{max}}) \tag{2}$$

where Hmax = 110 Oe. The maximum ratio at each frequency was denoted ΔZ/Zmax for the total impedance and ΔR/Rmax for its real part. An important characteristic of the MI response is the maximal sensitivity with respect to the external magnetic field. The MI sensitivity with respect to the applied magnetic field was calculated as follows:

$$\Delta(\Delta Z/Z) = \Delta(\Delta Z/Z)/\Delta \text{H} \tag{3}$$

$$\Delta\text{S(\Delta\text{R/R})} = \Delta(\Delta\text{R/R})/\Delta\text{H} \tag{4}$$

where ΔH ≈ 0.1 Oe is the field increment for calculation of ΔZ and ΔR.

#### **3. Results and Discussion**

The quasi-static magnetic properties of the meanders were measured by the MOKE microscope. Hysteresis loops taken from the characteristic sections of the samples (Figure 1) are shown in the Figure 3. The hysteresis loops in point A have the small coercive force and high magnetic permeability, which are

common for amorphous magnetically soft ribbons [10,29]. More complex types of magnetization reversal were observed for the non-external long sections of the meander due to the complicated process of magnetization interactions with the adjacent parts of the element. Although, one can notice a great difference between the magnetization processes in points B and C of the samples S1, S2 and S3. In the case of the sample S4, only a slight increase in the coercive force takes place. As this sample is longer than the others, one can suppose that the changes in the type of the hysteresis loops are caused by an influence of the smaller contribution of the meanders' round sections (as points D and H in Figure 2) as well as due to the stronger contribution of the demagnetizing factor of the elongated parts. Although the details of such a mechanism are not clear, the origin can be explained by the presence of the stray fields of different meanders' areas and surface, including the border defects that appeared during the samples' production process. At the same time, in order to obtain statistics and better insight, M(H) loops were measured many times at the same position and allow a small displacement. As the M(H) loops in these conditions did not change very much we have concluded that border effects were not crucial.

**Figure 3.** MOKE hysteresis loops taken from the corresponding characteristic sections A, B (G), C (F) of different Co75Fe10Ni2Si8B5 meander samples. The external magnetic field is applied parallel to the long side of the meanders and perpendicular to the induced magnetic anisotropy axis.

Also, one can notice that the magnetic properties of the turning sections of meanders (points D, E, H) differ from the properties of the middle sections (Figures 3 and 4). In these regions the material of the meander reaches a saturated state only in very high magnetic fields above 200 Oe. Moreover, in the case of the sample S4 a certain increase in the coercive force is observed. This fact supports our hypothesis about role of the shape, and to a lesser extent the defects caused by the etching on local magnetic properties and effective magnetic anisotropy axis dispersion.

Δ

Δ

Although point-by-point analysis of the local hysteresis loops is useful, one can also compare the whole set of the obtained shapes of M(H) loops. It is clear that in the S4 case, M(H) loops for very different points differ from each other to a lesser extent, i.e., the magnetic material shows a lower degree of inhomogeneity in the sense of the dominating magnetization mechanisms. A similar concept was previously discussed in the literature for non-patterned amorphous and nanocrystalline ribbon, we refer to the role of the anisotropy distribution in the formation of the MI response [30,31].

**Figure 4.** MOKE hysteresis loops taken from the same turning sections of the three-turn (**a**) and six-turn (**b**) Co75Fe10Ni2Si8B5 meander samples.

As it can be seen (Figures 5 and 6), complex quasistatic magnetic properties of the meander samples also reflect their MI responses. One can notice several field intervals with different curvature of the MI curves, i.e., behavior, which is usually not observed for simple amorphous ribbon quenched samples [10] in the shape of a single elongated stripe. These intervals are marked as A, B and C (Figure 6) characteristic areas.

Δ

**Figure 5.** Field dependence of the MI ratio for the total impedance (**a**,**c**) and its real part (**b**,**d**) for the Co75Fe10Ni2Si8B5 meander samples; (**c**,**d**)—the same dependencies in a small field range. "Down" curves for the magnetic field change from 100 Oe to −100 Oe are marked with solid symbols, "Up" curves for the magnetic field change from −100 Oe to 100 Oe are marked with empty symbols.

**Figure 6.** Comparison of the magnetization curves and field dependence of the MI ratio for total impedance of the three-turns Co75Fe10Ni2Si8B5 meander S2. Characteristic field intervals with different curvature of the GMI curves are marked as A, B and C.

In small magnetic fields (interval A) the border parts of the meanders (point A) quickly magnetize, meanwhile the middle sections keep staying almost demagnetized and hence do not contribute significantly to the MI response. In the higher fields (intervals B and C) the border sections become saturated and stop contributing to the MI. The second change of curvature of M(H) curves is observed for both points B and C. Although the explanation of the origin of such behavior requires an additional investigation of the position of about 10 Oe, for both M(H) and MI, the curves indicate a strong contribution of the anisotropy field.

Despite the complexity of the dynamic magnetization process described above the meander samples used in this work show high MI response and its sensitivity to an external magnetic field (Figures 7 and 8). As is shown in Figure 8, the S4 meander demonstrates the highest values for both parameters: GMI response ΔZ/Z = 244% and its sensitivity S(ΔZ/Z) = 35%/Oe. It also correlates with Figure 3, which shows that there is only a slight difference in magnetization curves for the different sample areas. As expected, the highest MI effect and its sensitivity are observed for the case where the most uniform anisotropy is insured. Both effects can be explained by a lower anisotropy axis dispersion in comparison with the other samples because of its longer length, and hence a smaller impact of the turning sections or the shape anisotropy.

**Figure 7.** Frequency dependence of the maximal MI ratio for the (**a**) total impedance and (**b**) its real part for Co75Fe10Ni2Si8B5 meander samples.

The frequency dependences of the maximum of the MI ratio for total impedance and the real part of the total impedance are shown in Figure 7. The maximum ΔZ/Zmax ratio of about 250% appeared at a frequency of 42 MHz for the six-turn sample S4 (Figure 7a). However, the ΔZ/Zmax ratios (162% for S1 and 146% for S2) at a lower frequency of 32 MHz was larger than that of the six-turn sample S3 (129%). The main reason may be that S1 and S2 samples had a better proportion of width and spacing. Compared with the ΔZ/Zmax ratios of the three-turn samples S1 and S2, we can find that the MI ratio of the sample S1 with a narrow line-width was larger than that of sample S2. These results were consistent with the earlier reports [26,30].

**Figure 8.** Frequency dependence of the sensitivity of the MI ratio for (**a**) total impedance and (**b**) its real part for Co75Fe10Ni2Si8B5 meander samples.

In the frequency range 100-200 MHz, there is no obvious difference for ΔZ/Zmax ratios of samples S1 and S3. Compared with the six-turn meanders, the increase of length had a strong impact on MI enhancement. The maximum ΔR/Rmax ratios was 254% obtained at a frequency of 53 MHz from the sample S4 (Figure 7b). The tendency for (ΔR/R)max is similar to that of (ΔZ/Z)max. However, the ΔR/Rmax ratios had a conspicuous distinction in the frequency range 1–200 MHz: the working frequencies correspond to the ΔR/Rmax ratios for samples S1–S4 are higher than that ΔZ/Zmax ratios.

Figure 8 shows the frequency dependence of the sensitivity of the MI ratio for total impedance and its real part for different meanders. A general view of the frequency dependence of the MI maximum (both for real part and the total impedance) is quite similar to the (ΔR/R)max (ΔZ/Z)max measured for single stripe amorphous ribbons. The origin of such behavior was previously discussed in the literature. Under conditions of strong impedance variation, the constant external magnetic field and transverse magnetic field created by the alternate current make a contribution to the transverse dynamic permeability. With the frequency increase, the domain walls become affected by stronger eddy-current damping, the anisotropy field gradually increases, magnetic permeability decreases leading to decrease in MI value. More details can be found elsewhere [2,32–34].

The sensitivity for the total impedance MI ratio maxima S(ΔZ/Z)max and for its real part maxima S(ΔR/R)max were calculated in the field of 7 Oe, 14 Oe and 12 Oe respectively. The ΔZ/Zmax sensitivity of meander samples S4, S3, S2 and S1 were 36%/Oe, 9%/Oe 12%/Oe and 14%/Oe, respectively. These dependences reveal the same tendencies as those found for the frequency dependence the MI ratio maximum for the total impedance and its real part (Figure 8). The highest S(ΔZ/Z)max and S(ΔR/R)max (36%) were observed in the case of the sample S4 with increased frequency. The sensitivity of the MI ratio for total impedance and its real part of sample S3 were median. The values of sensitivity were also adequate for sensor applications from the point of view of magnetic field sensitivity.

Table 2 lists the sensitivity of the MI ratio for total impedance and its real part for different samples and the corresponding different magnetic fields and frequencies. The sample S4 had better MI characteristics including a wider range of the fields suitable for application. Therefore, the field and frequency dependence of the MI ratio of the S4 meander were investigated in more detail (Figure 9). Measurements in the decreasing field after magnetic saturation were defined as "down" branch and the measurements in the increasing field after saturation were defined as the "up" branch.


**Table 2.** Comparison of sensitivity of the MI ratio for total impedance and its real part for Co75Fe10Ni2Si8B5 meander samples, and the corresponding different magnetic fields and frequencies.

**Figure 9.** (**a**) Field and (**b**) frequency dependence of the MI ratio of Co75Fe10Ni2Si8B5 patterned meander element S4.

The MI value is almost constant in higher fields due to the saturated sample state. Magnetoimpedance ratio in an external field of 30 Oe also varies slightly in the frequency range 40–200 MHz. A significant change in the MI ratio was observed by varying not only the magnitude of the external magnetic field from 0 to 15 Oe but also the frequency of the exciting current. The optimum mode of MI-detection by the S4 element is frequency range up to 40 MHz in low fields up to 15 Oe. As the biodetection of the magnetic markers requires the highest sensitivity with respect to the applied field, due to the very small value of the stray fields of magnetic nanoparticles employed as biomolecular labels [35], the S4 element seems to be the best candidate for this kind of application.

#### **4. Conclusions**

In summary, surface magnetic properties and the magnetoimpedance effect of patterned soft ferromagnetic Co75Fe10Ni2Si8B5 ribbon-based meander sensor elements have been investigated. Samples with a different number of turns, line width and length were fabricated and studied. The results showed that the length of the samples plays the most important role in the formation of well-defined magnetic anisotropy, and hence a higher homogeneity and MI response. The maximum MI ratio of the total impedance of 250% for the exciting current frequency of 45 MHz, and its sensitivity to the external magnetic field of 36%/Oe were observed for the longest six-turn meander sample. These results can be used for further investigations and the production of magnetic field sensors based on the MI effect for the cases focused on large drop analysis.

**Author Contributions:** Z.Y. and G.V.K. conceived and designed the experiments; P.G. contributed to the fabrication and primary characterization of the sensor elements; S.O.V., Z.Y. and E.V.G. performed the MI measurements and their primary analysis; S.V.S. fabricated the sample holder and discussed the high frequency resultsand the manuscript; E.V.G., A.A.C. and Z.Y. performed the MOKE studies and analyzed the data; Z.Y., E.V.G., A.A.C., G.V.K. comparatively analyzed the whole set of the data, prepared graphical materials and wrote the manuscript and responses to Reviewers.

**Funding:** This research was funded in part by the grant Postdoc Ural Federal University UrFU-2018", in part by Natural Science Foundation of Henan Province of China (162300410233), in part they were obtained within the financial support for state assignment of Minobrnauki of Russia (theme "Alloys") and in part by μ4F ELKARTEK grant of The Basque Country Government.

**Acknowledgments:** The authors are grateful to the Laboratory of magnetic sensors of Ural Federal University and V.O. Vas´kovskiy for special support. We thank A.N. Gor'kovenko's for advanced training with MOKE measurements.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Characterization and Relaxation Properties of a Series of Monodispersed Magnetic Nanoparticles**

**Yapeng Zhang 1, Jingjing Cheng 1,\* and Wenzhong Liu 1,2,\***


Received: 11 July 2019; Accepted: 31 July 2019; Published: 2 August 2019

**Abstract:** Magnetic iron oxide nanoparticles are relatively advanced nanomaterials, and are widely used in biology, physics and medicine, especially as contrast agents for magnetic resonance imaging. Characterization of the properties of magnetic nanoparticles plays an important role in the application of magnetic particles. As a contrast agent, the relaxation rate directly affects image enhancement. We characterized a series of monodispersed magnetic nanoparticles using different methods and measured their relaxation rates using a 0.47 T low-field Nuclear Magnetic Resonance instrument. Generally speaking, the properties of magnetic nanoparticles are closely related to their particle sizes; however, neither longitudinal relaxation rate *r*<sup>1</sup> nor transverse relaxation rate *r*<sup>2</sup> changes monotonously with the particle size *d*. Therefore, size can affect the magnetism of magnetic nanoparticles, but it is not the only factor. Then, we defined the relaxation rates *r <sup>i</sup>* (*i* = 1 or 2) using the induced magnetization of magnetic nanoparticles, and found that the correlation relationship between *r* <sup>1</sup> relaxation rate and *r*<sup>1</sup> relaxation rate is slightly worse, with a correlation coefficient of *R*<sup>2</sup> = 0.8939, while the correlation relationship between *r* <sup>2</sup> relaxation rate and *r*<sup>2</sup> relaxation rate is very obvious, with a correlation coefficient of *R*<sup>2</sup> = 0.9983. The main reason is that *r*<sup>2</sup> relaxation rate is related to the magnetic field inhomogeneity, produced by magnetic nanoparticles; however *r*<sup>1</sup> relaxation rate is mainly a result of the direct interaction of hydrogen nucleus in water molecules and the metal ions in magnetic nanoparticles to shorten the *T*<sup>1</sup> relaxation time, so it is not directly related to magnetic field inhomogeneity.

**Keywords:** magnetic nanoparticles; contrast agent; relaxation; relaxation rate; Langevin model; magnetic field inhomogeneity

#### **1. Introduction**

Magnetic iron oxide nanoparticles (MIONPs) have developed rapidly in recent years and have been widely used in biology, physics and medicine. They are quite small, usually nanoscale, and because of their scale, they can manifest many unique properties, such as superparamagnetism, i.e., when the applied magnetic field approaches zero, the induced magnetization and coercivity are also zero [1–4]. In addition, MIONPs have good temperature performance and can be used as temperature sensors. Some scholars used them to make some progress in the field of magnetic temperature measurement [5–11]. Due to their low toxicity, biocompatibility, and specificity after surface modification, MIONPs can be used as a target for drug delivery and disease treatment [12–15]. MIONPs are often used as contrast agents [16–20] in magnetic resonance imaging (MRI), which is one of the most important imaging methods in the field of medical diagnosis and scientific research [21–24]. MRI is a kind of imaging technology, which mainly uses the resonance effect of an electromagnetic field and hydrogen nucleus spin. Then, according to the collected magnetic resonance signal, imaging

information from the tested object can be established. MRI not only has many imaging parameters and can be imaged in any direction without ionizing radiation damage to the human body, but can also perform non-invasive imaging of the internal structure or tissue of the human body or organism. According to the energy exchange between nuclear spin and the outside, hydrogen protons have two main relaxation mechanisms: longitudinal relaxation (spin-lattice relaxation) and transverse relaxation (spin-spin relaxation), which correspond to two relaxation time parameters, respectively: longitudinal relaxation time (*T*<sup>1</sup> relaxation time) and transverse relaxation time (*T*<sup>2</sup> relaxation time). These two relaxation mechanisms have a direct impact on the quality of magnetic resonance imaging. When the contrast agent (such as MIONPs) is added to the tested object, it will produce induced magnetization under the excitation of the magnetic field, which will affect the distribution and uniformity of the magnetic field around it, and then change the relaxation mechanisms of the protons around it; in short, the relaxation times will change. More intuitively, it will enhance the image contrast and speed up the image efficiency [23,25,26]. The enhancement effect of contrast agents on MRI can be expressed by the relaxation rate (*r*<sup>1</sup> relaxation rate and *r*<sup>2</sup> relaxation rate). Current research focuses on how to reduce proton *T*<sup>1</sup> relaxation time and *T*<sup>2</sup> relaxation time, how to improve the contrast performance of lesions and surrounding tissues, and how to accelerate the relaxation rate. In these studies, MIONPs can play a significant role. For example, different synthetic methods, size control, surface modification, etc. are used to improve their performance as a contrast agent. In addition, some scholars studied the use of different proportions of other metal materials such as Co, Zn and Mn doped iron oxide to enhance its saturation magnetization, thereby improving the relaxation enhancement properties of magnetic nanoparticles [27–30].

Characterization of the properties of magnetic nanoparticles plays an important role in the application of magnetic particles. In this paper, a series of commercial single core magnetic nanoparticles (SHP series, Ocean Nanotech, San Diego, CA, USA) with different nominal particle sizes (5 nm, 10 nm, 15 nm, 20 nm, 25 nm, 30 nm) were characterized using different methods. They can be stably monodispersed in aqueous solutions. Generally speaking, the properties of magnetic nanoparticles are closely related to their sizes, so we firstly measured the particle sizes using transmission electron microscopy and dynamic light scattering. Then the relaxation time of samples with different Fe ion concentrations was measured in a 0.47 T low-field nuclear magnetic resonance (LF-NMR) instrument and fitted to obtain *r*<sup>1</sup> relaxation rate and *r*<sup>2</sup> relaxation rate. However, neither *r*<sup>1</sup> relaxation rate calculated nor *r*<sup>2</sup> relaxation rate calculated changes monotonously with the particle size *d*. Because the addition of magnetic nanoparticles mainly changes the uniformity of the ambient magnetic field of the surrounding water molecules, and then changes the relaxation time, we further seek the relationship between the relaxation time and the induced magnetization of the magnetic nanoparticles in the magnetic field, and define the *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate. Because the *T*<sup>2</sup> relaxation process is very sensitive to the inhomogeneity of the magnetic field, and the addition of magnetic nanoparticles can directly affect the inhomogeneity of the magnetic field, it is found that the correlation between *r* <sup>2</sup> relaxation rate and *r*<sup>2</sup> relaxation rate is good. The effect of magnetic nanoparticle contrast agent on *T*<sup>1</sup> relaxation mechanism is mainly due to the direct interaction of the hydrogen nucleus in water molecules and metal ions in magnetic nanoparticles; therefore *T*<sup>1</sup> relaxation mechanism is not directly related to the magnetic field inhomogeneity. Therefore, the magnetic properties of magnetic nanoparticles are influenced by many factors, among which particle size is only one.

#### **2. Materials and Methods**

#### *2.1. Magnetic Nanoparticles*

We use an SHP series commercial magnetic nanoparticle reagent (Ocean NanoTech, San Diego, CA, USA), which is a single core magnetic nanoparticle. It is composed of ferric oxide magnetic nanoparticles, which are coated with carboxylic acid groups on the surface with good water solubility and dispersity. Its original iron ion concentration is 5 mg/mL. Six kinds of magnetic nanoparticle reagents were selected: SHP-05, SHP-10, SHP-15, SHP-20, SHP-25 and SHP-30 (nominal particle sizes

are 5, 10, 15, 20, 25 and 30 nm, respectively, with a tolerance of < 2.5 nm). In addition, according to the measurement method of relaxation rate, samples with different Fe concentrations need to be prepared for each particle size of the magnetic nanoparticle reagent. Therefore, the magnetic nanoparticle reagent with the above particle size were diluted by deionized water to prepare five different Fe ion concentrations (1.79 mM, 1.12 mM, 0.89 mM, 0.45 mM, 0.22 mM), totaling 30 samples.

#### *2.2. Transmission Electron Microscopy*

The magnetic nanoparticles were imaged by transmission electron microscopy (TEM) (H-7000FA, HITACHI, Tokyo, Japan) with 110 kV to characterize their core size.

#### *2.3. Dynamic Light Scattering*

Dynamic Light Scattering (DLS) can detect the diffusion motion of particles and determine the hydrodynamic size (the overall size including magnetic core, polymer coating layer and the surrounding water layer) distribution of particles. Zetasizer Nano ZS90 (Malvern−Panalytical, Malvern, England) was used to measure the hydrodynamic size distribution of the above magnetic nanoparticles at a fixed scattering angle of 90 degree. The autocorrelation function of scattered light is analyzed, and the size distribution is calculated by assuming that the particle is an equivalent sphere.

#### *2.4. LF-NMR*

The relaxation time was measured using an LF-NMR instrument with a magnetic field of 0.47 T (MiniPQ001-20-15 mm, Niumag, Suzhou, China). The temperature of the main magnet and the sample chamber of the instrument is set at 35 ◦C To shorten the temperature balance time after the samples are put into the sample chamber, the samples are kept in an incubator set at 35 ◦C before the experiment. After starting the experiment, the samples were placed in the sample chamber of the LF-NMR instrument in turn for about 3 min, so that the temperature of the samples in the sample chamber could reach the thermal equilibrium as far as possible. The *T*<sup>1</sup> relaxation time is measured four times by using Inverse Recovery (IR) Sequence and then *T*<sup>2</sup> relaxation time was measured by using the CPMG (Carr-Purcell-Meiboom-Gill) sequence five consecutive times.

#### **3. Results**

#### *3.1. Characterization of Magnetic Nanoparticles Samples: TEM, DLS*

**TEM:** The TEM images of SHP-05, SHP-10, SHP-15, SHP-20, SHP-25 and SHP-30 magnetic nanoparticles samples in Figure 1 show that they are monodispersed magnetic nanoparticles.

**Figure 1.** TEM images of SHP series magnetic nanoparticles samples. (**a**) SHP-05; (**b**) SHP-10; (**c**) SHP-15; (**d**) SHP-20; (**e**) SHP-25; (**f**) SHP-30.

**DLS**: The hydrodynamic size distributions are shown in Figure 2. To reduce the measurement error, each magnetic nanoparticle sample was measured three times in succession, and the statistical mean values were used.

**Figure 2.** Hydrodynamic size distribution of SHP series magnetic nanoparticles. The discrete points are the measured hydrodynamic size distributions, and the solid lines are the fitting curve obtained using lognormal distribution.

Generally, we believe that the hydrodynamic size distribution of magnetic nanoparticles follows lognormal distribution [31–34]

$$f(d) = \frac{1}{d\sqrt{2\pi}\sigma} \exp\left[-\frac{1}{2\sigma^2} \left(\ln\frac{d}{\mu}\right)^2\right] \tag{1}$$

here, *d* is the diameter of particles, μ is the median diameter of the lognormal distribution, σ is the standard deviation of *lnd*. Therefore, the lognormal distribution function is used to fit the hydrodynamic size distribution measured by DLS, and the results are shown in Table 1.


**Table 1.** Parameters of lognormal distribution of the hydrodynamic size and the nominal size for SHP series magnetic nanoparticles.

Dynamic light scattering (DLS) is a physical characterization method, which can be used to measure the particle size distribution of solutions or suspensions, and also to measure the behavior of complex fluids such as concentrated polymer solutions. The irregular random diffusion of magnetic particles in aqueous solution will attract some water molecules to move together on its surface, that is to say, water film is formed on its surface. It can be seen that the measurement results seem to be somewhat abnormal and have little correlation with the nominal core sizes. The results of DLS measurements using the same magnetic particles as us are not entirely consistent in other studies [35–37]. This may be caused by measurement errors, methods, etc., or more complex underlying causes.

#### *3.2. Waiting Time Dependence of T*<sup>2</sup> *Relaxation Time*

The relaxation time of each magnetic nanoparticle samples was then measured using a 0.47 T LF-NMR instrument. In addition, it was reported in much of the literature that the relaxation time (especially *T*<sup>2</sup> relaxation time) of magnetic nanoparticle aqueous solution samples obtained from NMR measurements is time-dependent [38–41]. That is to say, the measured relaxation times are related to the waiting time that the sample undergoes after being put into the sample chamber of the NMR instrument. In our experiment, because each sample was kept for about 3 min in the sample chamber, then the *T*<sup>1</sup> relaxation time was measured several times, and then the *T*<sup>2</sup> relaxation time was measured several times in succession. Therefore, depending on the above-mentioned articles on the waiting time dependence of *T*<sup>2</sup> relaxation time, this paper did not set the waiting time accurately. However, in order to illustrate the problem as much as possible, we define the waiting time *t <sup>w</sup>*, and set the waiting time *t w* for the first measurement of the *T*<sup>2</sup> relaxation time of each sample to 0 s. The waiting time *t <sup>w</sup>* of the same sample for subsequent *T*<sup>2</sup> relaxation time measurement was set according to the time interval from the first measurement. Generally, we choose the *T*<sup>2</sup> relaxation time measurement data of the sample with the highest Fe concentration for each particle size, and plot the relationship between *T*<sup>2</sup> relaxation time and waiting time *t <sup>w</sup>*, as shown in Figure 3 below.

**Figure 3.** Waiting time dependence of *T*<sup>2</sup> relaxation time. It can be seen that the *T*<sup>2</sup> relaxation time of magnetic nanoparticle samples with different particle sizes hardly varies with the waiting time *t w* under the current test conditions.

It can be clearly seen that the *T*<sup>2</sup> relaxation time of the magnetic nanoparticles used in our experiment did not show dependence on *t <sup>w</sup>* waiting time. The main reason may be that the sizes of magnetic nanoparticle samples are relatively small, and surface-coated carboxylic acid groups produce electrostatic repulsion, which makes it possible for them to disperse stably in water phase without agglomeration under the effect of external magnetic field. Of course, it is also possible that the magnetic field (0.47 T) of the LF-NMR instrument in this paper is too low to make the magnetic nanoparticles in the magnetic field cluster into chains.

Regardless of the reason, the extrapolation method in these references is not needed in this paper [38–41], but the *T*<sup>1</sup> relaxation time and *T*<sup>2</sup> of relaxation time measured can be directly used to obtain the relaxation rate information of corresponding samples.

#### *3.3. Relaxation Rate*

In MRI, longitudinal relaxation rate *r*<sup>1</sup> and transverse relaxation rate *r*<sup>2</sup> are the main indicators to evaluate the enhancement effect of magnetic nanoparticles as contrast agent. Relaxation rate, in units of mM<sup>−</sup>1s−1, is the inverse of *T*<sup>1</sup> or *T*<sup>2</sup> relaxation time of protons when the concentration of Fe ion in magnetic nanoparticle dispersion solutions is 1 mM [39,42,43]:

$$1/T\_{1,sup} = 1/T\_{1,unter} + r\_1 c\_{\rm Fe} \tag{2}$$

$$1/T\_{2,sup} = 1/T\_{2,nutter} + r\_2 c\_{\rm Fe} \tag{3}$$

where *T*1,*sup* and *T*2,*sup* are the *T*<sup>1</sup> and *T*<sup>2</sup> relaxation time of magnetic nanoparticle suspension solution respectively; *T*1,*water* and *T*2,*water* are the intrinsic *T*<sup>1</sup> and *T*<sup>2</sup> relaxation time of water respectively; *c*Fe, in the unit of mM (mmol/L), is the concentration of Fe ion in magnetic nanoparticle suspension solution.

According to the above definition, we can simply prepare several magnetic nanoparticle water solution samples with different Fe ion concentrations, and use NMR instrument to measure their relaxation time respectively. Then taking *Ti*,*water* (*i* = 1 or 2) and *ri* (*i* = 1 or 2) as fitting parameters, by fitting the curve between the inverse of relaxation time and the concentration of Fe ion, the slope is the corresponding relaxation rate, as shown in Figure 4.

**Figure 4.** Relaxation rate of SHP series magnetic nanoparticle sample. (**a**) Inverse of longitudinal relaxation time 1/*T*<sup>1</sup> and (**b**) inverse of transverse relaxation time 1/*T*<sup>2</sup> with respect to Fe ion concentration *c*Fe.

To make it more intuitive, we summarized the relaxation rate information of SHP series magnetic nanoparticle samples, as shown in Figure 5.

**Figure 5.** Relaxation rate of SHP series magnetic nanoparticle samples. (**a**) *r*<sup>1</sup> relaxation rate; (**b**) *r*<sup>2</sup> relaxation rate.

The addition of contrast agent will affect *T*<sup>1</sup> and *T*<sup>2</sup> relaxation time, but the degree of influence on the two relaxation times may be different, that is to say, *r*<sup>1</sup> relaxation rate and *r*<sup>2</sup> relaxation rate may be different, so we can simply classify the contrast agent using *r*<sup>2</sup> to *r*<sup>1</sup> ratio, i.e., *r*2/*r*<sup>1</sup> [25,44–48]. It is generally believed that when the ratio *r*2/*r*<sup>1</sup> < 2, the contrast agent works better as *T*<sup>1</sup> contrast agent; when 2 < *r*2/*r*<sup>1</sup> < 10, the contrast agent can work as both *T*<sup>1</sup> contrast agent and *T*<sup>2</sup> contrast agent, that is to say, it is *T*1-*T*<sup>2</sup> dual mode contrast agent; when the ratio *r*2/*r*<sup>1</sup> > 10, the contrast agent works better as *T*<sup>2</sup> contrast agent.

After calculating the *r*2/*r*<sup>1</sup> ratio of the SHP series magnetic nanoparticles, and according to the above classification method, we then attempted to classify them, as shown in Figure 6.

**Figure 6.** The ratio *r*2/*r*<sup>1</sup> of SHP series magnetic nanoparticles.

It can be observed that the *r*2/*r*<sup>1</sup> ratios of SHP-05, SHP-10, SHP-15, SHP-20 and SHP-25 magnetic nanoparticle samples are between 2 and 10, so they can be considered to be *T*1-*T*<sup>2</sup> dual mode contrast agents. While the *r*2/*r*<sup>1</sup> ratio of the SHP-30 magnetic nanoparticle sample is close to 20, it will work more suitably as *T*<sup>2</sup> contrast agent.

#### *3.4. Analysis of Relaxation Rate*

In addition, it can be found that neither*r*<sup>1</sup> relaxation rate calculated nor*r*<sup>2</sup> relaxation rate calculated changes monotonously with the particle size *d* [49,50]. When magnetic nanoparticles are added, the induced magnetization thereof will be produced under the exciting of the static magnetic field, which will change the ambient magnetic field, increase their inhomogeneity and shorten the relaxation time of the surrounding water hydrogen proton. This is also the basic principle of magnetic nanoparticles as contrast agents in MRI. It can be assumed that the magnetic field inhomogeneity is directly related to the induced magnetization produced by magnetic nanoparticles in magnetic field, and the induced magnetization can be described by the Langevin model [8,51–54]:

$$M = Nm \left( \coth\left(\frac{mB}{kT}\right) - \frac{kT}{mB} \right) \tag{4}$$

where *N* is the number of magnetic nanoparticles per unit volume (i.e., the concentration of magnetic nanoparticles); *m* is the magnetic moment of a single magnetic nanoparticle; *B* is the static magnetic field; *k* is the Boltzmann constant and *T* is the absolute temperature.

It can be seen that the induced magnetization of magnetic nanoparticles system in a static magnetic field is related to the external excitation magnetic field, temperature, concentration of magnetic particles and magnetic moment of magnetic particles. Generally, magnetic nanoparticles are simplified to sphere shapes, so the magnetic moment *m* of magnetic nanoparticle can be expressed as the following equation:

$$m = M\_{\rm sat} V = M\_{\rm sat} \frac{\pi d^3}{6} \tag{5}$$

where, *Msat* is the saturation magnetization of magnetic nanoparticle. *d* is the diameter of magnetic nanoparticles.

In the previous calculation of the relaxation rate, the concentration of Fe ion is taken as a reference. Here we assume that the magnetic field inhomogeneity caused by the addition of magnetic particles is proportional to the induced magnetization of magnetic nanoparticles, so we define the relaxation rate by referring to the induced magnetization of each sample. that is to say, we define *r <sup>i</sup>* (*i* = 1 or 2) relaxation rate. The method for calculating the *r <sup>i</sup>* (*i* = 1 or 2) relaxation rate is similar to that shown in Equations (2) and (3), except that the induced magnetization *M* (unit A.m) at different magnetic particle concentrations can be used to replace the Fe concentration *c*Fe. When the induced magnetization intensity of MIONPs in water solution is 1 A.m, the inverse of *T*<sup>1</sup> relaxation time and *T*<sup>2</sup> relaxation time of the hydrogen proton is *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate respectively. It can be concluded that the unit of *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate is A<sup>−</sup>1m−1s−1.

Therefore, according to the Langevin model, combined with the actual relaxation time measurement experiment, the induced magnetization of each magnetic nanoparticle sample in LF-NMR instrument is simulated. The static magnetic field *B* = 0.47 T (the main magnetic field of LF-NMR instrument MiniPQ001-20-15 mm), temperature *T* = 308.17 K (the temperature of the sample chamber of the LF-NMR instrument MiniPQ001-20-15 mm). In much of the literature, the saturation magnetization *Msat* of SHP series magnetic nanoparticles was measured and involved, but the values measured (or assumed) are different, but the difference is not significant [35,55–58]. From Equation (5), it can be seen that magnetic moment *m* is proportional to the cube power of the particle size *d*, but is only proportional to the first power of saturation magnetization *Msat*. In other words, the influence of magnetic particle size *d* on magnetic moment *m* is much bigger than the influence of the saturation

magnetization *Msat* on magnetic moment *m*. Therefore, we can say that the magnetic moment *m* is mainly dominated by particle size *d*. Therefore, according to the above references, it is reasonable to assume that the saturation magnetic moments of SHP series magnetic nanoparticles are all the same, i.e., *Msat* <sup>=</sup> 4.5 <sup>×</sup> 105 <sup>A</sup>/m.

In addition, the induced magnetization of magnetic particle system is also affected by the concentration of magnetic nanoparticles. Because the Langevin model needs concentration information from the magnetic nanoparticles, however the samples previously prepared are based on the concentration of Fe ion, so we need a conversion process. According to the Ocean Nanotech official website [59], the ratios of magnetic nanoparticle concentration to Fe ion concentration of SHP series magnetic nanoparticles, with different particle sizes, are different. After these conversion processes, finally, the induced magnetization *M* of different magnetic particle samples can be calculated using the Langevin model as shown in Equation (4). Then, by fitting the curve between the inverse of relaxation time and the induced magnetization *M*, the slope is the corresponding *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate, as shown in Figure 7. Moreover, the ratios of magnetic nanoparticle concentration to Fe ion concentration of every SHP reagent can be seen in Table A1 in Appendix A. In addition, parameters include magnetic nanoparticle concentration, induced magnetization, mean values and standard deviations of the measured relaxation time of the all tested magnetic nanoparticle samples are listed in Table A2 in Appendix A.

**Figure 7.** Relaxation rate of SHP series magnetic nanoparticle sample. (**a**) Inverse of longitudinal relaxation time 1/*T*<sup>1</sup> and (**b**) inverse of transverse relaxation time 1/*T*<sup>2</sup> with respect to the induced magnetization *M*.

Similarly, in order to be more intuitive, we summarized the *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate information of SHP series magnetic nanoparticle samples, as shown in Figure 8.

**Figure 8.** Relaxation rate of SHP series magnetic nanoparticle samples. (**a**) *r* <sup>1</sup> relaxation rate; (**b**) *r* 2 relaxation rate.

It can be seen that the *r* <sup>1</sup> relaxation rate or *r* <sup>2</sup> relaxation rate still have little relationship with the particle size. Next, we analyze the correlation between the *r <sup>i</sup>* (*i* = 1 or 2) relaxation rate and the *ri* (*i* = 1 or 2) relaxation rate, and then linearly fit them, respectively, as shown in Figure 9. From the fitting results, it can be concluded that the correlation relationship between *r* <sup>1</sup> relaxation rate and *r*<sup>1</sup> relaxation rate is slightly worse, the correlation coefficient *R*<sup>2</sup> = 0.8939, while the correlation relationship between *r* <sup>2</sup> relaxation rate and *<sup>r</sup>*<sup>2</sup> relaxation rate is very obvious, the correlation coefficient *<sup>R</sup>*<sup>2</sup> <sup>=</sup> 0.9983.

**Figure 9.** Linear regression of (**a**) *r*<sup>1</sup> relaxation rate with *r* <sup>1</sup> relaxation rate and (**b**) *r*<sup>2</sup> relaxation rate with *r* <sup>2</sup> relaxation rate.

The CPMG pulse sequence, designed for MRI and NMR, is designed to eliminate the influence of magnetic field inhomogeneity on the measurement of *T*<sup>2</sup> relaxation time as much as possible. Thus, we can obtain intrinsic *T*<sup>2</sup> relaxation time induced by spin-spin interaction. However, when magnetic nanoparticles are added to the aqueous solution sample, there are interactions between proton dipoles, proton dipoles and lattices, and between proton dipoles and electron dipoles of magnetic particles. These interactions will affect the relaxation mechanism of proton subsystems. In particular, magnetic nanoparticles will produce induced magnetization with the exciting of the magnetic field, which will change the magnetic field around them, aggravate the magnetic field inhomogeneity, accelerate the dephasing of hydrogen proton spin, and then change the relaxation of protons in the magnetic field. Moreover, the intensity of this impact will vary with the distance between hydrogen protons and magnetic particles. MIONPs with superparamagnetism can produce strong induced magnetization under the exciting magnetic field, which has a great influence on the inhomogeneity of the environmental magnetic field. Therefore, the *T*<sup>2</sup> relaxation time measured at this time includes all the above effects, and it can be said that it is mainly affected by the magnetic field inhomogeneity (the magnetic field inhomogeneity caused by the addition of magnetic nanoparticles) [60,61].

$$\frac{1}{T\_{2, \text{observe}}} = \frac{1}{T\_2} + \frac{1}{T\_2'} = \frac{1}{T\_2} + \gamma \Delta B \tag{6}$$

where *T*2,*observe* is the transverse relaxation time measured; *T*<sup>2</sup> is the intrinsic lateral relaxation time; *T* 2 is the transverse relaxation time due to the inhomogeneity of the magnetic field and can be expressed by γΔ*B*, where γ is the gyromagnetic ratio of the hydrogen proton, Δ*B* is the inhomogeneity of the magnetic field in the sample system and can be given by the Langevin model. From Equation (6) we can see that the relationship between *T*2,*observe* relaxation time and induced magnetization of magnetic nanoparticles system is obvious, so the correlation between *r*<sup>2</sup> relaxation rate and *r* <sup>2</sup> relaxation rate is good.

#### **4. Discussion**

As can be seen in Figure 5, basically, the smaller the particle size of magnetic nanoparticles, the larger the *r*<sup>1</sup> relaxation rate. The effect of magnetic nanoparticle contrast agent on *T*<sup>1</sup> relaxation mechanism is mainly due to the direct interaction of hydrogen nucleus in water molecules and the metal ions in magnetic nanoparticles to shorten the *T*<sup>1</sup> relaxation time, which can be explained using the Solomon-Bloembergen-Morgan theory (SBM) [62,63], so it is not directly related to magnetic field inhomogeneity. In short, it is related to the number of coordination water molecules, the exchange rate of water molecules, the rotation time of complexes and so on. As far as the metal ions (Fe) in magnetic nanoparticles are concerned, they have unpaired electrons, which interact with water electrons, such as by coordinating. The smaller the particle size, the larger the specific surface area S/V, and the easier the interaction between unpaired electrons and water electrons, so the larger the *r*<sup>1</sup> relaxation rate is. As far as *r*<sup>2</sup> relaxation rate is concerned, it is directly related to the magnetic field inhomogeneity caused by magnetic nanoparticles in this paper. The magnetization induced by magnetic nanoparticles in the magnetic field can be considered to be directly affecting the magnetic field inhomogeneity. The induced magnetization of magnetic nanoparticles is directly related to the magnetic moment (*<sup>m</sup>* = *Msat* <sup>π</sup>*d*<sup>3</sup> <sup>6</sup> ). Therefore, if the saturation magnetization *Msat* of magnetic particles is constant, the larger the size of magnetic particles, the greater the induction magnetization and the larger the *r*<sup>2</sup> relaxation rate. Therefore, according to the respective influencing factors of *r*<sup>1</sup> relaxation rate and *r*<sup>2</sup> relaxation rate, it can be concluded that the larger the particle size, the larger the *r*2/*r*1, as shown in Figure 6. However, as far as the actual *r*<sup>2</sup> relaxation rate measured is concerned, it is basically shown that the larger the particle size is, the larger the *r*<sup>2</sup> relaxation rate is, but the data of SHP-20 and SHP-25 seem to be somewhat abnormal, as shown in Figure 5. The possible reason for this is that the saturation moments of SHP magnetic nanoparticles are not the same, and TEM imaging shows that the shape of SHP magnetic nanoparticles is not perfect spherical. Therefore, the magnetic properties of magnetic

nanoparticles are affected by many factors, including composition, preparation process, surface coating, particle size, saturation magnetization and so on, while relaxation rate is only a simple characterization parameter. Moreover, Dynamic light scattering (DLS), which is a physical characterization method, and can be used to measure the particle size distribution of solutions or suspensions, and also to measure the behavior of complex fluids such as concentrated polymer solutions. The irregular random diffusion of magnetic particles in an aqueous solution will attract some water molecules to move together on its surface, that is to say, a water film is formed on its surface. The results of DLS measurements of magnetic nanoparticles used by us in different studies are not entirely consistent, which may be caused by their own measurement errors, methods and so on.

#### **5. Conclusions**

Magnetic nanoparticles are widely used as contrast agents for MRI. In this paper, SHP series magnetic nanoparticles (Ocean Nanotech) with different nominal sizes were selected for characterization experiments, and their relaxation rates were measured using a 0.47 T LF-NMR instrument. It was found that neither *r*<sup>1</sup> relaxation rate nor *r*<sup>2</sup> relaxation rate calculated changes monotonously with the particle size *d*. Size can affect the magnetic properties of magnetic nanoparticles, but it is not the only factor. There are other factors, such as morphology, agglomeration and so on. Furthermore, the induced magnetization of magnetic particle system in a static magnetic field can be calculated using the Langevin model, which serves as the source of magnetic field inhomogeneity in the measurement of relaxation time. Then the relationship between relaxation time and induced magnetization of magnetic nanoparticle samples in magnetic field is defined as *r* <sup>1</sup> relaxation rate and *r* <sup>2</sup> relaxation rate. The *T*<sup>2</sup> relaxation process is very sensitive to the magnetic field inhomogeneity, and the addition of magnetic nanoparticles can directly affect the magnetic field inhomogeneity. Therefore, it is found that the correlation between the *r* <sup>2</sup> relaxation rate and the *r*<sup>2</sup> relaxation rate is very good, and the correlation coefficient reaches 0.9983. *T*<sup>1</sup> relaxation mechanism is not directly related to the magnetic field inhomogeneity. The effect of the magnetic nanoparticle contrast agent on *T*<sup>1</sup> relaxation mechanism is mainly due to the direct interaction of the hydrogen nucleus in water molecules and the metal ions in magnetic nanoparticles, so the correlation coefficient between the *r* <sup>2</sup> relaxation rate and the *r*<sup>2</sup> relaxation rate is only 0.8939.

**Author Contributions:** Conceptualization, Y.Z., J.C. and W.L.; Data curation, Y.Z.; Formal analysis, Y.Z.; Methodology, Y.Z. and W.L.; Supervision, J.C. and W.L.; Writing—original draft, Y.Z.; Writing—review & editing, J.C. and W.L.

**Funding:** This study was supported by NSFC project 61571199.

**Acknowledgments:** We are grateful for the technical and equipment support of the NMR provided by Yiping Chen and Yongzhen Dong from Huazhong Agricultural University, Wuhan, China. In addition, we would like to thank Pei Zhang and Bi-Chao Xu from The Core Facility and Technical Support, Wuhan Institute of Virology, for their help with producing TEM micrographs.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

We have sorted out the following two tables. Table A1 is the ratios of magnetic nanoparticle concentration to Fe ion concentration of every SHP reagent. Table A2 shows the parameters include magnetic nanoparticle concentration, induced magnetization, mean values and standard deviations of the measured relaxation time of the all tested magnetic nanoparticle samples.


**Table A1.** Fe concentrations and magnetic particle concentrations of the SHP series magnetic nanoparticles reagent. Data from the website of Ocean NanoTech.



#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Ferrogels Ultrasonography for Biomedical Applications**

#### **Felix A. Blyakhman 1,2, Sergey Yu Sokolov 1,2, Alexander P. Safronov 2,3, Olga A. Dinislamova 1, Tatyana F. Shklyar 1,2, Andrey Yu Zubarev 2,4 and Galina V. Kurlyandskaya 2,5,\***


Received: 16 July 2019; Accepted: 10 September 2019; Published: 13 September 2019

**Abstract:** Ferrogels (FG) are magnetic composites that are widely used in the area of biomedical engineering and biosensing. In this work, ferrogels with different concentrations of magnetic nanoparticles (MNPs) were synthesized by the radical polymerization of acrylamide in stabilized aqueous ferrofluid. FG samples were prepared in various shapes that are suitable for different characterization techniques. Thin cylindrical samples were used to simulate the case of targeted drug delivery test through blood vessels. Samples of larger size that were in the shape of cylindrical plates were used for the evaluation of the FG applicability as substitutes for damaged structures, such as bone or cartilage tissues. Regardless of the shape of the samples and the conditions of their location, the boundaries of FG were confidently visualized over the entire range of concentrations of MNPs while using medical ultrasound. The amplitude of the reflected echo signal was higher for the higher concentration of MNPs in the gel. This result was not related to the influence of the MNPs on the intensity of the reflected echo signal directly, since the wavelength of the ultrasonic effect used is much larger than the particle size. Qualitative theoretical model for the understanding of the experimental results was proposed while taking into account the concept that at the acoustic oscillations of the hydrogel, the macromolecular net, and water in the gel porous structure experience the viscous Stocks-like interaction.

**Keywords:** magnetic nanoparticles; ferrogels; medical ultrasound; sonography; biomedical applications

#### **1. Introduction**

Hydrogels are soft materials that are widely used in the area of biomedical applications [1]. Ferrogels (FG) are composites that contain a polymer swollen in a solvent and filled with nano- or micro-sized magnetic particles [2–4]. In particular, FG based on polyacrylamide (PAA) hydrogel with magnetic nanoparticles (MNPs) of iron oxides are the most studied and sought-after material for a wide range of biomedical applications, including magnetic biosensors, drug delivery, and regenerative medicine [5,6]. Different studies had established the fact that the elastic properties of PAA ferrogels can significantly vary, depending on the details of synthesis conditions, as well as change their mechanical characteristics in response to an external magnetic field [4,7,8]. It is also known that polyacrylamide ferrogels have low toxicity and good compatibility to living cells [9,10]. Based on this advantage, PAA

ferrogels have been used as substrates (scaffolds) for cell culturing for the needs of cellular technologies and tissue engineering [11].

Ferrogel scaffolds offer different directions of the research and applications. For example, the intensity of ultrasound that is reflected at a ferrogel/water interface is determined by the difference between the acoustic impedances of the two materials. The effect of magnetic nanoparticles on the ultrasonic parameters (also acoustic impedance) of gel phantoms has been previously shown [12]. The values of the impedance increased after the addition of nanoparticles, so the phantoms with magnetic nanoparticles exhibited increased echogenicity, owing to the significant number of scatters [13].

In addition, the MNPs forming the part of the PAA gels have high magnetic responses, often sufficient for the control of the movement of FG based micro-objects while using an external magnetic field [14]. This feature opens up prospects for the use of ferrogels for magnetic biosensor applications, regenerative medicine, or targeted drug delivery or controlled release of drugs [15–17]. The above-mentioned applications are associated with the solution of a number of problems, including the task of reliable visualization of FG in a living organism.

In fact, the scientific community has already moved from the concept of biomedical applications of magnetic nanoparticles toward the understanding of ferrogel models, which are much closer to realistic applications in which MNPs are distributed in living tissue. Very often, such distribution reflects the biological properties of the natural tissue. What is especially important, aggregation features can be conditioned by irregularly structured tissue with the disease-affected morphology [18]. The development of a new technique for detecting of ferrogel scaffolds in blood vessels while using medical ultrasound is highly desired. There is a strong request for FG use in vivo as a prototype of magnetically controlled platforms for targeted delivery of cell implants and drug substrates through arteries, as well as positioning indicators for low invasive surgery.

In the work, the features of ultrasonic location of samples of PAA based ferrogels with a variation of the concentration of Fe2O3 MNPs of iron oxide in a wide range are considered for FG scaffold of different shape. A theoretical interpretation of the experimental results is given.

#### **2. Experimental**

#### *2.1. Gel and Ferrogel Synthesis and Characterization*

Ferrogels with varying concentration of iron oxide magnetic nanoparticles were synthesized by three-dimensional (3D) radical polymerization of acrylamide in stabilized aqueous ferrofluid. First, electrostatically stabilized ferrofluid was prepared with stock concentration 5.1% of MNPs by weight. Fe2O3 MNPs (Figure 1a) were synthesized by the laser target evaporation (LTE) method while using commercial magnetite (Fe3O4) (Alfa Aesar, Ward Hill, MA, USA) as a precursor.

Technological details of the LTE method were previously described in earlier studies [19,20].

Stock ferrofluid for the synthesis of FGs was prepared by the ultrasound dispersion of maghemite MNPs in 5 mM solution of sodium citrate, taken as electrostatic dispersant. Ferrofluid was centrifuged for 5 min. at 10,000 rpm to eliminate large aggregates. The number averaged diameter of particles in ferrofluid determined by dynamic light scattering (Brookhaven ZetaPlus, Brookhaven Instruments Corp., Holtville, NY, USA) was found to be close to 33 nm. The resulted concentration of ferrofluid (5.1%) was determined as the dry weight residue after evaporation at 90 ◦C in an oven.

**Figure 1.** Transmission electron microscopy (TEM) image of laser target evaporation (LTE) iron oxide magnetic nanoparticles (MNPs) used for ferrogel synthesis (**a**). General view of gel and ferrogel samples from batch #1 (**b**) and batch #2 (**c**). See explanation in the text.

The stock ferrofluid was then diluted and used as a medium for the synthesis of FGs with varying content of MNPs. Monomer—acrylamide (AppliChem)—was used in 1.6 M concentration, a cross-linking agent—dimethylacrylamide (Merck)—was taken in 1/100 molar ratio to the monomer. Ammonium persulfate (APS) was used as an initiator in 3 mM concentration and the polymerization was performed at 70 ◦C for 2 h. N,N,N',N'-tetramethylethylene diamine (TEMED) (SigmaAldrich Inc. St. Louis MO, USA) in 6 mM concentration was used as a catalyst. After the synthesis, FGs were extensively washed in distilled water with daily water renewal for two weeks. During this period, FGs swelled to equilibrium. The equilibrium water uptake (*Q*) was determined by gravimetry while using the equation:

$$Q = \frac{m - m\_0}{m\_0},$$

with *m* denoting the weight of a swollen gel and *m*<sup>0</sup> denoting the weight of a residue after drying a gel in an oven at 70 ◦C. The values of *Q* were used for the calculation of the actual content of iron oxide MNPs in a swollen ferrogel (ω), according to the equation:

$$w = \frac{\mathcal{V}}{Q + 1}'\tag{2}$$

with γ denoting the weight fraction of iron oxide MNPs in the dry residue of ferrogel. The value of γ was determined based on the composition of the reaction mixture in the synthesis.

Two batches of FG samples were synthesized differently in their shape. Ferrogels of batch #1 were synthesized in cylindrical polyethylene moulds 8.5 mm in diameter and 50 mm in height. These gels were used for ultrasonography studies in water, and further on used for the mechanical testing experiments. Therefore, they were cut into cylindrical plaques of the size of approximately 5 mm (in height). The diameter of cylinders was approximately 13 mm conditioned by the equilibrium swelling of a gel in water after the synthesis. FGs of batch #1 contained 0.00, 0.33, 0.64, and 1.34% of maghemite iron oxide MNPs by weight. Further on, they are denoted as FG1-0, FG1-1, FG1-2, and FG1-3 samples. A general view of FG samples of batch #1 is given in Figure 1b.

Ferrogels of batch #2 were synthesized in capillary polyethylene moulds 1.7 mm in diameter and 20 mm in height. These gels were used for ultrasonography studies in the configuration modelling the blood vessel (tube). These samples were cut in small cylinders of approximately 6 mm in length. The diameter of the cylinders was approximately 2 mm, provided by the equilibrium swelling of a gel in water after the synthesis. Ferrogels of batch #2 contained 0.00, 0.55, 0.98, and 1.45% of iron oxide MNPs by weight. Further on, they are denoted as FG2-0, FG2-1, FG2-2, and FG2-3 samples. Figure 2 provides a general view of ferrogel samples of batch #2. The content of iron oxide MNPs in ferrogels of batch#1 and batch#2 slightly differed due to the variation in the composition of the reaction mixtures. In the

context of proposed study, we did not set out to synthesize samples with exact the same concentration of particles in two batches.

**Figure 2.** Scheme of the experimental setup to determine the echogenic properties of gels/ferrogels: 1—ultrasonic apparatus; 2—personal computer; 3—sensor of ultrasonic apparatus; 4—silicone tube with water; 5—sample of the gel/ferrogel; 6—soft pad; and, 7—cuvette with water. See also explanation in the text.

Synthesized ferrogels were uniformly colored and transparent (see Figure 1b,c). Visually, their appearance was similar to that of the precursor ferrofluid that was taken for the synthesis. No signs of turbidity were noticeable (including observations at the level of optical microscopy). Thus, it might be considered that there was no substantial aggregation of iron oxide MNPs in the synthesis of ferrogels and the distribution of MNPs in ferrogels was uniform, as in the precursor ferrofluid.

The elastic properties of the gels were evaluated by mechanical testing of the samples as described elsewhere [6,8,10]. Briefly, stepped strains for compression of up to 20% of the initial length were set to samples of gels while using a linear motor with a step of 1–2%. As a result, the "stress- strain" (σ-ε) dependencies were obtained, from the linear part of which the Young's modulus was determined for each one of the samples. For these series of experiments, samples of gels from the batch #1 (cylinders with a diameter of 13 mm and a height of 5 mm) were used (Figure 1b).

The magnetic hysteresis loops M(H) of the MNPs of iron oxide, gels, and ferrogels were measured by vibrating sample magnetometer (VSM, Faraday magnetometer of laboratory design). The maximum value of the magnetization was obtained for the external field of 1.5 kOe. For simplicity, it was denominated as saturation magnetization (Ms). The coercivity (Hc) was also estimated from the shape of the M(H) hysteresis loop. Thermomagnetic zero field cool–field cool curve (ZFC-FC) was measured for air dry MNPs following standard procedure for magnetic nanoparticles [19]. The external magnetic field for the ZFC-FC curve was as high as H = 100 Oe (it was applied for cooling and heating in the case of FC part of the curve and for heating only in the case of ZFC part of the curve).

#### *2.2. Experimental Setup for the Gels' Ultrasound Visualization*

Figure 2 shows an experimental setup for the study of the echogenic properties of gels and ferrogels. Samples of gels from the first batch (Figure 1b) were placed at the bottom of a cuvette with distilled water.

Samples from the second batch (Figure 1c) were located inside the silicone tube with an inner diameter of 6 mm and a wall thickness of 3 mm. The tube served for modelling the blood vessel configuration. It was filled with distilled water.

Fluid flow was not considered at this moment. Samples of the gels were visualized while using a Sonoline Adara (Siemens, Munich, Germany) medical device with a SIEMENS 7.5L45s Prima/Adara linear sensor. Ultrasonic sensor was immersed into a 500 mL cuvette that was filled with water for providing an acoustic contact. A gasket of soft viscose absorbent fibers was placed at the bottom of the cuvette in order to avoid the contribution of reflecting ultrasonic signal from the bottom of the cuvette. The video output of the ultrasound unit was connected to a computer equipped with an AverTV Hybrid VolarHX video capture device.

The dynamic range of the ultrasonic device in the mode of reception of the reflected oscillations was 66 dB, working frequency of 10 MHz, and the wavelength of 0.15 mm. In the experiments that were carried out within the framework of the corresponding batch of samples, the settings of the ultrasonic apparatus (radiation power, amplification, dynamic range, depth of visualization, etc.) were kept constant. The image of samples in two-dimensional (2D) mode in gray scale was recorded in a video file with a duration of several seconds with a frame rate of 25 frames per second, and the frame size is 720 pixels × 576 pixels.

Special software was developed to quantify the brightness of the image in various areas. It allowed to measure the brightness in the vicinity of a point specified by the user. In the experiment, the brightness of the image at the gel-water interface was measured and estimated. As a rule, the border thickness important for imaging was as high as 4–5 pixels. On this basis, the size of the area for assessing the brightness was limited to a square of 3 pixels × 3 pixels, which corresponds to linear dimensions of about 0.2 mm × 0.2 mm. For each sample, the measurements were carried out along the entire boundary of the gel. The number of measurements was at least 15 along the entire length of the sample. In each studied area, the minimum, maximum, and average image brightness were evaluated. The brightness was characterized in arbitrary units and it ranged from 0 (black) to 255 (white). For each type of FG, the average value of the maximum and average brightness, as well as the limits of the confidence interval at a significance level of *p* = 0.05, were calculated. In addition, in all experiments, 20 pixels × 20 pixels square image was used to estimate the background, i.e., the brightness of the image area where the water was located. The maximum, minimum and average background brightness in all cases varied insignificantly. Therefore, finally, the adjustment that was associated with changes in the brightness of the background was not carried out.

#### **3. Results and Discussion**

#### *3.1. Structural and Magnetic Characterization of Nanoparticles and Ferrogels*

Figure 1a shows an example of transmission electron microscopy (TEM) image of iron oxide MNPs (JEOL JEM2100, Tokyo, Japan). The majority of MNPs have spherical shape. Very few of them contain hexagonal corners. Particle size distribution (PSD) of MNPs was lognormal with the median d0 = 11.7 nm and the logarithmic dispersion σ = 0.423, as determined by the graphical analysis of 2150 TEM images. According to PSD, the average diameter of 93% of MNPs (by weight) fits a 5–40 nm range. According to X-ray diffraction (Bruker D8 Discover, Billerica, MA, USA), the crystalline structure of MNPs was an inverse spinel with space group Fd3m. The lattice parameters corresponded to maghemite (Fe2O3). The oxidation number +3 of Fe ions in the chemical composition of MNPs was confirmed by Ox/Red titration (TitroLine, Schott Instruments).

Measurements of the saturation magnetization of as-prepared air dried MNPs showed that their average size and defined composition (γ-Fe2O3) are quite consistent with each other: Ms ≈ 40 emu/g. Detailed discussion on the magnetic structure of "core-shell" LTE MNPs can be found elsewhere [19,20].

As before, pure gel without nanoparticles showed linear non-hysteretic diamagnetic response on the application of external magnetic field (Figure 3a). At the same time, the ferrogel's M(H) loops had a typical S-shape with negligible coercivity for the small concentrations of MNPs (Figure 3b). The evolution of the Ms value as a function of the concentration of nanoparticles in the ferrogel shows linear dependence: the higher concentration, the higher the Ms (Figure 3b). The magnetization value for the FG scaffold in the applied magnetic field of certain strength is a very important parameter in a view of FGs applications for drug delivery and the controlled movement of micro-objects by magnetic field. For the highest concentration of 1.45 wt. % in the external field of 0.5 kOe (reasonably low an accessible for generation), the magnetic moment of the FG was as high as 0.5 emu/g. Taking into account the scaffold FG2-3 volume, one can obtain the magnetic moment of the sample in the 0.5 kOe external magnetic field: m <sup>=</sup> 0.9 <sup>×</sup> <sup>10</sup>−<sup>3</sup> emu.

**Figure 3.** Magnetic hysteresis loop of air-dry nanoparticles measured at room temperature; inset shows thermomagnetic zero field cool–field cool curve (ZFC-FC) curve (**a**). Hysteresis loops for FG1-0, FG1-1, FG1-2, and FG1-3 samples measured at room temperature (**b**); inset shows diamagnetic response of the blank gel.

#### *3.2. Gels Elasticity*

Figure 4a shows a plot of 'stress-strain' relationship for one of the samples of the first batch of gels (0.00, 0.33, 0.64 and 1.34 wt.% of MNPs). It is seen that, at any fixed strain, the stress in the gel is the greater, the higher the concentration of MNPs. The caption contains the linear regression equations for each sample, where the value of ε corresponds to the value of Young's modulus in kPa.

Figure 4b shows the dependence of the Young's modulus on the concentration of MNPs in the gel/ferrogel for all the tested samples (six samples for each type of gel/ferrogel). First of all, it can be seen that the addition of MNPs to the PAA gel in the minimum concentration (0.33%) leads to a significant increase in the Young's modulus of the composite material. Secondly, a gradual increase in the concentration of MNPs in ferrogel is accompanied by a further increase in its elasticity. The results that were obtained are in good agreement with the data of our earlier studies [6,8,11] and the findings of other authors [7,21].

**Figure 4.** Example of the 'stress-strain' relationship for gels of batch #1 (**a**) and the dependence of Young's modulus on the MNPs concentration in gels of batch #1 (**b**). Vertical bars reflect the confidence interval with p = 0.05. Following fit parameters were obtained for stress (σ). For concentration 0.00%: <sup>σ</sup> <sup>=</sup> 20.2<sup>ε</sup> <sup>−</sup> 0.2, R2 <sup>=</sup> 0.995. For concentration 0.33%: <sup>σ</sup> <sup>=</sup> 28.9<sup>ε</sup> <sup>−</sup> 0.3, R2 <sup>=</sup> 0.994. For concentration 0.64: <sup>σ</sup> <sup>=</sup> 36.4<sup>ε</sup> <sup>−</sup> 0.3, R2 <sup>=</sup> 0.997. For concentration 1.34: <sup>σ</sup> <sup>=</sup> 39.2<sup>ε</sup> <sup>−</sup> 0.1, R2 <sup>=</sup> 0.998.

#### *3.3. Gel*/*water Boundary Echogenicity*

Figure 5 shows an example of a single ultrasound image frame when scanning a gel sample positioned at the bottom of a cuvette (a) and inside a model vessel (b) (Figure 2). The images very clearly show the boundaries of the gel samples lining at the bottom of the cuvette and the walls of the tube with water. It is also seen that the highest echogenicity of the gels (i.e., the largest amplitude of the reflected ultrasonic vibrations, and, accordingly, the brightness of the image) corresponds not to the sample body, but to the interface between the gel surface and the water. In experiments with the first batch of gels, the visualization was performed with an ultrasound device amplification of 15 dB. Four samples were tested for each concentration of MNPs in the gel. The average value of the maximum brightness of the water in the cuvette in all tests of the gels was 34.1 ± 0.2 (n = 16).

Figure 6a shows the dependence of the maximum and the average brightness at the gel/water interface on the concentration of MNPs in the gel. The graphs show the boundaries of confidence intervals at p = 0.05. It can be seen that, by increasing the weight fraction of the MNPs in the samples, both the maximum brightness (1) and the average brightness (2) of the echo reflected from the surface of the gels were increased. The data are well approximated by the linear regressions: (1) y = 16.783x + 205.4, R<sup>2</sup> = 0.988; (2) y = 8.166x + 183.8, R<sup>2</sup> = 0.931.

Figure 6b shows the dependences of the maximum and average brightness of the gel/water interface on the Young's modulus of the samples. It can be seen that the echogenicity of the surface of the gels is directly related to the elastic properties of the tested materials. Moreover, the higher the stiffness of the samples, the more accurately the gels are visualized. Again, the data (Figure 6b) are well approximated by the linear regressions: (1) y = 1.529x + 169.45, R2 = 0.989; and, (2) y = 0.7666x + 165.63, R<sup>2</sup> = 0.987.

In a series of experiments with the second batch of gels (samples were placed in a model "blood" vessel (Figures 1c and 5b), the ultrasonic amplification of the apparatus was increased to 20 dB to compensate for the signal loss through the tube wall. Totally, seven samples were tested for each concentration of MNPs in the gel. The average brightness of the water inside the tube was 44.4 ± 0.2 (n = 28).

**Figure 5.** Examples of ferrogels samples visualization at the bottom of water cuvette (**a**) and inside a silicone tube filled with water (**b**). The distance from sensor to objects is about 20 mm. 1—soft pad (a) and wall of silicone tube (b); 2—water in cuvette (a) and in tube (b); 3—upper boundary of gel/water; 4—gel body.

**Figure 6.** Dependences of maximal (1) and average brightness (2) at gel/water boundary on the MNPs concentration for samples of batch #1 (**a**). Vertical bars reflect the confidence interval with p = 0.05. Dependences of maximum (1) and average brightness (2) at gel/water boundary on Young's modulus for samples of batch #1 (**b**). Vertical and horizontal bars reflect the confidence interval of relevant parameter with p = 0.05.

Figure 7 shows a graph of the maximum and average brightness of the reflected echo signal at the gel/water interface in a tube versus the concentration of MNP in the sample. The graphs show the boundaries of confidence intervals at p = 0.05. The data (Figure 7) are well approximated by the linear regressions: (1) y = 61.652x + 130.07, R2 = 0.996; (2) y = 31.9x + 81.6, R2 = 0.984. It can be seen that the echogenicity of the surface of the ferrogel significantly increases in comparison with the PAA gel, even with the minimum concentration of MNPs. At the maximum concentration of MNPs in ferrogel (1.45%), the brightness of the reflected echo signal from its boundary with water is approximately two times higher than for the baseline PAA of the sample. This conclusion is valid for both the use of maximum and average brightness as a measure of the echogenicity of the material. The result that was obtained for the samples of gels (the first batch) inside the model vessel is in full compliance with the test data of the echogenicity of the samples (second batch) in water (see Figure 6a).

**Figure 7.** Dependences of maximum (1) and average brightness (2) at gel/water boundary on the MNPs concentration for samples of batch #2. Vertical bars reflect the confidence interval with *p* = 0.05.

It should be noted that the dependence of brightness at the gel/water interface on the concentration of MNPs is more pronounced for the samples in a model vessel than for gels that were placed in a cuvette filled with water.

We have studied the ultrasound reflection from the non-deformed sample in condition, which mimic the ferrogel in a blood vessel. It is important to mention that effect of the sample preliminary tension on the sound reflection is out of scope of this work. Figures 4, 6 and 7 demonstrate that the Young modulus and the brightness of the reflected signal both increase with the particle concentration. It allows for making simple comment on the relation between the Young's modulus and the impedance and to conclude that the impedance increases with the modulus. Note that classical results of the acoustic theory demonstrate the increasing relation on the basis of the general considerations of the theory of continuous media.

#### **4. Discussion**

The experience of ultrasound imaging of such polymer soft materials as gels for medical purposes is well known. In particular, the results of the location of gel phantoms of internal organs and tissues were used for testing and calibration of ultrasound diagnostic equipment [22,23], as well as implants that are based on gels [24,25]. Here, the visualization of FG sample geometrical features was for the first time achieved by using the ultrasonic location method. While taking into account the fact that FGs are considered to be promising materials for medical applications, the study was performed by a standard ultrasound apparatus that is in use for medical purposes. Regardless the shape of the samples and the conditions of their location, the boundaries of ferrogels are confidently visualized while using medical ultrasound over the entire range of concentrations of MNPs.

An increase in the MNPs concentration in the PAA gel was accompanied not only by an increase in the echogenicity of the gel/water interface, but also by the elasticity of the samples. Moreover, we established a linear relationship between the brightness of the echo signal reflected from the boundary and the Young's modulus of the FG (Figure 6b). This result was obtained for the samples from the first batch of gels, while visualizing them at the bottom of a container with water.

It should be mentioned that in a series of experiments with a model vessel, the elastic properties of FGs from the second batch were not determined due to the design of the equipment for mechanical properties evaluation. When the diameter of the samples was below 8 mm, the installation did not allow for correct setting of deformations in compression. However, all of the materials and procedures used for the synthesis of gels were the same. The only exception was the moulding of gels for relevant needs. This circumstance makes it possible to insure the possible connection between the echogenicity of the surface of the gels and the Young's modulus of samples from the second series with a high degree of confidence. Below, we attempt to describe the relationship between the concentration of MNPs in the gel and its echogenicity at the interface with water theoretically.

In this part, we suggest some physical interpretation of the experimental results. It is based on the concept that, at the acoustic oscillations of the hydrogel, the macromolecular net and water in the gel porous experience the viscous Stocks-like interaction. Thus, in the first approximation, one can suppose that, in each small volume of the hydrogel, the net and water move with the same velocity and the hydrogel can be considered as a unite continuum. In the frame of this physical approximation, the coefficient *R* of the sound reflection on the border between hydrogel and water out of it, can be estimated, as follows [26]

$$R = \left(\frac{c\_2\rho\_2 - c\_1\rho\_1}{c\_2\rho\_2 + c\_1\rho\_1}\right)^2\tag{3}$$

Here, the Subscribes 1 and 2 correspond to the water out of the hydrogel and the hydrogel, considered as a continuous medium, respectively, ρ is mass density of the corresponding media.

The sound speed can be presented as in Ref. [26]

$$
\sigma = \sqrt{\frac{K}{\rho}} \tag{4}
$$

where *K* is the compression modulus of the media. Therefore, Equation (3) can be rewritten as form:

$$R = \left(\frac{\sqrt{K\_2 \rho\_2} - \sqrt{K\_1 \rho\_1}}{\sqrt{K\_2 \rho\_2} + \sqrt{K\_1 \rho\_1}}\right)^2 \tag{5}$$

The hydrogel compression modulus *K*<sup>2</sup> is determined by the modulus of the water, modulus of the macromolecular net, and modulus of the embedded particles (see, for example, general discussion in [27]. Since the volume concentration of the gel and particles in the hydrogel are low, in the first approximation *K*<sup>2</sup> ≈ *K*1. The hydrogel mass density is more than the density of water, i.e., ρ<sup>2</sup> > ρ1. Therefore, the inequality (*K*2ρ2) <sup>1</sup>/<sup>2</sup> > (*K*1ρ1) <sup>1</sup>/<sup>2</sup> is held and the coefficient *R* can have quite significant value, which is enough to provide the visible reflection signal (see Figure 4). The addition of the rigid particles increases both the modulus *K*<sup>2</sup> of the hydrogel and its density ρ2. Obviously, in the range of small concentrations of the particles, coefficient *R* (defined for Equation (5)) should show linear dependence on the concentration (Figures 6a and 7).

The suggested theoretical interpretation of the experimental results is rather qualitative. Since the ultrasound wavelength is much more than the size of the particles and heterogeneities, provoked by the particles, we have used classic considerations of the acoustics of continuous media. It appeared enough for, at least, principal explanation of the experimental results. Detailed experimental study of the particles distribution inside the hydrogel are required in order to achieve reliable quantitative description of the reflection effects at higher level of understanding.

Let us make short remark on possible future directions of ultrasound location research. As it was mentioned in the introduction, magnetically controlled platforms for targeted delivery of cell implants and drug substrates through arteries, as well as positioning indicators for low invasive surgery, is a hot topic of the research and applications. Recently, we proposed using giant magnetoimpedance based multilayered sensitive element for the monitoring of FG scaffold position inside the blood vessel in regenerative medicine case of application [8,28].

Generally speaking, the goal to define the FG scaffold position can be completed either by magnetic or by ultrasound detection. What is most important is that both techniques can probably be used at a time or just one after another in two simple non-invasive tests. The concept of usage of different techniques for material characterization is well established in the nanomedicine for nanomaterials characterization [16]. Ferrogels offer a new opportunity for extending this concept on the non-invasive tests, keeping in mind not a material characterization, but rather complex diagnostic solution. Different techniques have their advantages and disadvantages and the application of multiple techniques can be viewed as additional advantage, especially keeping in mind than ultrasonic equipments are available for routine diagnostics.

#### **5. Conclusions and Outlook**

Samples of ferrogels with different concentrations of MNPs were synthesized in various forms to simulate different peculiarities of the visualization of sample location for future development in the area of biomedical applications. In particular, thin cylindrical samples were used to simulate the situation in which ferrogels can be used as platforms for targeted drug delivery or cell cultures through blood vessels. Samples of larger size in the form of cylindrical plates were used in order to simulate cell grafts that are based on ferrogel, intended for use as substitutes for damaged structures, such as bone or cartilage tissues.

We found that, regardless of the shape of the samples and the conditions of their location while using medical ultrasound, the boundaries of ferrogels are confidently visualized over the entire range of concentrations of MNPs. Moreover, the intensity of the reflected echo was greater, the greater the concentration of MNPs in the gel. Obviously, the result that was obtained is not related to the influence of the MNPs directly on the intensity of the reflected echo signal, since the wavelength of the ultrasonic effect used is much larger than the particle size. Therefore, we can point out the indirect effect of MNPs on the echogenicity of ferrogels.

Qualitative theoretical interpretation of the experimental results was proposed while taking into account the concept that, at the acoustic oscillations of the hydrogel, the macromolecular net and water in the gel porous experience the viscous Stocks-like interaction.

**Author Contributions:** F.A.B., S.Y.S., A.P.S. and G.V.K. conceived and designed the experiments; F.A.B., S.Y.S., O.A.D., T.F.S. and A.P.S. performed the experiments; S.Y.S. developed the special software; F.A.B., O.A.D., T.F.S., A.P.S. and G.V.K. analyzed the data; A.Y.Z. proposed the theoretical justification of data obtained; F.A.B., A.P.S., A.Y.Z. and G.V.K. wrote the manuscript. All authors discussed the results and implications, and commented on the manuscript at all stages. All authors read and approved the final version of the manuscript.

**Funding:** The Russian Scientific Foundation (grant 18-19-00090) supported the experimental parts of this study, including the design, performance and analysis of experiments.

**Acknowledgments:** A.Yu. Zubarev thanks the program of the Ministry of Education and Science of the Russian Federation (project 3.1438.2017/46) for the support of his mathematical studies. We thank K.R. Mekhdieva, P.A. Shabadrov, V.Ya. Krokhalev, I.V. Beketov and A.M. Murzakaev for special support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Size-Dependent Properties of Magnetosensitive Polymersomes: Computer Modelling**

**Aleksandr Ryzhkov 1,\*,† and Yuriy Raikher 2,†**


Received: 22 October 2019; Accepted: 26 November 2019; Published: 29 November 2019

**Abstract:** Magnetosensitive polymersomes, which are amphiphilic polymer capsules whose membranes are filled with magnetic nanoparticles, are prospective objects for drug delivery and manipulations with single cells. A molecular dynamics simulation model that is able to render a detailed account on the structure and shape response of a polymersome to an external magnetic field is used to study a dimensional effect: the dependence of the field-induced deformation on the size of this nanoscale object. It is shown that in the material parameter range that resembles realistic conditions, the strain response of smaller polymersomes, against *a priori* expectations, exceeds that of larger ones. A qualitative explanation for this behavior is proposed.

**Keywords:** magnetic polymersomes; magnetic vesicles; magnetic nanoparticles; magnetoactive composites; nanocapsules; coarse-grained molecular dynamics; computer simulation

#### **1. Introduction**

Synthesis of microscale particles capable of drug transportation and/or active manipulations with cells is one of the most actively developing trends in modern biomedicine [1]. A promising class of such objects, well tunable and controllable, are polymersomes: vesicle-like submicron capsules whose walls are formed by a bilayer membrane built of an amphiphilic block copolymer [2–7]. The polymersome might be loaded with biomedical substances (cargo) whereas the membrane might be functionalized to be stimuli-sensitive to a number of factors: pH, temperature, oxidation/reduction, electric/magnetic fields, light, ultrasound, etc. Chemical versatility and stability of polymersomes ensure a variety of their foreseen applications: biosensing systems, nanoreactors, drug carriers with externally activated release, imaging, and even prototypes of artificial cell organelles.

The objects of current study are magnetosensitive polymersomes (magnetopolymersomes, MPSs) whose membrane is modified by introducing inside it magnetic (e.g., maghemite) nanoparticles (MNPs) [8–11]. Due to the hydrophilic/hydrophobic interplay, the MNPs are confined inside the sandwich structure formed by the inner and outer amphiphilic polymer layers (shells); the width of the intershell gap is adjusted in such a way that it just a bit exceeds the MNP size. With such a construction, magnetodeformational susceptibility of MPSs comes out several orders of magnitude higher than that of any other types of microcapsules.

Nowadays, chemical synthesis of various modifications of MPSs is rapidly developing, and they are available in different shapes and morphologies [12,13]. In [14], membranes of poly(trimethylene carbonate)-*b*-poly(L-glutamic acid) (PTMC-*b*-PGA) with incorporated maghemite (*γ* − Fe2O3) nanoparticles are reported. The monolayer, double-layer and multilayer vesicles with poly(styrene)-*b*-poly(acrylic acid) (PS-*b*-PAA) membranes of tuned thickness and stuffed with MNPs

are obtained in [15]. The tests demonstrate that the polymersomes with thicker membrane and higher MNP density display enhanced MRI contrast, higher magnetization and better release profile of their drug cargo. In structure investigations, it is found that larger MNPs drift closer to the inner membrane boundary that leads to larger curvature of the latter [16]. Besides dilute systems, preparation of size-controlled assemblies of densely packed submicron PS-*b*-PAA polymersomes is also possible [16].

Now a commonly established fact is that under an applied external field, MPSs notably stretch along the field direction. Moreover, as revealed by small-angle neutron scattering (SANS), the field causes changes in the membrane structure making it anisotropic, and this anisotropy increases with the applied field. The evaluated scattering anisotropy factor is also found to be dependent on the MNP content, size and curvature of the membrane. According to the SANS observations, the field strength at which the field-dependence of the anisotropy factor attains a plateau coincides with that saturating the MNP magnetic moments [14].

The granted biocompatibility of MPSs and experimentally proven opportunity to magnetically control their shape as well as the changes of MNP distribution inside the membrane, commend them as really smart micro-objects for biomedical use. For further progress, one needs a valid concept of complex magnetomechanical and magnetostructural properties of MPSs that, as for now, is virtually nonexistent. A promising, if not the only, way to fill in this gap, i.e., to study and predict the deformational and structure responses of MPSs, is an extensive use of computer simulations. In what follows, we describe a flexible computational model of an MPS and use it to analyze the field-induced shape and volume effects.

#### **2. Model and Simulations**

A coarse-grained molecular dynamics description of a magnetic polymersome was developed in [17]. Here, we use it to investigate the dependence of magnetodeformational behavior of an MPS on the overall size of the latter.

The model MPS is built of the particles of two types: non-magnetic polymer ones (beads) and MNPs. The sandwiched amphiphilic membrane, within which the MNPs are confined, is presented as two nested spherical shells, the inner and outer ones, see Figure 1. Each shell consists of an equal number of beads arranged in a quasi-2D triangular mesh, so that the centers of beads are the mesh nodes; the diameters of the beads are denoted as *d*in and *d*out, respectively, where the subscript indicates the shell.

Inside each shell the bead centers are connected with stiff springs to ensure virtual constancy of the inter-bead distances and, thus, the area of the triangle built of any three neighboring beads. At the surface organized in such a way, any pair of side-abutting triangles is, however, free to fold along their mutual border. In other words, the overall surface area of the shell is conserved but the shell bending elasticity is negligible.

Inside this double-shell membrane, in a number of points uniformly distributed over its surface, the subtending beads (nodes) of the shells are linked with identical linear elastic springs; the stress-free length *h* of the spring defines the equilibrium thickness of the intershell layer. Given that the total membrane thickness is *h* + <sup>1</sup> <sup>2</sup> (*d*in <sup>+</sup> *<sup>d</sup>*out), whereas the gap accessible for the MNPs is *<sup>h</sup>*gap <sup>=</sup> *<sup>h</sup>* <sup>−</sup> <sup>1</sup> <sup>2</sup> (*d*in + *d*out). The connectivity parameter *c*<sup>b</sup> of the membrane is defined as the ratio of the number of spring-bonded pairs to the whole number of particles in the shell; evidently, diminution of *c*<sup>b</sup> enhances the extent of the layer thickness fluctuations.

Inside the MPS membrane, a certain number of monodisperse spherical magnetic nanoparticles is confined, thus making a kind of quasi-2D magnetic fluid. The volume fraction *φ* of the MNPs is defined with respect to the volume of the intershell space where they are allowed to move. From the calculation viewpoint, each MNP is treated as a structureless bead of diameter *d*<sup>p</sup> with a built-in magnetic (dipole) moment fixed at its center. The intershell gap *h*gap but slightly exceeds *d*p, so that the intershell layer might accommodate only a monolayer of MNPs. In magnetic aspect, the MNPs are coupled with each other as point dipoles; in steric aspect, they interact as soft spheres. The diameters *d*in and *d*out of the shell beads are chosen is such a way that the shells are impenetrable for the MNPs.

To commence simulation, first, under the above-presented conditions a multi-element object (a model MPS) is constructed as a hollow sphere of outer diameter *D* with a double-shell wall, within which a given number of MNPs is uniformly distributed; the number of the beads in the shells is chosen accordingly. Then all the interparticle interactions are "switched on", and the model MPS is set in contact with Langevin thermostat that induces Brownian motion of all the elements of the system. Therefore, the thermostat imitates the presence of isothermal solvent (consisting of light-weight molecules) which uniformly fills in all the space outside and inside the MPS.

From this instant the coarse-grained molecular dynamics calculation starts and is carried out until the system comes to equilibrium; the criterion for the latter is stabilization of the overall energy value. This stage yields the basic (field-free) state of the MPS and enables one to obtain its characteristics. Then a uniform magnetic field is imposed, i.e., the Zeeman energy is added to the energy of each magnetic element, and the calculation process is run anew.

Technically, each calculation implies the numerical solution of the set of coupled equations of motion for all the center-of-mass position vectors*ri* (*t*) where subscript *i* enumerates all the elements of the model MPS, beads or magnetic particles:

$$m\_i \frac{d^2 \vec{r}\_i}{dt^2} = \vec{F}\_i - \zeta \frac{d\vec{r}\_i}{dt} + \vec{f}\_i\left(t\right);\tag{1}$$

here *mi* is the element mass, - *Fi* the force derived from the total potential energy. The second term in the right-hand side of Equation (1) is the dissipative force with translational friction coefficient *ζ*, and *fi* (*t*) is the random force generated by Langevin thermostat.

The force experienced by each bead of any shell is

$$F\_i = F\_{\mathbf{s},i} + F\_{\mathbf{a},i} + F\_{\text{bcond},i} + F\_{\mathbf{MNP}\text{-membrane},i}$$

with - *F*s, *<sup>i</sup>* being the total stretching/compression force on the part of neighboring mesh nodes, - *F*a, *<sup>i</sup>* a sum of forces depending on relative change of the areas of the mesh triangles which have the *i*-th node as a common vertex, - *F*bond, *<sup>i</sup>* an elastic force entailed by the presence of the bonds connecting the *i*-th node of one shell with the subtending node of another one, - *F*MNP-membrane, *<sup>i</sup>* a total force of soft mutual repulsion between the *i*-th and all the other MNPs, this set of forces is defined by pairwise Weeks-Chandler-Andersen (truncated Lennard-Jones) potential [18].

The force acting on each MNP is

$$F\_i = F\_{\text{dipolar},i} + F\_{\text{MNP-MNP},i} + F\_{\text{MNP-membrance},i} \tag{2}$$

Here - *F*dipolar, *<sup>i</sup>* is the sum of pairwise forces derived from the dipolar magnetic interaction of the *i*-th MNP that bears magnetic moment *μ* directed along unit vector *ei* with all the others located at the intercenter distances*rij*. This force has the form

$$-\nabla \left[ \mu\_0 \mu^2 \left( \frac{\left( \vec{e}\_i \cdot \vec{e}\_j \right)}{r\_{ij}^3} - \frac{3 \left( \vec{e}\_i \cdot \vec{r}\_{ij} \right) \left( \vec{e}\_j \cdot \vec{r}\_{ij} \right)}{r\_{ij}^5} \right) \right];\tag{3}$$

here *μ*<sup>0</sup> is vacuum permeability. The second and third terms in the right-hand part of Equation (2) are the soft repulsion forces between MNPs and between MNPs and the confining shells, respectively.

Note that for MNPs, besides translational degrees of freedom, the rotational ones matter as well, since the magnetic moment orientations enter the interparticle forces, see Equation (3). The pertinent equations of rotary dynamics with the corresponding torques induced both by the local fields and external field *H*-<sup>0</sup> are included in the whole set of equation as well.

**Figure 1.** Schematic cross-section of the model MPS. The membrane consists of the internal (red) and external (blue) shells made of equal number of polymer particles (beads) arranged in triangular mesh; the intershell space is filled with MNPs(gray spheres with arrows).

All computer simulations were performed with the aid of ESPResSo code [19], the shells were implemented following the scheme proposed in [20]. The computational experiments included preliminary steps to obtain equilibrium distribution of MNPs inside the MPS membrane under zero external field (basic state) and magnetization steps to obtain the changes induced by the applied field. For every MPS size and for every value of the field strength, the calculations were carried out on 10 copies of the model MPS which differed only in initial orientational distribution of the MNP magnetic moments.

The nondimensional parameters which characterize the system under study are as follows. The intensity of the magnetic dipolar interaction

$$
\lambda = \mu\_0 \mu^2 / d\_\mathbf{p}^3 k\_\mathbf{B} T\_\prime \tag{4}
$$

is defined as the ratio of energy of magnetic dipolar interaction of two identical MNPs placed at the closest possible distance, i.e., *d*p, to thermal energy with *kB* being the Boltzmann constant and *T* temperature.

The second parameter is the reference Zeeman energy of an MNP in the field of strength *H*<sup>0</sup> scaled with thermal one:

$$
\xi = \mu\_0 \mu H\_0 / k\_{\rm B} T. \tag{5}
$$

Let us clarify the relations between the dimensional parameters of the problem and their nondimensional counterparts used in the calculations. The nanoparticle diameter *d*<sup>p</sup> is set to 15 nm that with the typical magnetization of a ferrite (magnetite or maghemite) *M* = 500 emu yields for the MNP magnetic moment *μ* = (*π*/6)*Md*<sup>3</sup> <sup>p</sup> ≈ <sup>8</sup> × <sup>10</sup>−<sup>16</sup> emu. Then, assuming room temperature that is the only choice for aqueous solutions, for the dipole interaction parameter (4) one gets *λ* ≈ 5.

The Langevin argument *ξ* evaluated for the same conditions comes out is related to dimensional field strength as *ξ* ≈ 200*H*0, so that *ξ* = 10 corresponds to *H*<sup>0</sup> = 2 kOe that is completely feasible value.

The intershell distance *h* is taken as the length unit; in this scale, *d*p/*h* = 0.3 and *h*gap/*h* = 0.35. With the above-introduced value of the MNP diameter *d*<sup>p</sup> = 15 nm, for the MPS parameters one finds: *h* ≈ 50 nm and *h*gap ≈ 17 nm. The size of simulated MPSs varies from *q* ≡ *D*/*h* = 6 to *q* = 14 that makes 2.3 time difference; the value of *D* refers to the initial geometry of the MPS, i.e., a sphere. Taking the above-given value of *h*, one finds that the dimensional size of the tested MPS spans from 300 to 700 nm. In the membranes of all the samples, the volume content of MNPs is constant and equal *φ* ≈ 11 vol.%, and the connectivity of the MPS shells is set to *c*<sup>b</sup> = 0.2.

Keeping the MNP size *d*p, dipole parameter *λ*, layer thickness *h*gap, volume content *φ* and connectivity *c*<sup>b</sup> constant, we ensure that the "quality" of the MPS membranes is the same (at least, before the field is applied). The next section presents the results of simulating the field-induced responses of such MPSs under variation of their overall sizes *D*.

#### **3. Results**

The tested MPSs are shown schematically in Figure 2 just for visual comparison.

**Figure 2.** Schematic sketches (drawn at the scale) of model MPSs with nondimensional sizes *q*:6(**a**); 8 (**b**); 10 (**c**); 12 (**d**); 14 (**e**); for all samples *φ* ≈ 11% and *c*<sup>b</sup> = 0.2.

A series of snapshots of equilibrium states for MPSs of different sizes under variation of applied field is presented in Figure 3.

**Figure 3.** Snapshots of model polymersomes with the size *q* = 6 (**a**)–(**c**) and *q* = 14 (**d**)–(**f**) under applied field *ξ* = 2 (**a**) and (**d**) , *ξ* = 6 (**b**) and (**e**) , *ξ* = 10 (**c**) and (**f**) . The field is directed upward; for all samples *φ* ≈ 11% and *c*<sup>b</sup> = 0.2.

Simulations of the model MPSs under the field point out the common tendency to stretch along the field direction assuming axisymmetric ellipsoidal-like shape. Because of that, it suffices to describe this deformation by a single elongation parameter *ε* that we define as the ratio of the major semi-axis of the deformed sample to its minor one minus unity. These results are shown in Figure 4.

The presented plots reveal that the smaller polymersome is subjected to magnetization, the greater is its field-induced deformation. Indeed, under field *ξ* = 10 the elongation parameter is *ε* ≈ 0.25 for an MPS of size *q* = 6 whereas for the largest one (*q* = 14) it is *ε* ≈ 0.17, i.e., about 30% lower.

**Figure 4.** Elongation parameter *ε* = <sup>2</sup>*<sup>b</sup>* (*a*+*c*) − 1 as a function of external field strength parameter *ξ* for the MPSs of different initial sizes *q*; all the curves are obtained for *φ* ≈ 11% and *c*<sup>b</sup> = 0.2.

Being soft hollow objects, MPSs do not conserve neither their overall nor inner volume under deformation. In view of the drug delivery application, it is interesting to consider the field-induced volume changes of the MPS. The estimation is obtained from simulations by taking any actual configuration of the polymersome and building up a nested polyhedron whose vertexes are fixed at the the centers of the beads of the inner shell. These results are shown in Figure 5, where *V*<sup>0</sup> corresponds to the basic state of the MPS and is approximately equal to the volume of a sphere of diameter *D* − 2*h*. As seen, small polymersomes demonstrate a non-monotonic dependence of the "volume defect" (*V* (*ξ*) − *V*0) /*V*<sup>0</sup> on the field strength whereas larger ones show regular decreasing behavior.

**Figure 5.** Dependence of the "volume defect" (*V* − *V*0) /*V*<sup>0</sup> of the MPS cavity on applied magnetic field *ξ*; for all samples *φ* ≈ 11% and *c*<sup>b</sup> = 0.2.

#### **4. Discussion**

The coarse-grained molecular dynamics model is applied to investigate the field-induced overall deformation of an MPS and the internal restructuring accompanying it. This enables one to understand the dimension effect: the influence of the size factor on the polymersomes with the same properties of their membranes. The obtained results point out that in these objects the overall changes (shape anisotropy, volume defect) are essentially determined by the structure rearrangements which take place in the magnetically active membrane. As the snapshots of Figure 3 show, the MNPs, formerly dwelling in randomly oriented loose aggregates, re-group and unite in well-formed chains fairly well

aligned with the direction of the imposed field; the increase of the field enhances the straightness of the chains. Therefore, one comes to a conclusion that the field-induced chaining of the particles is the main mechanism of MPS elongation. Moreover, it is clear that the equilibrium shape of an MPS is established as a result of interplay between the magnetostatic forces which group the particles and align the chains, and the steric forces which maintain the MNPs confinement in the intra-membrane space.

At a first sight, in the membrane of a larger polymersome (lower curvature), the nanoparticles are more free to align, and, thus, in such an object the conditions for the field-induced elongation are more favorable. However, as the simulation results presented in Figure 4 show, our modelling points out the opposite tendency. To explain this, in below we present qualitative considerations which, if not being exhaustive, should be an important part of the effect.

In our view, the found dependence is a manifestation of the anisotropic character of the dipole-dipole interaction in a confined geometry of a spherical layer. As known, the dipolar particles with parallel orientation of their magnetic moments attract each other if positioned in a "head-to-tail" pattern and experience mutual repulsion in "side-by-side" configuration. More broadly, the particles repel each other if their center-to-center vector is inclined to the field under the angles Δ*ψ* ≈ (90 ± 35)◦ and are mutually attracted in all the other positions.

When such particles are enclosed in a spherical layer, which is the case of an MPS subjected to a strong field, the situations in the "equatorial" and "polar" zones of the membrane are qualitatively different. (For convenience, we liken an MPS to a globe whose poles are at the points where the direction of external field is parallel to the surface normal.) Indeed, as long as the MPS is sufficiently large *D d*p, those MNPs that inhabit the equatorial zone, are in quite favorable situation for building meridional chains of the "head-to-tail" structure . Meanwhile, for those which at zero field occupied the near-polar zone, the situation strongly depends on the curvature of the layer.

At high curvature (small MPS), virtually all feasible center-to-center vectors fall outside the Δ*ψ* interval. This implies that the formerly "polar" particles are attracted by the ends of the meridional chains, drift in their directions, and, thus, deplete the polar zone. At low curvature (large MPS), for a notable number of particles in the near-polar zone have their center-to-center vectors inside the Δ*ψ* interval and, thus, experience mutual repulsion. Instead of joining long meridional chains, those MNPs would be repelled by their ends and would stably dwell in the polar zone as single entities or very short weakly linked aggregates. An illustration for this conclusion is given by snapshots in Figure 6.

Evidently, those non-chained particles do not contribute to the stretching effect and by that reduce to some extent the number and/or length of the formed chains. Moreover, the repulsion exerted by those "polar" particles on the nearly-situated chains should extend the MPS in the direction transverse to the field direction and, albeit weakly, but also contribute to diminution of the field-induced stretching of larger MPSs. In Appendix A we propose a "toy" model that justifies the effect of this chain-length reduction on the size-dependent magnetic deformation of MPSs.

**Figure 6.** Top views of the MPSs with sizes *q* = 6 (**a**) and 14 (**b**) magnetized by field *ξ* = 10; to improve vision, the outer shell is not shown; these top views correspond to the side views given in Figure 3c,f.

Another effect that is worth of discussion is the non-monotonic field dependence of the inner volume of small polymersomes, see Figure 5. In general, as it is could be shown analytically, when a sphere is deformed to spheroid under condition of constancy of its lateral area, the "volume defect" is always negative. Therefore, the found negative volume change, see Figure 5, confirms the assumption of high surface tension of the membrane shells. Looking to details, we surmise that the initial stretching of the MPS in the low field range (*ξ* = 0 to ≈ 3), see Figure 3 (**a**), where the chains are very curvilinear, is due to orientation of some chain fragments without breaking their overall structure arrangement.

In small polymersomes, on further growth of the field (*ξ* ≈ 4 to ≈ 8), the structure rearrangement requires numerous breaks of the formerly existing chains. When the extensive chain rupture takes place, the particle structure becomes more loose, and this transformation, although not completely (see curve for *q* = 6 in Figure 5), but to some extent reduces the volume defect. As soon as the chain fragments unite in a new conformations which are plausible for making quasi-meridional lines, the diminution of *V* resumes. Finally, the field-induced restructuring results in building up inside the membrane a barrel-like superstructure (we remind of the afore-mentioned effect of depleting the polar zones) that makes a small MPS to efficiently stretch along the field direction, see Figure 3c. In large polymersomes, the already existing chains have much more freedom for their conformational changes and perform them with almost no breaks. Therefore the initially formed aggregates gradually reorganize in long-chain patterns; because of that, in such an MPS compression of the inner cavity goes in monotonic way, see plots for *q* = 12 and *q* = 14 in Figure 5 and Figure 3d–f.

#### **5. Conclusions**

The size effect, i.e., the dependence of structure and deformation of a magnetic polymersome on the applied field strength is studied with the aid of a coarse-grained model. It is shown that in the realistic size range, the field-induced strain—the polymersomes elongation along the applied field—is the higher the smaller the objects. This tendency is related to the arrangement and size of the nanoparticle chains which form and align in the polymersome membrane under magnetization. The field-induced change of the polymersome inner cavity volume is negative, and for small polymersomes its field dependence turns out to be non-monotonic.

The presented results infer that in terms of specific effects—the field-induced strain as well as the volume defect—smaller polymersomes turn out to be more efficient than the larger ones. From application view point, the volume defect is important, in the first place, for drug delivery. The smallness of the obtained value indicates that polymersomes of the considered kind hardly have wide prospects. On the other hand, the 20–25% strain effect might fit in a fairly good way the requirements for cell membrane stimulations which are realized either via turning an already stretched polymersome by a rotating field or by inducing its periodic elongation in the given direction with the aid of alternating field. Certainly, the obtained results on deformational properties of magnetic polymersomes, apart from static cases, might also provide reliable estimates for sufficiently low-frequency magnetodynamic regimes.

Besides the above-presented particular points, it is worth noting that the calculation model that we use, may be easily modified and/or extended in many ways that is an advantage if one would need to describe a magnetic polymersome in more detail.

**Author Contributions:** Conceptualization, A.R. and Y.R.; data curation, A.R.; formal analysis, A.R.; funding acquisition, A.R. and Y.R.; investigation A.R. and Y.R.; methodology A.R. and Y.R.; project administration, Y.R.; resources (computing resources), ICMM UB RAS; software, A.R.; supervision, Y.R.; visualization, A.R.; writing–original draft preparation, A.R. and Y.R.

**Funding:** The research was funded by Russian Foundation for Basic Research under grant #17-42-590504.

**Acknowledgments:** The work was performed using *Triton* supercomputer of ICMM UB RAS. Authors are indebted to Olivier Sandre for valuable discussions.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **Appendix A**

Consider an assembly of identical single-domain spherical particles coupled with each other via a sufficiently strong dipolar potential. Under an imposed external field, the basic state (lowest energy) configuration of such a system is a perfectly straight line parallel to the field direction. Evidently, any distortion of this contour enhances the energy of the chain and generates the forces striving to recover the basic state. If the chain is confined, these forces are exerted on the boundaries/walls which restrict its conformational freedom. This is the case of a magnetized MPS: in a strong external field the MNPs align their magnetic moments with the field and aggregate in chains but, being inside the membrane, those chains come out arc-shaped with the curvature equal to that of the membrane in the "meridional" plane, i.e., the plane that contains the field vector and passes through the MPS center. The tendency of the confined chains to straighten, imparts to the membrane an excess of surface energy, and this energy diminishes as the MPS stretches in the field direction.

In an MPS, the approximate volume of spherical layer accessible for MNPs is *V* = *πD*2*h*gap, whereas the total volume of all *N* particles is (*π*/6)*d*<sup>3</sup> <sup>p</sup>*N*. Taking into account that the intershell gap is close to the MNP diameter (*h*gap ≈ *<sup>d</sup>*p), the volume fraction of MNPs comes out as *<sup>φ</sup>* = *Nd*<sup>2</sup> p/6*D*2. We remind that the above-presented modelling is performed under condition *φ* = const.

Let us assume that the chains stretch meridionally and they are symmetrical with respect to equator of the membrane, so that the chain length is *νd*p; the maximal value of the length is *ν*<sup>0</sup> = *πD*/2*d*p, i.e., the chain makes a pole-to-pole semi-circle. The expression for energy Δ*U* for a model chain of constant curvature could be obtained from general expressions for long dipolar chains, see [21], for example, and taken in the form

$$
\Delta \mathcal{U} \approx 6 \zeta(3) \left( \nu \mu^2 / d\_p^3 \right) \left[ 1 - \cos^2 \theta \right]. \tag{A1}
$$

As the chain is considered to be long enough (say, *ν* > 10), it is described in continual limit; here *ζ*(3) is Riemann's function and *ϑ* the local angle between the tangent to the contour of the chain and the field direction; note that we count Δ*U* from the lowest energy, where cos2 *ϑ* = 1. Under assumption of constant curvature of the arc (2/*D*), the cosine function in expression (A1) could be averaged over the chain and yields

$$\cos^2 \theta = \frac{1}{2} \left[ 1 + \frac{\sin \left( \pi \nu / \upsilon\_0 \right)}{\pi \nu / \upsilon\_0} \right],\tag{A2}$$

so that substitution to (A1) gives

$$
\Delta II \approx 3\zeta(3)\frac{\nu\mu^2}{d\_p^3} \left[1 - \frac{\sin\left(\pi\nu/\nu\_0\right)}{\pi\nu/\nu\_0}\right].\tag{A3}
$$

The part of the membrane surface per one chain is Δ*S* = *πD*2*ν*/*N* = *πνd*<sup>2</sup> p/24*φ*. Then the surface energy density in question is

$$
\sigma = \Delta \mathcal{U} / \Delta \mathcal{S} = 72\zeta(3) \frac{\phi \mu^2}{d\_\mathbb{P}^5} \left[ 1 - \frac{\sin \left( \pi \nu / \nu\_0 \right)}{\pi \nu / \nu\_0} \right]. \tag{A4}$$

As seen, in expression (A4) the coefficient before the bracket is independent of the MPS structure. Had the ratio *ν*/*ν*<sup>0</sup> been the same for any of the considered MPSs, then this independence would have been inherent to the bracket as well. However, as pointed out in section 4, the larger the MPS diameter *D*, the greater number of MNPs does not take part in stretching. This means that in larger MPSs the ratio *ν*/*ν*<sup>0</sup> is lower than in smaller ones. This entails diminution of the value of the factor in brackets and, thus, the decrease of the excess of the magnetic surface energy *σ* that, in our view, is the driving mechanism of the field-induced stretching of MPSs. To illustrate this, the *ν*-dependent function of Equation (A4) is presented in Figure A1.

**Figure A1.** The factor depending on the relative chain length in Equation (A4).

#### **References**


c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Modulating the Spin Seebeck Effect in Co2FeAl Heusler Alloy for Sensor Applications**

**Marcus Vinicius Lopes 1,2, Edycleyson Carlos de Souza 1, João Gustavo Santos 1, João Medeiros de Araujo 1, Lessandro Lima 1, Alexandre Barbosa de Oliveira 1, Felipe Bohn <sup>1</sup> and Marcio Assolin Correa 1,\***

<sup>1</sup> Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil

<sup>2</sup> Instituto Federal de Educação Ciência e Tecnologia do Ceará, Quixadá 63902-580, CE, Brazil

**\*** Correspondence: marciocorrea@fisica.ufrn.br

Received: 06 February 2020; Accepted: 29 February 2020 ; Published: 3 March 2020

**Abstract:** The thermoelectric conversion technique has been explored in a broad range of heat-flow sensors. In this context, the Spin Seebeck Effect emerges as an attractive candidate for biosensor applications, not only for the sensibility improvement but also for the power-saving electronic devices development. Here, we investigate the Longitudinal Spin Seebeck Effect in films with a Co2FeAl/W bilayer structure grown onto GaAs (100) substrate, systems having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. From numerical calculations, we address the magnetic behavior and thermoelectric response of the films. By comparing experiment and theory, we explore the possibility of modulating a thermoelectric effect by magnetic anisotropy. We show that the thermoelectric voltage curves may be modulated by the association of magnetic anisotropy induction and experimental parameters employed in the LSSE experiment.

**Keywords:** spintronics; CFA; thermoelectric effect; spin seebeck effect

#### **1. Introduction**

Presently, the thermoelectric effects, such as the Seebeck effect, are widely explored in the direct conversion of heat-flow in voltage signal [1–3]. However, usually, these systems present a high heat resistance, leading to limitations in biosensor applications [4]. On the other hand, thermoelectric effects based on spin dynamics have received increasing attention in recent past, not just to the great technological potential in power-saving electronic devices [5–9], but also for photodetectors [10,11], diode [12], and temperature sensor [13].

As a result, numerous studies have been performed in a broad range of nanostructures, promoting significant advances in the performance of such effects [4,14,15].

Within this field, Anomalous Nernst (ANE) and the Longitudinal Spin Seebeck (LSSE) effects have distinguished positions, emerging as interesting phenomena for biosensors and spin caloritronics devices [16–18]. Both effects generally consist in the application of a temperature gradient ∇*T* and a magnetic field *H*- , thus generating an electric field - *E* that can be expressed as [19]

$$\mathcal{E} = -\mathcal{S}(\mathfrak{m} \times \nabla T),\tag{1}$$

where *S* = *λμ*◦*ms*, *μ*◦ is the vacuum magnetic permeability, and *ms* is the saturation magnetization of the ferromagnetic alloy, which is oriented along to the unit vector *m*ˆ . Here, *λ* is a fundamental coefficient that is straightly related to the nature of the involved effect. Specifically, it is common to assume *λ* = *λN*, i.e., the well-known Anomalous Nernst coefficient, for a sample consisting of a single ferromagnetic metallic layer in which ANE is the unique effect in the system. However, for a bilayer structure composed by a ferromagnetic metallic layer capped by a non-magnetic metal in turn, an effective *λeff* coefficient shall be taken into consideration. Remarkably, for this latter, both ANE and LSSE contribute to the generation of the electric field - *E*.

In a typical LSSE experiment, the electric field associated with the effect is measured through the Inverse Spin Hall Effect (ISHE). Nevertheless, we may find in the literature several studies uncovering distinct ways to overcome this experimental adversity, split the contributions of the LSSE and ANE effects [5,20], or improve the thermoelectric conversion efficiency. For instance, very recently, Holanda and colleagues [20] proposed a Si/NiFe/NiO/Pt heterostructure to detect the ANE and LSSE thermoelectric voltages simultaneously, thus allowing the comparison of the results with the values acquired for a single Si/NiFe film. Following a distinct approach, aiming to obtain optimized responses, one may focus on bilayer structures and play with the choice of the ferromagnetic material and the metallic capping layer, both having deep impacts on the thermoelectric conversion efficiency. In this case, it is well known that capping-layer materials with high spin-orbit coupling are the main elected for investigations of spintronics effects [21]. This fact is justified given that they enable the interconversion between charge current and spin current [5]. Nonetheless, the ferromagnetic material has a fundamental role in this interconversion, being responsible for the spin current injection. Therefore, properties as magnetic permeability, magnetic anisotropy, damping parameter, and capability to generate spin-polarized current are key features that must be tuned to improve the thermoelectric effects in bilayer structures [22–24].

Within this spirit, Heusler alloys appear as attractive candidates for thermoelectric applications [25–27], given that in theory, they can present energy gap around the Fermi level, making possible the achievement of 100% spin-polarized currents [28]. Among the numerous Heusler alloys, Co2FeAl (CFA) is a conspicuous material due to its high magnetic permeability and controllable magnetic anisotropies [29,30], features often found in CFA films. Theoretically, this alloy has been widely studied through first-principle calculations [31–34]. Experimentally, the magnetic properties in CFA films are strongly dependent of parameters used during the production process, such as temperature deposition and annealing after the deposition [35], as well as on the employed substrate. Therefore, the control of the features of the CFA alloy as magnetic anisotropy [35–38], associated with the integration between electrical and magnetic properties, may open new roads to explore this material and to modulate its thermoelectric response.

In this work, we explore the possibility of modulating a thermoelectric effect by magnetic anisotropy. Specifically, we investigate the Longitudinal Spin Seebeck Effect in films with a CFA/W bilayer structure grown onto GaAs (100) substrate, systems with induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. From numerical calculations, we address the magnetic behavior and thermoelectric response of the films. By comparing experiment and theory, we show that the thermoelectric voltage curves may be controlled by the association of magnetic anisotropy induction and experimental parameters employed in the LSSE experiment. These results enable us to modulate the thermoelectric response as a function of the applied magnetic field, opening new possibilities for sensor application.

#### **2. Materials and Methods**

Here, we perform experiments in a set of films with a CFA/W bilayer structure, in which the CFA layer in each sample was grown at a given temperature. Specifically, CFA layers were prepared at the selected temperatures of 300, 573, 673 and 773 K [35]. The thickness of the ferromagnetic and metallic non-magnetic layers in the bilayer structure is 53 and 2 nm, respectively. The films were deposited by magnetron sputtering onto GaAs (100) substrates with dimensions of 3 × 6 mm2, previously annealed at 923 K, and covered by a 2-nm-thick W buffer layer. The deposition process was carried out with the following parameters: base pressure of 7.8 × <sup>10</sup>−<sup>8</sup> Torr, Ar pressure during disposition of 3 × <sup>10</sup>−<sup>3</sup> Torr with flow of 14 sccm, current of 200 mA set in the DC source for the CFA layer deposition, and 140 mA set in similar source for the grown of the W layer. Using these parameters, we reach deposition rates were 0.6 nm/s and 0.53 nm/s for the CFA and W, respectively. During the whole production process

for all samples, a constant 1.0 kOe magnetic field was applied perpendicularly to the main axis of the substrate.

The structural characterization of the samples was obtained by x-ray diffraction. The experiments were performed using CuK*α* radiation. While low-angle x-ray diffraction was employed to determine the deposition rate and calibrate the film thickness, high-angle x-ray diffraction measurements were used to verify the structural character of the samples.

Quasi-static magnetic characterization was obtained using a LakeShore Model 7404 Vibrating Sample Magnetometer (VSM). Specifically, the in-plane magnetic properties were verified through magnetization curves, acquired with a maximum magnetic field value of ±500 Oe. The set up allowed us the rotation of the sample. Thus, to verify the magnetic anisotropy induced in the films, we measured magnetization curves for the different *ϕ* values, the angle between the magnetic field and the shortest axis of the samples.

Ferromagnetic resonance (FMR) measurements were carried out with a Bruker EPR system operating at 9.838 GHz (TE011 mode). In this case, the sample was placed in the center of a cylindrical cavity, in which the microwave magnetic field is maximized, and the electrical field is minimized. The set up also allowed us the rotation of the sample and experiments were performed at different *ϕ* values. The magnetic field, applied in the film plane, varied from 2.0 up to 3.5 kOe. It was modulated in the amplitude of 0.1 Oe at 100 kHz. Due to the modulation, the FMR power absorption curve took the shape of an absorption derivative, which was fitted by a Lorentzian-derivative function to extract resonance field and linewidth.

At last, we used a home-made Longitudinal Spin Seebeck Effect system (LSSE) to perform thermoelectric voltage measurements. Further information on the experimental system can be found in Ref. [39]. The system consists of a heat source (Peltier modulus) and a heat sink composed by a Cu block, in which the film is placed between them. The thermal conductivity was improved by the thermal paste, while the electrical contacts were made using silver paint. The system (heat sources and film) was connected to a step-motor, making possible the sample rotation and the measurement of the thermoelectric voltage at different *ϕ* values. Here, following the previous definition considered for the magnetic characterization, we kept the definition of *ϕ* as the angle between the magnetic field and the shortest axis of the sample. Figure 1 depicts a schematic representation of our bilayer structure and the LSSE experiment.

**Figure 1.** Schematic representation of our bilayer structure and the LSSE experiment. (**a**) Bilayer structure and definition of the coordinate system used in the numerical calculations. Given that *ϕ* is the angle between the magnetic field and the shortest axis of the sample, *ϕ* = 0◦ is found when *H* is along the *x* axis. (**b**) LSSE experimental setup employed for the thermoelectric voltage measurements. The system allowed us the rotation of the sample during the experiment. Notice that the configuration represented in (**b**) corresponds to *ϕ* = 90◦.

#### **3. Results and Discussion**

It is known that the structural features of films have a strong influence on their magnetic properties.

In ferromagnetic films produced onto amorphous substrates, a considerable out-of-plane anisotropy contribution is observed as the thickness is increased [40]. This behavior is related to the local stress storage in the film. On the other hand, by employing oriented substrates, we may promote a significant reduction of the local stored stress, favoring the appearance of magnetic anisotropy of magnetocrystalline nature.

This is precisely our intent in this work, in which we made use of an oriented substrate and annealing during the deposition to produce films having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy.

#### *3.1. Structural Results*

Regarding the structural properties, Figure 2 shows the high-angle XRD results obtained for our set of films with CFA/W bilayer structure grown onto GaAs (100) substrate. First, the diffractograms disclose the (002) planes of the GaAs substrate [41–43] , assigned by the well-defined and high-intensity peak located at 2*θ* ≈ 31.9◦. Second, no evidence of the W layer is verified here, as expected, a fact that is associated with the reduced thickness of this layer. Going beyond, with respect to the CFA layer, the results clearly reveal a peak located at 2*θ* ≈ 44.73◦ that is a fingerprint of the (022) texture of the CFA alloy, and peaks at 2*θ* ≈ 31.55◦ and 59.15◦, which are signatures of the CFA (002) texture. All these CFA peaks are identified from the pattern found in ICDD 01-0715670. Similar structural results have been previously reported in the literature for CFA films grown onto distinct oriented substrates [35,37]. In particular, the peaks observed here enable us to infer the polycrystalline character of the CFA alloy, with an A2 structure, suggesting disorder of the Co, Fe, and Al sites [38,44,45].

**Figure 2.** (**a**) High-angle x-ray diffraction results for the Co2FeAl/W bilayers grown onto GaAs (100) substrate. (**b**) Detailed view of the curves, in which the CFA(002) peak can be visualized. The CFA pattern is obtained from ICDD 01-0715670. Notice the polycrystalline character of the CFA alloy in all samples of the set.

#### *3.2. Magnetic Properties*

With respect to the magnetic properties, Figure 3 presents the magnetization curves measured for the CFA/W bilayer films at selected *ϕ* values. The angular dependence of the magnetization curves confirms the induction of magnetic anisotropy in all films. Notice the remarkable differences among the curves obtained at different *ϕ* values, especially for the samples produced with the temperatures of 573 K and 673 K. For all studied bilayers, the curve acquired at *ϕ* = 0◦ suggests the existence of an intermediate magnetic axis along this direction. Furthermore, the results reveal an easy magnetization axis along the direction of *ϕ* = 90◦, as well as a hard axis close to *ϕ* = 45◦ (This latter is clearly observed through the FMR measurements, as we will see in the following). At last, no evidence of an out-of-plane anisotropy contribution is verified in the curves. Our results also corroborate previous studies reported in the literature, in which the CFA films were grown onto oriented substrates, such as Si, MgO, and GaAs [16,17,35]. All these features uncover the combination of induced uniaxial magnetic anisotropy and cubic magnetic anisotropy in the bilayers [46].

**Figure 3.** Normalized magnetization curves for the Co2FeAl/W bilayers grown onto GaAs (100) substrate, in which the CFA layer was deposited at the temperatures of (**a**) 300 K, (**b**) 573 K, (**c**) 673 K, and (**d**) 773 K. Here we present just the curves measured for *ϕ* = 0◦, 30◦, 60◦ and 90◦. All the samples of the set present uniaxial magnetic anisotropy combined with cubic magnetic anisotropy, although these features are more evident for the ones produced at the temperatures of 573 K and 673 K.

#### *3.3. Modeling a System with Uniaxial Magnetic Anisotropy Combined with Cubic Magnetic Anisotropy*

Given all the state above, we took into account a modified Stoner–Wohlfarth model [39,47] to mimic our Co2FeAl/W bilayers having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. For the numerical calculations, we considered a system with 50 non-interacting magnetic domains, in which the free energy density for each domain is described by

$$\xi\_i = -\vec{m}\_i \cdot \vec{H} + 4\pi m\_{si}^2 (\hat{m}\_i \cdot \hat{n})^2 - k\_{ui} (\hat{m}\_i \cdot \hat{u}\_{ki})^2 - \frac{1}{4} (\xi\_{c1i} + \xi\_{c2i}).\tag{2}$$

Here, the first term is associated with the Zeeman interaction, the second one describes the shape anisotropy, the third tells on the uniaxial magnetic anisotropy, and the last term is related with the magnetocrystalline anisotropy. Furthermore, the considered quantities are defined as the following: *m*ˆ*<sup>i</sup>* is the unit vector of the magnetization, *msi* is the saturation magnetization, *H* is the magnetic field, *<sup>n</sup>*<sup>ˆ</sup> the unit vector normal to the film plane (*θ<sup>n</sup>* = <sup>0</sup>◦), and *kui* = *msihki* <sup>2</sup> , where *hki* is the anisotropy field related to the uniaxial magnetic anisotropy oriented along *u*ˆ*ki* for each domain. At last, for the cubic magnetic anisotropy energy density,

$$\mathbf{a}\_{c1i} = k\_{c1i} \left( a\_{1i}^2 a\_{2i}^2 + a\_{1i}^2 a\_{3i}^2 + a\_{2i}^2 a\_{3i}^2 \right),\tag{3}$$

and

$$
\zeta\_{c2}^x = k\_{c2} \left( \alpha\_{1i}^2 \alpha\_{2i}^2 \alpha\_{3i}^2 \right) \tag{4}
$$

where *α*1*i*, *α*2*i*, and *α*3*<sup>i</sup>* are the components of the unit vector of the magnetization, *α*1*<sup>i</sup>* = cos *ϕmi* sin *θmi*, *α*2*<sup>i</sup>* = sin *ϕmi* sin *θmi* and *α*3*<sup>i</sup>* = cos *θmi*.

For the case in which the uniaxial anisotropy lies in the film plane and the magnetic field is also applied plane, Equation (2) is drastically simplified and can be rewritten as

$$\xi\_i^x = -m\_{si} \, H \, \cos(\varphi - \varphi\_{mi}) - k\_{ui} \, \sin(\varphi\_{li} - \varphi\_{mi})^2 - \frac{1}{4} k\_{c1i} (\cos(\varphi\_{mi})^2 \sin(\varphi\_{mi})^2). \tag{5}$$

From the minimization of Equation (5) for a given magnetic field *H*- , we are able to find the equilibrium angle of the magnetization of the *i* − *th* domain. This angle is a result of the competition between the contributions of the magnetic field and the magnetic anisotropies in the system. To account the whole magnetic behavior, in turn, we also need to consider the magnetic anisotropy dispersion of the system. Further information on the numerical calculations will be provided in the next sections, combining theory and experiment.

#### *3.4. Magnetic Response at Saturated State*

Moving forward, evidence of the combination of anisotropies was also investigated through ferromagnetic resonance experiments. In particular, angular FMR measurements enable us to confirm the observed anisotropies, as well as to infer their relative contribution to the whole magnetic behavior. From the FMR absorption derivative signal obtained in the experiments for our samples, not shown here, we determined the linewidth Δ*H* and resonance field *Hr*, this latter presented in Figure 4.

**Figure 4.** Angular dependence of the resonance field *Hr* obtained from the FMR absorption derivative signal measured for the Co2FeAl/W bilayers in which the CFA layer was grown at (**a**) 300 K, (**b**) 573 K, (**c**) 673 K, and (**d**) 773 K. The red lines are fittings obtained with Equations (6) and (5).

From a general point of view, all bilayer films share the very same angular dependence of the resonance field *Hr*. In particular, the curves are characterized by four peaks with similar amplitude and four valleys, which are split in two groups according to the amplitude values. This behavior is a clear signature of the uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. Furthermore, as expected, we confirm here that the samples produced with the temperatures of 573 K and 673 K do have more intense magnetic anisotropies, which are depicted by the larger amplitude variations of *Hr*.

In order to obtain further information of our system and estimate anisotropy constants, we considered the well-known angular resonance frequency *ω<sup>r</sup>* and linewidth of the resonance absorption Δ*ω*, which can be written as [24,48,49]

$$
\omega\_r = \frac{\gamma}{m\_\varepsilon \sin \theta\_m} \sqrt{1 + a^2} \sqrt{\xi\_{\theta\theta}^\* \xi\_{\varphi\varphi} - \xi\_{\theta\varphi}^2} \tag{6}
$$

and

$$
\Delta\omega = \frac{\alpha\gamma}{m\_s} \left(\xi\_{\theta\theta} + \frac{\xi\_{\phi\varphi}}{\sin^2\theta\_m}\right). \tag{7}
$$

Here, *<sup>γ</sup>* = |*γG*|/(<sup>1</sup> + *<sup>α</sup>*2), in which *<sup>γ</sup><sup>G</sup>* is the gyromagnetic ratio and *<sup>α</sup>* the damping parameter; and *ξθθ*, *ξϕϕ*, *ξϕθ*, and *ξθϕ* are the second derivatives of the magnetic free energy density, defined by the magnetization vector oriented by the angles *θ<sup>m</sup>* and *ϕm*, at a given magnetic field.

Then, we performed fittings of the angular dependence of the resonance field *Hr* using Equation (6) and taking into account the free energy density for a system with uniaxial magnetic anisotropy combined with cubic magnetic anisotropy, i.e., Equation (5). The magnetic parameters *ms*, *ku* and *kc*<sup>1</sup> obtained from the fits of the FMR data are summarized in Table 1.


**Table 1.** Parameters obtained from the fits of the experimental FMR data for our set of Co2FeAl/W bilayers. For the fits, we assumed *<sup>α</sup>* <sup>≈</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> and *<sup>γ</sup>* <sup>=</sup> 2.8 MH/Oe.

#### *3.5. Experimental Results for Thermoelectric Effect*

Based on the experimental results obtained in the structural and magnetic characterizations so far, from now, we focus our attention on the thermoelectric voltage measurements performed in the Co2FeAl/W bilayers in which the CFA layer was deposited at the temperatures of 573 K and 673 K.

Figure 5 shows the experimental results of the magnetic response and the thermoelectric voltage for both samples. Specifically, Figure 5a,b presents the thermoelectric voltage as a function of the magnetic field, at selected *ϕ* values and setting Δ*T* = 27 K. Notice the quite-interesting evolution in the shape of the curves as the magnitude and orientation of the field are altered. The one measured at *ϕ* = 0◦ leads to a field configuration in which the thermoelectric voltage has a shape similar to that presented in the magnetization characterization, as we can clearly confirm from the plots shown in Figure 5c,d. However, with the increase of the *ϕ*, we verify a decrease of the thermoelectric voltage at saturation, leading to the suppression of the signal at *ϕ* = 90◦, as expected. It is worth remarking that the overall thermoelectric voltage response is a result of the combination of effects associated with magnetic anisotropies in the samples and the thermoelectric voltage measurement configuration employed in the experiment [39].

Figure 5e,f shows *V* behavior as a function of *ϕ*, at *H* = +500 Oe, for selected Δ*T* values. At this field value, our system is magnetically saturated, in a sense that the magnetization follows the orientation of the magnetic field. As expected, the curves draw a clear dependence of *V* with *ϕ*, shown by a well-defined cosine shape. Furthermore, although the angular dependence is kept constant, the amplitude of the curves is altered with Δ*T*. All these features are in concordance with our theoretical predictions, discussed in the next sections.

#### *3.6. Theoretical Approach for Thermoelectric Effect*

As aforementioned, for ANE and LSSE effects, the application of a temperature gradient ∇*T* and a magnetic field *H* generates an electric field - *E* given by Equation (1). Based on our experimental findings, for our theoretical approach, we considered a typical experiment in a film, in which the temperature gradient is normal to the film plane, while the magnetization lies in the plane, as depicted in Figure 1a.

The corresponding thermoelectric voltage, detected by electrical contacts at the ends of the main axis of the film, is thus given by

$$V = -\int\_0^L \mathcal{E} \cdot d\mathcal{I},\tag{8}$$

where *L* is the distance between the electrical contacts and *dl* = *dl*ˆ*j* in our case.

Then, using Equations (1) and (8), we obtain

$$V = \lambda \mu\_\diamond L \Delta T\_f m\_s \cos q\_m. \tag{9}$$

**Figure 5.** Experimental thermoelectric effect results. Thermoelectric voltage as a function of the magnetic field, at selected *ϕ* values and setting Δ*T* = 27 K, for the (**a**) CFA/W bilayers in which the CFA layer was grown at (**a**) 573 K and (**b**) 673 K. (**c**,**d**) Comparison of the shape of normalized magnetization and thermoelectric voltage curves acquired at *ϕ* = 0◦, with Δ*T* = 27 K, for these samples. (**e**,**f**) Angular dependence of the thermoelectric voltage at *H* = +500 Oe for distinct Δ*T* values for the very same samples.

In this case, Δ*Tf* is the temperature variation across the bilayer, which is related with temperature variation Δ*T* measured experimentally across the sample [19,39],

$$
\Delta T\_f = \frac{t\_f K\_{sub}}{t\_{sub} K\_f} \Delta T\_\prime \tag{10}
$$

where *Ksub* and *tsub* are the thermal conductivity and thickness of the substrate, while *Kf* and *tf* are the respective quantities for the CFA alloy. Here, we assumed *Ksub* = 55 W/Km and *tsub* = 0.7 mm, while *Kf* = 129 W/Km and *tf* = 55 nm for the CFA layer.

Notice that the *V* response given by Equation (9) is straightly dependent on the magnetic state of the sample through *ϕm*, which in turn is a result of the minimization process of free energy density of the system. This latter brings information on the magnetic field and the magnetic anisotropies in the system, given by Equation (5) in our case.

#### *3.7. Numerical Calculations and Comparison between Theory and Experiment*

We performed numerical calculations for two magnetic systems, distinct just with respect to the magnetic anisotropy dispersion. Remember that our system has a combination of induced uniaxial magnetic anisotropy and cubic magnetic anisotropy. Then, first, we calculated the magnetic and thermoelectric properties for a system without magnetic anisotropy dispersion, with *msi* = *ms*<sup>1</sup> = ... =

*ms*<sup>50</sup> = *ms* = 1330 G, *kui* = *ku*<sup>1</sup> = ... = *ku*<sup>50</sup> = *ku*, with *hk* = 220 Oe and *ϕki* = *ϕk*<sup>1</sup> = ... = *ϕk*<sup>50</sup> = 0◦ (*x* direction in Figure 1a), as well as *kc*<sup>1</sup>*<sup>i</sup>* = *kc*<sup>11</sup> = ... = *kc*<sup>150</sup> = 2.8 *ku*. In a second moment, to mimic a magnetic system with a given uniaxial anisotropy dispersion, we considered the very same parameters, but with the fundamental difference of having *ϕki* dispersed linearly around 0◦, with dispersion range of Δ*ϕ<sup>k</sup>* = 10◦.

Figure 6 shows the numerical calculations of the magnetic response and the thermoelectric voltage for systems having induced uniaxial magnetic anisotropy and cubic magnetic anisotropy, without and with uniaxial anisotropy dispersion.

**Figure 6.** Numerical calculations of magnetic properties and thermoelectric voltage. (**a**) Normalized magnetization and (**b**) thermoelectric voltage curves, at selected *ϕ* values, for a system having induced uniaxial magnetic anisotropy and cubic magnetic anisotropy, without anisotropy dispersion. The calculations were performed with *msi* = *ms*<sup>1</sup> = ... = *ms*<sup>50</sup> = *ms* = 1330 G, *kui* = *ku*<sup>1</sup> = ... = *ku*<sup>50</sup> = *ku*, with *hk* = 220 Oe and *ϕki* = *ϕk*<sup>1</sup> = ... = *ϕk*<sup>50</sup> = 0◦, as well as *kc*<sup>1</sup>*<sup>i</sup>* = *kc*<sup>11</sup> = ... = *kc*<sup>150</sup> = 2.8 *ku*. Furthermore, we considered Δ*T* = 27 K. In (**b**), the inset illustrates a simple view of magnetic domains in the system without anisotropy dispersion. (**c**,**d**) Similar plots for the the same system having uniaxial anisotropy dispersion, in which *ϕki* dispersed linearly around 0◦, with dispersion range of Δ*ϕ<sup>k</sup>* = 10◦. In (**d**), the inset also brings the simple view of the magnetic domains in the system without anisotropy dispersion. (**e**) Schematic representation of our bilayer structure in the experiment, in which we depict *ϕ<sup>m</sup>* that is inserted in Equation (9) for the calculations. (**f**) Angular dependence of the thermoelectric voltage at Δ*T* = 27 K for distinct field values for the system with anisotropy dispersion. The curves are normalized in order to make easier the direct comparison between results.

For the system without anisotropy dispersion (Figure 6a,b), we verify that the magnetization curve calculated for *ϕ* = 0◦ reflects the behavior of an intermediate magnetic axis, a result of the competition between the uniaxial and cubic magnetic anisotropies. Furthermore, as expected, the easy and hard magnetization axes are aligned to *ϕ* = 90◦ and 45◦, respectively [46]. This behavior is in

concordance with the experimental results previously discussed in Sections 3.2 and 3.4. Regarding the thermoelectric calculations, the results obtained for the *ϕ* = 0◦ leads to a curve with a similar shape to that one obtained in the magnetization calculation. With the increase of *ϕ*, we confirm the decrease in the thermoelectric voltage at saturation, reaching zero for *ϕ* = 90◦. These features are in perfect agreement with our discussion presented in Section 3.5.

When the magnetic anisotropy dispersion is inserted in the system (Figure 6c,d), the overall effective magnetic anisotropy is not strongly altered. As a consequence, the shapes of the curves in the magnetization response and thermoelectric voltage are globally kept. However, remarkably, the anisotropy dispersion refines the model, introducing details of the magnetic behavior that are fundamental to the description of real systems. Specifically, the inclusion of the anisotropy dispersion leads to smoother magnetization variations and is responsible for modifications in the magnetic permeability, coercive field and remanent magnetization. All these changes yield deep impacts in the thermoelectric voltage response.

As aforementioned, the thermoelectric voltage response is a combination of effects associated with magnetic anisotropies in the samples and the thermoelectric voltage measurement configuration employed in the experiment. In some sense, it is reasonable its dependence with *ϕ* (Figure 6e). Therefore, we also perform numerical calculations of the *V* behavior as a function of *ϕ* for the system with anisotropy dispersion, at distinct *H* values, shown in Figure 6f. As expected, the curves of the thermoelectric voltage are strongly dependent on both the *ϕ* angle and the amplitude of the magnetic field *H*. The equilibrium angle of magnetization, *ϕ<sup>m</sup>* obtained from the minimization of Equation (5), is the result of the competition between the energy density contributions of magnetic induced uniaxial and cubic anisotropies with the Zeeman energy density. For field values high enough to saturate the system magnetically, the angular dependence of *V* is in perfect concordance with Equation (9), given by a cosine of *ϕ*, given *ϕ<sup>m</sup>* = *ϕ*. However, for unsaturated states, the cosine behavior is lost, bringing information on the magnetic anisotropy and anisotropy field.

It is interesting to notice that the previous calculations have qualitatively described the main features of the magnetic behavior and thermoelectric voltage response in a system having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy.

However, the most striking findings here are shown in Figure 7. Here we directly compare theory and experiment and uncover the evolution of the magnetic response and thermoelectric voltage with the amplitude and direction of the magnetic field. Furthermore, we corroborate the major role of the magnetic anisotropy dispersion to the description of the magnetic behavior and thermoelectric effect.

Notice the remarkable agreement between experiment and theory for the different conditions of measurement. Specifically, we disclose experimental results for the CFA/W bilayer in which the CFA layer was grown at 573 K. For the numerical calculations, we considered a system with uniaxial anisotropy dispersion, with *msi* = *ms*<sup>1</sup> = ... = *ms*<sup>50</sup> = *ms* = 1330 G, *kui* = *ku*<sup>1</sup> = ... = *ku*<sup>50</sup> = *ku*, where *hk* = 220 Oe and *ϕki* is dispersed linearly around 0◦, with dispersion range of Δ*ϕ<sup>k</sup>* = 10◦, as well as *kc*<sup>1</sup>*<sup>i</sup>* = *kc*<sup>11</sup> = ... = *kc*<sup>150</sup> = 2.8 *ku*. Remember that these magnetic parameters are the very same used for the previous calculations shown in Figure 6, all of them obtained from the magnetic characterization discussed in Sections 3.2 and 3.4. Therefore, from the comparison, we confirm the validity of our theoretical approach, including the description of our system given by Equation (5), as well as we corroborate magnetic parameters as the anisotropy constants and the saturation magnetization, presented in Table 1.

Hence, we were able to describe through the numerical calculations all the main features of the magnetic behavior and thermoelectrical effect in a magnetic system having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. From a general point of view, we highlight that this theoretical approach may be modified to describe any magnetic system if considered the appropriate free energy density. Furthermore, here, we showed the possibility of modulating the LSSE thermoelectric effect by the magnetic anisotropy induction. Specifically, the thermoelectric

**Figure 7.** Comparison between theory and experiment: Normalized magnetization curves, at (**a**) *ϕ* = 0◦ and (**b**) 30◦, for the CFA/W bilayer in which the CFA layer was grown at 573 K. (**c**,**d**) Corresponding normalized thermoelectric voltage curves. (**e**) Schematic representation of our bilayer structure in the experiment, in which we depict *ϕ<sup>m</sup>* that is inserted in Equation (9) for the calculations. (**f**) Normalized curves of the angular dependence of the thermoelectric voltage, at Δ*T* = 27 K, for *H* = ±500 Oe. In particular, the calculations here were performed system with uniaxial anisotropy dispersion, with *msi* = *ms*<sup>1</sup> = ... = *ms*<sup>50</sup> = *ms* = 1330 G, *kui* = *ku*<sup>1</sup> = ... = *ku*<sup>50</sup> = *ku*, where *hk* = 220 Oe and *ϕki* is dispersed linearly around 0◦, with dispersion range of Δ*ϕ<sup>k</sup>* = 10◦, as well as *kc*<sup>1</sup>*<sup>i</sup>* = *kc*<sup>11</sup> = ... = *kc*<sup>150</sup> = 2.8 *ku*.

effect, measured through LSSE, emerged as a powerful tool to investigate fundamental parameters of a magnetic system, such as anisotropy configuration and anisotropy dispersion.

#### **4. Conclusions**

In conclusion, we investigated the Longitudinal Spin Seebeck Effect in films with a CFA/W bilayer structure grown onto GaAs (100) substrate. We verified that the magnetic properties of the CFA films are strongly dependent of parameters used during the production process, such as temperature deposition and annealing after the deposition. By setting optimal conditions, we manufactured systems having induced uniaxial magnetic anisotropy combined with cubic magnetic anisotropy. We observed clear dependence of the thermoelectric voltage curves with the magnetic anisotropy and experimental parameters employed in the LSSE experiment. By comparing experiment and theory, we confirmed

the possibility of modulating a thermoelectric effect by magnetic anisotropy in Co2FeAl Heusler alloy. Our results raise important features, contributing to the integration between electrical and magnetic properties that may promote improvements of the thermoelectric response in such nanostructures. These results enabled us to modulate the thermoelectric response as a function of the external magnetic field, an essential feature for sensor applications.

**Author Contributions:** M.V.L. and M.A.C. designed the experiments and conceived this study. M.V.L., E.C.d.S. and J.G.S. fabricated the samples. M.V.L. and E.C.d.S. performed the experimental measurements under supervision of A.B.d.O. and M.A.C., M.A.C., J.M.d.A., F.B. and L.L. performed the theoretical approach. The manuscript was written by M.A.C., M.V.L. and F.B. All authors have given approval for the final version of the manuscript.

**Funding:** This research was funded by CNPq: 407385/2018-5.

**Acknowledgments:** The authors acknowledge financial support from the Brazilian agencies CNPq and CAPES.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **The Performance of the Magneto-Impedance E**ff**ect for the Detection of Superparamagnetic Particles**

#### **Alfredo García-Arribas 1,2**


Received: 4 March 2020; Accepted: 29 March 2020; Published: 31 March 2020

**Abstract:** The performance of magneto-impedance sensors to detect the presence and concentration of magnetic nanoparticles is investigated, using finite element calculations to directly solve Maxwell's equations. In the case of superparamagnetic particles that are not sufficiently magnetized by an external field, it is assumed that the sensitivity of the magneto-impedance sensor to the presence of magnetic nanoparticles comes from the influence of their magnetic permeability on the sensor impedance, and not from the stray magnetic field that the particles produce. The results obtained not only justify this hypothesis, but also provide an explanation for the discrepancies found in the literature about the response of magneto-impedance sensors to the presence of magnetic nanoparticles, where some authors report an increasing magneto-impedance signal when the concentration of magnetic nanoparticles is increased, while others report a decreasing tendency. Additionally, it is demonstrated that sensors with lower magneto-impedance response display larger sensitivities to the presence of magnetic nanoparticles, indicating that the use of plain, nonmagnetic conductors as sensing materials can be beneficial, at least in the case of superparamagnetic particles insufficiently magnetized in an external magnetic field.

**Keywords:** magneto-impedance; biosensor; finite-element method

#### **1. Introduction**

Magnetic nanoparticles (MNPs) are used in numerous biomedical applications, both for diagnosis and therapy [1]. In diagnosis, they are used for magnetic resonance imaging enhancement [2] and, after adequate functionalization, for magnetic separation, concentration, and detection of specific analytes [3]. In therapy, MNPs are used in drug delivery and for hyperthermia treatments, among others [4]. The most relevant type of magnetic particles for these applications are superparamagnetic iron oxide nanoparticles, SPIONs. In order to detect the presence of MNPs and to quantify their concentration, different types of magnetic sensors have been proposed [5,6]. In particular, the magneto-impedance (MI) effect's extraordinary sensitivity to small magnetic fields has motivated the active development of MI-based biosensors which, fundamentally, detect the presence and concentration of magnetic particles [7–13].

The MI effect consists in the large variation of the electrical impedance Z of a soft magnetic conductor when subjected to an external magnetic field [14]. The phenomenon can be understood from the classical electromagnetic theory as a consequence of the skin effect's dependence on the permeability μ of the material. The skin effect—that is, the limited penetration of the alternating electromagnetic field in a conductor, is characterized by the penetration depth δ given by

$$
\delta = (\pi f \sigma \mu)^{-1/2} \tag{1}
$$

where *f* is the frequency of the field, and σ the conductivity of the material. Depending on the magnetic behavior of the sample, the external magnetic field modifies the permeability, which subsequently changes the effective electromagnetic cross section of the conductor, and produces concomitant variations in the impedance. Figure 1 shows a sketch of a typical MI curve in a planar sample with transverse anisotropy. The maximum impedance *Z*max is obtained for an applied field similar in magnitude to the anisotropy field *Hk*, when the transverse permeability reaches its maximum value μmax. The minimum impedance *Z*min is obtained when the sample is magnetically saturated and the permeability μmin is close to μ0.

**Figure 1.** Sketch of the dependence of the impedance on the applied magnetic field in a soft magnetic sample with transverse anisotropy (in-plane easy axis, perpendicular to the current flow and the applied field).

In this kind of sample, the largest sensitivity to the external magnetic field is reached in the region between *H* = 0 and at the peak where *H* = *Hk*. For instance, the sensitivity of a multilayered planar sample can reach a value of 27 kΩ/T, occurring at an applied field of μ0*H* = 200 μT (*H* = 180 A/m) and measured at 23 MHz [15].

The MI is usually quantified as the ratio of impedance change, and its maximum value (at each frequency), given by [14]

$$\text{MI}\_{\text{max}}(\%) = \frac{Z\_{\text{max}} - Z\_{\text{min}}}{Z\_{\text{min}}} \times 100 \tag{2}$$

is usually used as a figure of merit for MI sensors. In the literature, when used for detecting the presence and concentration of MNPs, it is usual to report the changes produced by the presence of nanoparticles in the complete MI curve and in particular, in its maximum value MImax. Wang and collaborators [16] have compiled the results from quite a number of works that use the MI effect to detect magnetic particles. Overall, the comparison of the results seems to be utterly inconsistent, because some authors report an increase in the MI response when increasing the concentration of particles (for example, Devkota and collaborators [17]), while others describe a decreasing tendency (for example, Yang and collaborators [18]). As the MI materials and the nature of the particles differ between studies, it becomes necessary to adopt a systematic approach to evaluate the sensitivity of the MI effect to quantify the concentration of MNPs. The present work attempts to shed light on this issue from a theoretical point of view, using a numerical procedure (finite element method) to solve Maxwell's equations and calculate the impedance in the conditions of the experiments described in the literature.

An important point is that the authors of the mentioned works compiled in [16], in which contradicting results are reported, usually do not provide a satisfactory explanation regarding the physical origin of the MI effect's sensitivity to the presence of magnetic nanoparticles. It is assumed that it is a consequence of the MI effect's extraordinary sensitivity to low magnetic fields. The fact, however, is that superparamagnetic particles do not display remanence, and therefore do not produce external magnetic fields unless magnetized by an appropriate biasing field. However, a large applied

magnetic field saturates the MI sensor and drastically reduces its sensitivity. In these circumstances, the sensitivity of the MI sensor to the presence and concentration of the particles cannot be caused by the magnetic field that they produce. Of course, this is true only if the particle system shows true superparamagnetic behavior. Agglomeration, or a large particle-size distribution, can produce a finite remanence which affects the MI signal of the sensor. The analysis of experimental data becomes difficult without a detailed particle characterization. There are some works in which the MI effect has been properly used to quantify the concentration of superparamagnetic nanoparticles in a clever configuration by measuring their stray field when magnetized by a strong external field [10], but in most of the works that claim the detection of magnetic nanoparticles using the MI effect, there is no satisfactory explanation of the involved mechanism.

In this work, we make the more realistic assumption that it is the permeability of the magnetic nanoparticles that produces the change in the MI response of the sensor. The sensing mechanism is therefore very simple: the presence of a high permeability medium in the proximity of the MI sensor modifies the distribution of the electromagnetic field associated with the alternating current flowing in the sensor. This produces a variation of the sensor's impedance, but it is not related to the intrinsic sensitivity of the MI to low magnetic fields.

As explained in the next section, this concept is implemented in this work in the calculation of the MI response. The results from the numerical solution of Maxwell's equations not only confirm that our assumption qualitatively reproduces the experimental results, but also help to explain the discrepancies reported in the literature compiled in [16], about the MI behavior when detecting magnetic nanoparticles.

#### **2. Numerical Calculation Procedure**

We aim to evaluate the response of a magneto-impedance sensor in the presence of a sample containing superparamagnetic particles. The electrical impedance of a conductor can in principle, be analytically calculated using Maxwell equations. In practice, only in very simple cases with highly symmetric geometries can a closed expression be derived, usually with the use of severe approximations. For instance, in planar samples, infinite width and length is assumed to calculate the impedance, producing an expression as [19]:

$$Z = R\_{dc} \sqrt{j} \theta \coth \sqrt{j} \theta \tag{3}$$

for a sample of thickness 2*a*, where *Rdc* is the *dc* resistance, *<sup>j</sup>* <sup>=</sup> <sup>√</sup> −1, the imaginary unit, and θ = *a* <sup>2</sup>π*f*σμ <sup>=</sup> <sup>√</sup> 2*a*/δ. Similar expressions are obtained for the case of cylindrical samples (wires).

Using this type of expression, the magneto-impedance curve can be computed by incorporating the field dependence of the permeability, using models for the magnetization process and the dynamical behavior of magnetization [20,21]. Although useful, these models systematically overestimate the magnitude of the MI effect [22,23] when compared with actual measurements, mainly because the real conditions of the experimental setup are not usually considered. In particular, the contribution of the measuring circuit to the total impedance is not usually considered in the models.

Numerical simulation using Finite Element Methods (FEM) can overcome these limitations as the elements of the measuring circuit can be easily incorporated in the model. After specifying the material properties and the adequate boundary conditions, the impedance can be calculated by numerically solving Maxwell's equations for an arbitrary geometry. If the dependence of the material properties, especially the permeability, on the magnetic field *H* are known, the complete *Z*(*H*) can be calculated. If only the performance (expressed as the MI ratio in Equation (2)) is of interest, FEM can be used to calculate the impedance for two values of permeability: μmax, corresponding to the maximum value of transverse permeability (and the impedance *Z*max) and μmin = μ0, corresponding to the saturated state (and the impedance *Z*min) as depicted in Figure 1.

The versatility of FEM makes it possible to calculate the impedance of the MI sample in a variety of environments accurately resembling the experimental conditions. For the purpose of this work, using FEM, we calculate the impedance of an MI material in the presence of a sample of magnetic nanoparticles which is modeled as a homogeneous continuum material with a given permeability μ*P*. As explained before, the permeability of the particles is the only relevant magnetic property in this approach. There is no attempt to model the individual magnetic behavior of the particles. To reproduce the conditions of the experiments found in the literature, the MI response is evaluated as a function of the concentration of the nanoparticles. If we assume that the nature of the particles is always the same, the mean permeability of the sample of magnetic nanoparticles is simply proportional to its concentration. That is, we can calculate the evolution of the MI sensor's response in the presence of a sample of magnetic nanoparticles with different concentrations by simply modifying the value of μ*P*—the permeability of the MNPs system.

For the numerical calculations, the free 2D (two-dimensional) software package FEMM [24] is used. Its implementation is restricted to low-frequency electromagnetic problems, ignoring the displacement current. Therefore, it cannot simulate propagating effects or account for the dielectric properties of the materials. However, it can accurately resolve MI problems in which the important effects are the skin effect and the magneto-inductive effect [25].

As previously discussed, the contribution from the measuring circuit to the impedance must be considered to obtain realistic results. For that reason, the simulation is performed with the MI sample inserted in a microstrip transmission line, which is a popular text fixture for measuring MI in planar strips. Figure 2a schematizes the setup of the simulated experiment. The sample of magnetic nanoparticles is placed in the shape of a drop on the MI sensor in the microstrip transmission line. The sketch Figure 2b illustrates the layout of the 2D finite element problem. The simulation domain represents the middle plane of the real problem. Due to the symmetry, only half of it needs to be simulated. The simulation domain (including the space surrounding the microstrip line) is kept small to reduce computation time. Built-in FEM open boundary conditions are imposed on the boundary to guarantee correctness of the solution.

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**Figure 2.** (**a**) Illustration of the experiment simulated by FEM: a drop containing a certain concentration of magnetic nanoparticles (MNPs) is placed on the MI material, which is inserted in a microstrip line to determine its impedance. (**b**) Layout (not at real-scale) of the two-dimensional problem solved by FEM, which corresponds to the middle plane of the setup as indicated in (**a**). Only half of the plane needs to be simulated due to symmetry.

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The drop of magnetic nanoparticles is modeled as a nonconducting, homogeneous continuum material with a given permeability μ*P*. As previously discussed, increasing values of μ*<sup>P</sup>* correspond to increasing concentrations of MNPs.

The MI sample is modeled as a homogeneous conductor (<sup>σ</sup> = 6.6 <sup>×</sup> 105 S/m) with a constant permeability μ. No definite magnetization process is assumed, and the MI is calculated as the relative ratio between the values of the impedance obtained with a high value of permeability μmax and with a value of μmin = μ0. The geometry of the MI sample is kept constant through all the simulations: 1 mm wide and 20 μm thick (the length is not relevant for the 2D problem, and the net value of the impedance is calculated for a sample 1 m long).

In the microstrip line, the ground plane is modeled from pure cooper (<sup>σ</sup> = 5.8 <sup>×</sup> 107 S/m, <sup>μ</sup> = <sup>μ</sup>0) with a thickness of 35 μm. The 0.8 mm thick dielectric presents no conductivity, and μ = μ0.

To calculate the impedance, an alternating current of a given frequency is imposed to flow through the sample, perpendicular to the plane of simulation. The current returns in the opposite direction through the ground conductor.

In this work, the MI is calculated for a large number of configurations with different values of μmax and μ*P*. For each configuration, the MI is calculated as a function of the frequency, in a range from 0 to 150 MHz or 0 to 1 GHz, depending on the case. To accommodate the intensive computational resources needed, we have made use of the XFEMM implementation of the software [26], which is run in a computer cluster.

#### **3. Results and Discussion**

Let us consider first the case of the MI sensor without any MNPs. Figure 3 presents the calculated MI response as a function of the frequency for a sample 1 mm wide and 20 μm thick. With the value of μmax = 5000 μ<sup>0</sup> used in the simulation, the maximum value of MI ratio is MImax = 568%. The inset in Figure 3 shows the experimentally measured MI ratio of an amorphous ribbon composed of Co65Fe4Ni2Si15B14. We can observe that the shapes of both curves are essentially similar, although the MI experimental values are significantly lower, indicating that the permeability μmax = 5000 μ<sup>0</sup> used in the simulation is largely overestimated. Nevertheless, this case, which corresponds to a very sensitive MI sensor, is considered the starting point in our goal of studying the relevance of MI to detect magnetic nanoparticles.

**Figure 3.** Magneto-impedance ratio MI as defined in Equation (2), calculated using FEM for the case of a planar sample 1 mm wide and 20 μm thick, with the permeability μmax = 5000 μ0. For comparison, the inset shows the MI ratio experimentally measured in an amorphous ribbon.

When a drop containing MNPs is placed on top of the MI sensor as described in Figure 2, the complete MI curve as a function of the frequency is modified. Figure 4 shows the variation of the region of the MI curves around the maximum when the concentration of MNPs is monotonically increased (increasing values of μ*P*). The simulation results are divided into two plots for better clarity. Figure 4a determines that the MI response decreases when the permeability of the MNPs system increases from 2 μ<sup>0</sup> to 15 μ0. However, when μ*<sup>P</sup>* is increased further, Figure 4b shows that the MI response changes tendency and start to increase. In both plots, the large red and black dots indicate the position of MImax for the different values of μ*P*. Figure 5 compiles these results, plotting the evolution of MImax for the whole range of tested μ*<sup>P</sup>* values.

**Figure 4.** Variation of the MI curves calculated for a sensor with μmax = 5000 μ<sup>0</sup> when a drop with increasing MNPs concentration is placed on it. (**a**) for concentrations up to μ*<sup>P</sup>* = 15 μ0, the magnitude of MI decreases. (**b**) For larger concentrations, from μ*<sup>P</sup>* = 20 μ0, the magnitude of MI increases. Large red and black dots indicate the position of MImax for each curve.

**Figure 5.** Maximum MI ratio of a sensor with μmax = 5000 μ<sup>0</sup> when a drop of MNPs is placed on it, as a function of the concentration of nanoparticles (expressed as increasing permeability μ*<sup>P</sup>* values).

Figure 5 shows that depending on the value of the permeability of the system of MNPs, the sensitivity of a very sensitive MI sensor can have a negative or positive value. That is, the MI ratio can display either a decreasing (for μ*<sup>P</sup>* < 15) or an increasing (for μ*<sup>P</sup>* > 20) behavior. This can certainly explain the discrepancies found in the compiled works [16] indicated in the introduction: the situation in the works where a decrease in the MI ratio is reported when increasing the concentration of MNPs, according to the results shown in Figure 5, can correspond to situations in which the permeability of the nanoparticle ensemble is low (due to a low intrinsic permeability of the nanoparticles or low concentrations). In contrast, the situation in the works reporting an increasing MI response with concentration can correspond to cases in which the permeability of the MNPs system is large.

As the maximum impedance ratio MImax is calculated as a quotient as displayed in Equation (2), the negative slope of the curve in Figure 5 for μ*<sup>P</sup>* < 15 indicates that *Z*min increases more than (*Z*max − *Z*min) in this range. This is easily explained considering that the increase in the impedance is due to the presence of a magnetic medium (the particles) near the MI conductor. It is the same phenomenon occurring when a soft ferrite increases the impedance of a wire in a RF choke. When the permeability of the medium is very low compared with the permeability of the conductor itself, as in *Z*max, the influence of the magnetic medium is low. However, when the permeability of the conductor is low, as in *Z*min, even a surrounding medium with a low permeability produces a change in the impedance.

It is expected that the intrinsic MI performance of the sensor must have an influence on its sensitivity to the presence on MNPs. The same type of calculations that produced Figures 4 and 5 for the case of an MI sensor with μmax = 5000 μ<sup>0</sup> have been performed for sensors with μmax/μ<sup>0</sup> = 500, 100, and 10—that is, with a decreasing intrinsic MI response (intrinsic MImax values are 156%, 46%, and 5.5%, respectively). We introduce a new parameter, η, to compare the capacity of the different sensors to detect MNPs with increasing concentrations, defined as

$$\eta(\%) = \frac{\text{MI}\_{\text{max}}(\mu\_P) - \text{MI}\_{\text{max}, \text{woP}}}{\text{MI}\_{\text{max}, \text{woP}}} \times 100,\tag{4}$$

where MImax,woP is the maximum value of the MI ratio in the sensor without particles (the intrinsic MImax value). The parameter η therefore quantifies the sensitivity of an MI sensor to the presence of MNPs, expressed as the change in the MI ratio experienced by the sensor when a drop of MNPs is placed on top of it. Figure 6 plots the results obtained for η in the sensors with different MI performance (represented by their values of μmax). Note that the curve for the sensor with μmax = 5000 μ<sup>0</sup> is the same as the one plotted in Figure 5.

**Figure 6.** Relative change of the MImax response, experienced by sensors with different MI performance (different values of μmax) when a system of MNPs with increasing concentration is placed on top.

The data in Figure 6 is certainly conclusive: the sensors with worse MI performance are more sensitive to the presence of MNPs. If extrapolated, the best sensor material for detecting NMPs should be one with no MI effect at all. This is not completely surprising, as there is experimental evidence of a larger response from a plain Cu sensor than from an MI amorphous ribbon in a measurement performed in the same conditions [27]. In fact, this behavior could have been anticipated: if the change in the impedance of the sensor in the presence of MNPs is a consequence of changes in the distribution of the electromagnetic field due to the permeability of the particles, then this effect should be larger when the permeability of the sensor itself is smaller than that of the system of MNPs. The approach of using the impedance changes of nonmagnetic conductors to quantify the concentration of MNPs is being used successfully in the development of magnetic biosensors [28].

In accepting these conclusions, one should be aware of the limitations of the present analysis. The results from the FEM calculations do not include many relevant physical effects that occur in real systems, such as the dependence of the permeability on the frequency, or the possible agglomeration effects that takes place when the particle concentration is high, which completely change the magnetic behavior of the ensemble. In particular, the latter effect is difficult to model, but probably will modify the aspect of Figures 5 and 6 in which the MI sensitivity continuously increases with an increase in particle concentration.

Finally, it should be reminded that the analysis presented here was made for the case of superparamagnetic nanoparticles that do not produce stray magnetic fields unless magnetized. Highly sensitive magnetic sensors can still be used to detect larger monodomain nanoparticles presenting a net magnetic moment [29]. The modeling of the MI signal produced by ferromagnetically behaving particles requires a different approach to the one used here [30].

#### **4. Conclusions**

The performance of MI sensors to detect the presence and concentration of magnetic nanoparticles is investigated using finite element calculations to directly solve Maxwell's equations. The assumption is made that the sensitivity to MNPs comes from their magnetic permeability, and not from the stray magnetic field that they produce. This should be the case for superparamagnetic particles if they are

not magnetized by an external magnetic field of sufficient strength. In this hypothesis, the variation of impedance experienced by the MI sensor is a consequence of the change in distribution of the electromagnetic field due to the permeability of the MNPs system.

The results obtained not only confirm that the sensitivity of MI sensors can be justified considering only the permeability of MNPs, but also help explain the origin of the discrepancies found in the literature about the response of magneto-impedance sensors to the presence of magnetic nanoparticles, where some authors report an increasing MI signal when the concentration of MNPs is increased, while others report a decreasing tendency. The results show that the change of the MI response when increasing the concentration of MNPs can be positive or negative, depending on the effective permeability of the particle system.

Additionally, the study demonstrated that a good intrinsic MI performance of the sensor has a detrimental effect on its capacity to detect MNPs: sensors with a lower MI response display larger sensitivities to the presence of magnetic nanoparticles. This seems to confirm that the correct strategy for detecting MNPs is to use the impedance change of plain, nonmagnetic conductors as sensing materials, at least in the case of superparamagnetic particles that are not magnetized in an external magnetic field.

**Funding:** This work is supported by the Spanish government (Project: MAT2017-83632-C3) and by the Basque government under grants KK-2019/00101 and IT1245-19.

**Acknowledgments:** SGI/IZO-SGIker (UPV/EHU) is acknowledged for allocation of computational resources and support.

**Conflicts of Interest:** The author declared no conflict of interest.

#### **References**


© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Specific Loss Power of Co**/**Li**/**Zn-Mixed Ferrite Powders for Magnetic Hyperthermia**

#### **Gabriele Barrera 1,\*, Marco Coisson 1, Federica Celegato 1, Luca Martino 1, Priyanka Tiwari 2,3, Roshni Verma 2, Shashank N. Kane 2, Frédéric Mazaleyrat <sup>4</sup> and Paola Tiberto <sup>1</sup>**


Received: 12 March 2020; Accepted: 9 April 2020; Published: 10 April 2020

**Abstract:** An important research effort on the design of the magnetic particles is increasingly required to optimize the heat generation in biomedical applications, such as magnetic hyperthermia and heat-assisted drug release, considering the severe restrictions for the human body's exposure to an alternating magnetic field. Magnetic nanoparticles, considered in a broad sense as passive sensors, show the ability to detect an alternating magnetic field and to transduce it into a localized increase of temperature. In this context, the high biocompatibility, easy synthesis procedure and easily tunable magnetic properties of ferrite powders make them ideal candidates. In particular, the tailoring of their chemical composition and cation distribution allows the control of their magnetic properties, tuning them towards the strict demands of these heat-assisted biomedical applications. In this work, Co0.76Zn0.24Fe2O4, Li0.375Zn0.25Fe2.375O4 and ZnFe2O4 mixed-structure ferrite powders were synthesized in a 'dry gel' form by a sol-gel auto-combustion method. Their microstructural properties and cation distribution were obtained by X-ray diffraction characterization. Static and dynamic magnetic measurements were performed revealing the connection between the cation distribution and magnetic behavior. Particular attention was focused on the effect of Co2<sup>+</sup> and Li<sup>+</sup> ions on the magnetic properties at a magnetic field amplitude and the frequency values according to the practical demands of heat-assisted biomedical applications. In this context, the specific loss power (SLP) values were evaluated by ac-hysteresis losses and thermometric measurements at selected values of the dynamic magnetic fields.

**Keywords:** magnetic hyperthermia; specific loss power; magnetic mixed ferrites; hysteresis losses; thermometric measurements

#### **1. Introduction**

Nanotechnology addressed to a nanoscale design of materials is one of the utmost researched topics in the present century, involving disciplines like engineering, physics, chemistry and biology, concerning different application areas such as electronics, telecommunications, energy harvesting, sensors and biomedicine [1–7].

Although magnetic nanoparticles have been extensively studied in recent decades, they resulted in exciting materials to be used in these application areas due to their considerably size-dependent chemical and physical properties [8–10]. In particular, in the biomedical area, the tuning of the structure, size and composition of particles has led to the development of different applications such as magnetic biosensors, magnetic resonance imaging (MRI), drug-delivery and magnetic hyperthermia [6,11–20].

When exposed to an alternating magnetic field, magnetic particles, considered in a broad sense as passive sensors, are able to detect and transduce it in a controlled and localized release of heat; this ability has promoted the use of these materials for advanced therapeutic applications such as magnetic hyperthermia and heat-assisted drug release [13,21–23]. The physical mechanism at the base of heat generation has been recently identified to be mainly the magnetic hysteresis losses [24]. The efficiency of the heat generation, estimated by the specific loss power (SLP) value, depends on several parameters; some of these can be identified as "external", such as the intensity and the frequency of the applied magnetic field and the liquid medium properties, whereas others, identified as "internal", depend on the intrinsic properties of the magnetic particles such as composition, size, shape and magnetic state [25,26].

Because of the strict restrictions required on the applied alternating magnetic field parameters for the human body's exposure [27–29], a huge research effort should be primarily focused on the design of the intrinsic properties of magnetic particles in order to optimize the efficiency of the heat release according to practical demands [30,31].

In this context, spinel ferrite powders attract extraordinary attention because of their high biocompatibility, easy synthesis procedure, physical and chemical stability and easily tunable magnetic properties [32–37]. The general formula of ferrite is MeFe2O4 where Me represents a divalent metal ion (e.g., Fe2<sup>+</sup>, Co2<sup>+</sup>, Ni2<sup>+</sup>, Zn2<sup>+</sup>, etc.) or a combination of ions with the average valence of two (e.g., Li<sup>+</sup> and Fe3<sup>+</sup> in lithium ferrite, etc.) [33]. Moreover, combinations of these ions are also possible, obtaining mixed-structure ferrites with different compositions [33,38].

Generally, in the biomedical area, ferrite particles based on magnetic Co2<sup>+</sup> ions are proposed as promising heat generators due to their strong magnetocrystalline anisotropy and moderate magnetization [39–41]. Instead, Li<sup>+</sup> ions, combined in magnetic (Li<sup>+</sup> 0.5Fe3<sup>+</sup> 0.5) species in ferrite structures, have attracted attention because of their low toxicity [42,43]. On the other hand, the non-magnetic Zn2<sup>+</sup> ion is usually used as a partial substitutional of magnetic divalent ions or species in order to finely tune the magnetic properties of the ferrite particles [38], especially the saturation magnetization [33].

Together with the chemical composition changes, the manipulation of the cation distribution on octahedral and tetrahedral sites represents another suitable strategy to control the magnetic behavior of ferrites due to the strong connection between the spinel structure and its magnetism [44–47].

The biocompatibility evaluation of ferrite particles represents a preliminary and fundamental step towards their use in biomedical applications. The variety of ions in the ferrite composition represents one of the several parameters that influence the viability of the cells [48,49]; e.g., Co-ferrite is less biocompatible than Fe3O4 and Mn-ferrite [50]. However, different coating materials such as polymer or surfactants can be used as protective layers minimizing the direct exposure of the less biocompatible ions present on the ferrite surface to the biological environment [39,51].

In the present work, Co0.76Zn0.24Fe2O4, Li0.375Zn0.25Fe2.375O4 and ZnFe2O4 mixed-structure ferrites were synthesized in a 'dry gel' form by a sol-gel auto-combustion method. Here, X-ray diffraction (XRD) was exploited to calculate the cation distribution. Static and dynamic magnetic characterizations were performed to study the connection between the cation distribution and magnetic behavior. Particular attention was devoted to clarifying the role of Co2<sup>+</sup> and Li<sup>+</sup> ions on the magnetic behavior of ferrites at a magnetic field amplitude and the frequency values appropriate to foresee heat-assisted biomedical applications. Moreover, the hysteresis losses and thermometric measurements at selected values of ac-magnetic fields were performed to evaluate the specific loss power (SLP) of the samples.

#### **2. Materials and Methods**

Li0.375Zn0.25Fe2.375O4, Co0.76Zn0.24Fe2O4 and ZnFe2O4 powder ferrite samples were synthesized by sol-gel auto-combustion method [52]. In summary, the powders were synthesized via utilizing AR grade citrate-nitrate/acetate precursors (Zn(NO3)2.6H2O, Ferric nitrate—Fe(NO3)3.9H2O, Lithium acetate—CH3.COOLi.2H2O, cobalt nitrate—Co(NO3)2 6H2O and citric acid—C6H8O7), were mixed in the stoichiometric ratio. Citric acid was used as the 'fuel' and the ratio of metal salts to fuel was taken as 1:1. In the beginning, the citric acid acted as a chelating agent for the metal ions of varying ionic sizes, which helped in preventing their selective precipitation to maintain compositional homogeneity among the constituents. Subsequently, it also served as a fuel in the combustion reaction. To start the synthesis process, all the precursor materials for the desired composition were dissolved in deionized water in a beaker under constant stirring, to get a homogeneous solution and the pH was maintained at 7 by adding ammonia solution. Then, the solution was heated at ~110 ◦C for 1 h in air till a fluffy powder was formed called 'dry gel' or 'as-burnt powder', which was ground to get a fine powder. After the synthesis, the Li0.375Zn0.25Fe2.375O4 and ZnFe2O4 samples were annealed at 450 ◦C for 3 h; instead, no post-synthesis heat treatments were performed on the Co0.76Zn0.24Fe2O4 sample.

The Zn concentration (x ≈ 0.25) and the resulting composition of LiZn- and CoZn-ferrites were chosen in order to induce an increase in the saturation magnetization compared to the corresponding simple ferrites (CoFeO and LiFeO) [33,53], taking into account the practical requests to optimize the heating efficiency. A higher concentration of Zn ions (x > 0.5) should be avoided as it lowers the magnetization saturation. [33,53].

The structural properties of powder samples were analyzed by X-ray diffraction (XRD) using Cu-K<sup>α</sup> radiation (wavelength 'λ' = 0.1541 nm) in θ–2θ configuration (step size of 0.02◦), equipped with a fast counting Bruker LynxEye detector, with Silicon strip technology. Rietveld refinement was performed by MAUD (material analysis using diffraction) software [54]. XRD data were analyzed to obtain structural parameters: experimental (*aexp.*) lattice parameters, X-ray density (ρ*xrd*) and mean grain diameter (<*Dxrd*>). The distribution of cations on tetrahedral and octahedral sites in the studied samples was determined by analyzing the XRD pattern, employing the Bertaut method [55], as was also reported in earlier reports [56–58]. XRD intensity depends on the atomic position in the spinel unit cell whereas the XRD peak position relies on the size and the shape of the unit cell. Bertaut's method utilizes the following pair of reflections: (400), (422) and (220), (400), according to the expression:

$$\frac{I\_{hkl}^{\text{obs}}}{I\_{h'k'l'}^{\text{obs}}} = \frac{I\_{hkl}^{\text{cal}}}{I\_{h'k'l'}^{\text{cal}}} \tag{1}$$

where *Ihklobs* and *Ihklcal* are respectively the observed and estimated intensities for the reflection (hkl). These ratios were evaluated for the numerous groupings of cationic distribution at tetrahedral and octahedral sites as described in [56]. The best distribution of cations was taken among the sites for which theoretical and experimental lattice parameters agreed clearly.

Room-temperature-static-magnetization curves were measured by the means of a vibrating sample magnetometer (VSM), operating in the magnetic field range −1200 < *H* < 1200 kA/m. The dc-hysteresis loops were measured at selected vertex fields in the interval 0–1200 kA/m. From the major loops, the coercive field (*Hc*), the magnetic remanence (μ*0Mr*) and the saturation magnetization (μ*0Ms*) were evaluated; specifically, the latter was determined by fitting the high-field portion of dc-hysteresis curves with the standard expression μ0*M* = μ0*Ms* − *a*/*H*, representing the first-order approximation of the series expansion that describes the law of approach to saturation [59].

Room-temperature dynamic hysteresis loops were measured by the means of a custom-built B-H loop tracer [60] operating with the ac-magnetic field amplitude in the range 8–42 kA/m at the fixed frequency of ~69 kHz; the ac-hysteresis loops were measured at selected vertex fields in the allowable range. The area enclosed by ac-hysteresis loops was calculated in order to estimate the specific loss power by the means of the hysteresis losses (SLP).

Thermometric measurements were performed by an ad hoc-developed hyperthermia setup described in detail elsewhere [60]. In summary, the magnetic particle suspension at desired concentration was placed in the center of a copper coil with a diameter of about 5 cm which generated an electromagnetic field with a frequency of 100 kHz and an intensity up to 47.7 kA/m. The geometry of the set-up guaranteed a homogenous field through the entire sample and the used field frequency and intensity fell within the general safety [27,28]. The magnetic particle suspension was prepared by dispersing the Li0.375Zn0.25Fe2.375O4 powder in a liquid medium, consisting of sodium citrate tribasic dispersed in deionized water (0.2 g/L), obtaining a magnetic solution concentration of about 27 mg/mL. Sodium citrate tribasic favors the stabilization of ferrite particles in deionized water due to the adsorption of citrate anions onto their surface resulting in a stable and well dispersed magnetic solution [61]. These liquid suspensions were adequate to perform thermometric measurements but did not present conditions for in vitro and in vivo biomedical applications. The thermodynamic conditions of the experiment were fully modeled to obtain a direct measurement of the SLP of the magnetic powders by taking into account the heat exchange with the surrounding environment in non-adiabatic conditions and the parasitic heating of the water [60].

#### **3. Results and Discussion**

#### *3.1. Structural Properties*

Rietveld-refined X-ray diffraction (XRD) patterns of the studied samples validating the formation of the nanocrystalline mixed cubic spinel structure are presented in Figure 1. For the sample of ZnFe2O4 (Figure 1c), small traces of Fe2O3 were also observed and can be ascribed to a partial decomposition of the ferrite phase [62].

**Figure 1.** Rietveld-refined XRD patterns of: (**a**) dry gel Co0.76Zn0.24Fe2O4, (**b**) Li0.375Zn0.25Fe2.375O4 annealed at 450 ◦C/3 h, (**c**) ZnFe2O4 annealed at 450 ◦C/3 h.

The experimental lattice parameter (*a*exp) values of the ferrite phases obtained from the Rietveld refinement of the XRD data are given in Table 1; the value of the Zn-ferrite sample results is higher than the ones of the LiZn-ferrite and CoZn-ferrite samples. This observed increase was due to the replacement of the Co2<sup>+</sup> and Li<sup>+</sup> ions characterized by an ionic radius of 0.78 and 0.70 Å, respectively, with the bigger Zn2<sup>+</sup> ions (0.83 Å) [63–65], in agreement with Vegard's law [66]. Moreover, the X-ray density (ρXRD) for each sample was calculated by using the lattice parameter (*a*exp) and the standard formula [67]; the obtained values, ranging in the typical interval of this kind of ferrites [33,68], are given in Table 1.

**Table 1.** Experimental lattice parameters (aexp); X-ray density (ρXRD); grain mean diameter <DXRD> and cation distribution.


The mean diameter <DXRD> values of the grains were obtained from the XRD data analysis by Scherrer's equation [69] for all the samples (Table 1) and they were in the interval 32–38 nm, indicating the formation of nanocrystallites. However, the reactions used to synthesize the particles could induce a non-negligible degree of agglomeration, which could result in polycrystalline aggregates forming particles with diameters larger than <DXRD> [44].

These small values of <DXRD> revealed a significant advantage of the auto-combustion synthesis compared to the more conventional ceramic methods in order to produce ferrite particles: the lower temperature and shorter time used in the auto-combustions synthesis resulted in the grains' smaller diameter with a greater surface area [70,71], preventing the particles from coarsening and aggregating, which is promoted by the very high temperature (T > 1000 ◦C) typically used in the ceramic methods.

In addition, the XRD spectra were also analyzed by the Bertaut method [55] in order to obtain the cation distribution. In particular, the cation distributions of the studied samples are given in Table 1, where the ions on the tetrahedral site (site A) are given in parentheses and the ions on the octahedral sites (sites B) between square brackets. The Zn2<sup>+</sup> ions in Zn-ferrite were mainly located on the B site, whereas the CoZn-ferrite and LiZn-ferrite samples showed only a slight preference of the Zn2<sup>+</sup> ions to occupy the octahedral (B) sites with respect to the tetrahedral (A) one. These observed deviations, with respect to the general preference of the Zn2<sup>+</sup> ions to occupy the tetrahedral (A) site, clearly proved a non-equilibrium cation distribution in the samples. This effect was ascribed to the sol-gel auto-combustion synthesis method at a low temperature (<110 ◦C) and to the low efficiency of the post-synthesis heat treatment (for sample Zn-ferrite and LiZn-ferrite) which did not effectively induce a diffusion of the Zn2<sup>+</sup> ions on the tetrahedral sites towards a distribution closer to the equilibrium. Instead, in the CoZn-ferrite and LiZn-ferrite samples, the divalent Co2<sup>+</sup> metal ions and the divalent combination of two the metal ions [Li<sup>+</sup>0.5Fe3<sup>+</sup>0.5] [68,72] were almost totally located, as their preference, on B sites.

The cation distribution reported as the general formula MeII δFeIII 1−δ MeII <sup>1</sup>−<sup>δ</sup>FeIII 1+δ O4 revealed the inversion degree of all the studied samples (δ = 0.10, 0.15, 0.09 for the CoZn, LiZn and Zn-ferrite samples, respectively), indicating an intermediate configuration of their structure between the completely inverse spinel structure (δ = 0) and the totally random distribution one (δ = 0.33).

The intermediate and tunable values of the inversion degree and its effect on the magnetic properties (see the following sections) are advantages ascribed to the auto-combustion synthesis, in which the low temperature and the fast cooling rate hinder the diffusion of the metal ions towards the equilibrium that it is typically obtained with the more conventional high-temperature ceramic methods.

#### *3.2. DC-Magnetic Properties*

An enlargement of the room-temperature dc-hysteresis loops of all the samples taken at the maximum magnetic field of 1200 kA/m is shown in Figure 2.

All curves display the typical magnetic hysteretic behavior resulting from the ferrimagnetic ordering of spinel ferrite structure [73,74], confirming the blocked state of the ferrite particles as expected by the <DXRD> values of the grains obtained from the XRD data analysis. The observed coercive field (*Hc*), saturation magnetization (μ*0Ms*) and the magnetic remanence (μ*0Mr*) are listed in Table 2.

**Figure 2.** (**a**) Room-temperature major dc-hysteresis loops of all the studied samples; (**b**) dc-hysteresis loops areas as a function of the vertex field for all the studied ferrites.

**Table 2.** Saturation magnetization (μ*0Ms*), coercive field (*Hc*), magnetic remanence (μ*0Mr*), theoretical saturation magnetization (μ*0Ms th*) at 0 K and the area enclosed by the major dc-hysteresis loops for all the samples.


The complete replacement of the magnetic Co2<sup>+</sup> ions with the non-magnetic Zn2<sup>+</sup> ions induced a reduction of *Hc* from 31.90 (CoZn-ferrite) to 10.65 (Zn-ferrite) kA/m. The higher value of *Hc* of CoZn-ferrite sample was connected to the high anisotropy of Co2<sup>+</sup> ions characterized by a remarkable spin-orbit coupling [36,75]. On the other hand, the replacement of the magnetic [Li<sup>+</sup>0.5Fe3<sup>+</sup>0.5] species with the non-magnetic Zn2<sup>+</sup> ions promoted a slight increase of *Hc* from 7.37 (LiZn-ferrite) to 10.65 kA/m (Zn-ferrite) and also a marked reduction of the μ*0Ms* values from 0.415 T (LiZn-ferrite) to 0.066 T (Zn-ferrite). This μ*0Ms* reduction can be ascribed to the different distribution of the Fe3<sup>+</sup> ions in the spinel structure (see cation distribution in Table 1). In particular, in the LiZn sample, the Fe3<sup>+</sup> ions were preferentially located on the octahedral sites, leading to a higher net magnetic moment than the one of the Zn sample in which a quasi-balanced distribution of Fe3<sup>+</sup> ions occurred.

The experimental μ*0Ms* values can be compared to the theoretical magnetization (μ*0Ms th*) values (see Table 2) calculated in accordance to Néel's two-sublattice model of ferrimagnets [76], where the magnetic moments of the ions (Fe3<sup>+</sup> = 5 μB, Co2<sup>+</sup> = 3 μ<sup>B</sup> and Li<sup>+</sup> = Zn2<sup>+</sup> = 0 μB) on the tetrahedral and octahedral sites are considered perfectly anti-parallel, totally neglecting any temperature effect and spin disorder. The μ*0Ms th* values for the LiZn-ferrite and CoZn-ferrite samples were very similar; therefore, the experimental μ*0Ms* values are also expected to be comparable. Instead, a marked difference was measured (Table 2). This evidence clearly proves that the magnetic moments in these two ferrite samples were not perfectly antiparallel, but rather were characterized by a spin canting resulting in a non-collinear arrangement in the two-sublattices [77], especially in the CoZn-ferrite samples. The three-lattice model, suggested by Yafet and Kittel [77], confirms this hypothesis by extrapolating the canting angle values from the XRD data: 38◦, 30◦ and 24◦ for the CoZn-ferrite, LiZn-ferrite, and the Zn-ferrite, respectively. Of course, the observed reduction of μ*0Ms* can also be accentuated

by the probable presence of a spin disorder on the ferrite surface that induced a magnetically dead layer [78,79].

The calculated values of the area (see Table 2) enclosed by the dc-hysteresis loops were proportional to the energy lost as heat by the samples in one complete major loop (hysteresis losses). It can be noted that the mixing of magnetic divalent ions (Co2+) or species [Li<sup>+</sup>0.5Fe<sup>3</sup><sup>+</sup>0.5] with non-magnetic Zn<sup>2</sup><sup>+</sup> ions increased the area enclosed by the major loop with respect to the Zn-ferrite structure. This effect was particularly efficient in the CoZn-ferrite sample due to the high anisotropy of Co2<sup>+</sup> ions.

Minor dc-hysteresis loops were measured for all the samples by applying selected vertex fields lower than the saturation field of the CoZn sample. The values of the area enclosed by these minor dc-loops were calculated in order to evaluate the dc-hysteresis losses as a function of selected the vertex fields (*Hv*), see Figure 2b. All samples showed a non-linear dependence of the dc-hysteresis losses on the vertex field amplitude, which can be well described by a third-order power law in the limit of the small applied field [59]. Up to the field value of about 75 kA/m, the mutual relationship of the dc-hysteresis losses intensity of the three samples was markedly changed with respect to the dc-hysteresis losses evaluated from major dc-hysteresis loops (Table 2). In particular, in the vertex field interval 0 < *Hv* < 75 kA/m, the LiZn-ferrite sample showed the highest hysteresis losses values whereas those of the CoZn-ferrite sample were very low because the high anisotropy of Co2<sup>+</sup> ions was not completely overcome and the magnetization described narrow minor loops. When *Hv* > 75 kA/m, the area enclosed by CoZn samples becomes the highest among the studied samples restoring the mutual relationship of the dc-hysteresis losses intensity evaluated from major dc-hysteresis loops.

#### *3.3. Ac-Measurements and SLP Evaluation*

Magnetic hyperthermia therapy has to comply with a variety of biological and technical constraints, among which emerges the limit for the product of magnetic field amplitude and frequency (*H* × *f*) in relation to the induced current loop diameter (D) to avoid non-specific heating in healthy areas due to Eddy currents and to avoid the stimulation of cardiac muscles and nerves [80,81]. This limit was initially proposed by Atkinson et al., as *H* <sup>×</sup> *f* < 4.85 <sup>×</sup> 108 Am−1s−<sup>1</sup> for a loop diameter of about 30 cm [27]; further experiments with a smaller diameter of the exposed body region have increased the criterion up to *<sup>H</sup>* <sup>×</sup> *<sup>f</sup>* <sup>&</sup>lt; 5.0 <sup>×</sup> <sup>10</sup><sup>9</sup> Am<sup>−</sup>1s−<sup>1</sup> [28].

The range between these two criteria seems to be currently the most convenient and most used in several in vivo trials [82], at least until new studies about the biological safety of the alternating magnetic field are carried out.

In addition to this biological limitation, some engineering difficulties combined with increasing costs arise with the aim of concurrently increasing the field frequency and amplitudes in the wide space (several centimeters) required for hyperthermia treatment.

In this work, the ac-characterization was performed at the field frequency of 69 kHz and at the maximum applied magnetic field intensity, limited to 42 kA/m in order to fall within both general safety [27,28] and our technological limits. A selection of ac-hysteresis loops acquired at selected vertex fields for all samples is shown in Figure S1 of the Supplementary Materials.

Dynamic ac-hysteresis loops (*f* = 69 kHz and *Hv* = 37 kA/m) of all the studied powder ferrite samples are shown in Figure 3a.

**Figure 3.** (**a**) Room-temperature minor ac-hysteresis loops of all the studied samples (f = 69 kHz and *Hv* = 37 kA/m); (**b**) specific loss power (SLP) values for all the samples as a function of the vertex field obtained by the ac-hysteresis loops areas.

In all the samples, the magnetization did not reach complete saturation, leading to minor loops. The area enclosed by the hysteresis loops represented the irreversible work dissipated in the surrounding as thermal energy profitably usable for magnetic hyperthermia [60,83–85].

The specific loss power is defined as the power released in the form of heat by powders submitted to electromagnetic field radiation, normalized to the mass of the solid component of the sample. In our case, the SLP was calculated from the area enclosed by the ac-hysteresis loops by the means of the following integral of the dynamic magnetization versus the applied field strength:

$$SLP = \frac{f}{c} \oint \mu\_0 \mathcal{M}(t) dH(t) \tag{2}$$

where *f* is the field frequency and *c* the weight concentration of ferrite powder. The integration was done over one period of the oscillating magnetic field.

The SLP dependence on the vertex field intensity *Hv* of all the studied samples is shown in Figure 3b. The evaluation of this parameter represented one of the primary criteria to determine the suitability of the ferrite sample for hyperthermia applications.

In the entire investigated field range, the LiZn-ferrite sample displayed the highest SLP values indicating how the low-magnetic anisotropy divalent species [Li<sup>+</sup>0.5Fe<sup>3</sup><sup>+</sup>0.5] favor the heat released by hysteresis losses with respect to the high-magnetic anisotropic divalent Co2<sup>+</sup> ions; in particular, the SLP value of the LiZn-ferrite sample at *Hv* = 42 kA/m is 3.6 times bigger than the one of CoZn-ferrite sample at the same vertex field. As observed from the dc-characterization reported in Figure 2b, only a further increase of *Hv* (exceeding our technological limit) can reduce the gap between the SLP values produced by two samples leading to the promotion of the CoZn-ferrite sample. Moreover, the total replacement of the magnetic divalent ions Co2<sup>+</sup> or species [Li<sup>+</sup>0.5Fe3<sup>+</sup>0.5] with non-magnetic Zn2<sup>+</sup> ions hinders the heat production by hysteresis losses, resulting in low SLP values in the investigated field range with a tendency to reach a saturation value of about 15 W/g.

#### *3.4. Thermometric Measurements and SLP Evaluation*

Thermometric measurements were conducted in order to evaluate the ability of ferrite powders to heat the magnetic solution, in which they were dispersed, under different applied field intensities. Only the LiZn-ferrite composition was examined by thermometric measurements because it resulted in, by the ac-loops characterization, the most promising sample among those studied for hyperthermia

therapy. In particular, the time dependence of the temperature of the magnetic solution containing the LiZn-ferrite powder (concentration of about 27 mg/mL) under an applied field for 40 kA/m at 100 kHz is shown in Figure 4.

**Figure 4.** Time dependence of the temperature of the magnetic solution containing LiZn-ferrite powder under an applied field of 40 kA/m at 100 kHz. Black symbols: experimental data. Green line: best fit the by theoretical model.

The reported curve is taken as representative of all the measurements done at different applied field values from 23.9 to 47.7 kA/m. At *t* = 0 s, the radiofrequency field was switched on and the temperature of the magnetic solution increased towards the equilibrium temperature. After one hour, the radiofrequency field was switched off and the magnetic solution cooled down to room temperature. As a result, the thermometric SLP values were extrapolated by fitting the whole time evolution of the temperature of the magnetic solution by a mathematical model that takes into account the non-adiabatic condition of the exploited hyperthermia setup [60]. In Figure 4, the black symbols are the experimental data, whereas the green line is the theoretical best fit. The model based on Newton's cooling law [86] evaluates the exchange of heat among the various components of the setup and/or the surrounding environment induced by their temperature difference. In particular, the heat released by the magnetic particles excited by an r.f electromagnetic field is all transferred to the liquid medium in which they are dispersed. Subsequently, the heat is transferred to all the experimental components and eventually to the surrounding environment. An accurate calibration procedure allows to determine the time constant of the heat exchange mechanism among the various experimental components and the other physical quantities appearing in the mathematical model. The only free parameter of the fit procedure is the power (*P*) released by the ferrite powders that it is adjusted to reproduce the whole experimental curve providing a direct estimation of the thermometric SLP of the samples:

$$SLP = \frac{P}{m} \tag{3}$$

where *m* is the mass of ferrite powders in the liquid solution.

A summary of the SLP values determined with the two techniques for LiZn-ferrite samples is plotted in Figure 5. The SLP values calculated from thermometric measurements (empty red dots in Figure 5) turned out to be larger than the ones obtained by dynamic hysteresis loops (full red dots in Figure 5).

**Figure 5.** SLP values for the LiZn sample as a function of the vertex field obtained by: ac-hysteresis loops areas (full red dots) at the operation frequency of 69 kHz and the thermometric measurements (empty red dots) at the operation frequency of 100 kHz.

This effect was mainly due to the higher operating frequency of the thermometric setup (100 kHz) with respect to the B-H loop tracer (69 kHz) and it also included the contribution to the SLP of the Brown relaxation process that took place only in the magnetic liquid solution and not in the dried sample used for dynamic hysteresis loops measurements [24,87]. In fact, the Brown relaxation mechanism is associated with the physical rotation of the whole particle in the fluid generating heat due to the viscous friction between the rotating particles and the surrounding liquid medium [24,87,88]. However, recent studies, both in vivo and ex vivo, have demonstrated that the particles are generally immobilized when directly injected into the tumor tissues highlighting that the Brown process is largely suppressed during hyperthermia treatments [89–91]. Another significant aspect to be taken into consideration is the effect of the strong magnetic interaction that is generated by the agglomerations of particles in dried samples. In particular, the formation of agglomerates can entail an alteration of the hysteresis loop area and consequently influence the SLP value [92–94].

SLP values obtained for the LiZn-ferrite sample (SLP = 85–180 W/g) as reported in Figure 5 are in the same order of magnitude as the ones already reported in the literature. As examples, Mallik et al. [42] report SLP = 334 W/g (H = 33.5 mT, f = 290 kHz) for Li0.31Zn0.38Fe2.31O4 particles; Dalal et al. [95] report SLP = 143–166 W/g (H = 33.5 mT, f = 290 kHz) for Li0.35Zn0.3Co0.05Fe2.3O4 particles embedded in carbon nanotubes. It should be noted that the experimental results are hardly comparable as they refer to different applied fields and frequencies and strongly depend on the intrinsic properties of particles such as size, shape and composition. This comparison shows that Li-based ferrites can be considered an efficient alternative to more conventional iron-oxides such as maghemite (SLP = 106 W/g [96]) and magnetite [60] and some other ferrite compositions (SLP = 300 W/g for Gd-ferrite [97], SLP = 73 W/g for Ba-ferrite [98] and SLP = 58 W/g for Sr-ferrite [99]); however, the heat efficiency of Li-based ferrites remains much lower than Mn- and MnCo-based ferrites (SLP = 3024 W/g [100]) and magnetosomes (SLP = 960 W/g [101]).

#### **4. Conclusions**

Co0.76Zn0.24Fe2O4, Li0.375Zn0.25Fe2.375O4 and ZnFe2O4 mixed-structure ferrite powders were synthesized by a sol-gel auto-combustion method. XRD spectra analysis revealed an out-of-equilibrium cations distribution ascribed to the low efficiency of the synthesis method which did not induce an effective diffusion of the Zn2<sup>+</sup> ions towards the equilibrium positions. This out-of-equilibrium cation distribution strongly influenced the static and dynamic magnetic properties of the ferrites.

Dc-major loops clearly indicated that the suitable mixing of non-magnetic Zn2<sup>+</sup> ions with magnetic divalent ions (Co2+) or species [Li<sup>+</sup>0.5Fe<sup>3</sup><sup>+</sup>0.5] is a tool to tune the magnetic properties of the ferrite particles. In particular, the high anisotropy of Co2<sup>+</sup> ions enhanced the coercive field, whereas the divalent species [Li<sup>+</sup>0.5Fe3<sup>+</sup>0.5] increased the saturation magnetization.

The magnetic energy dissipated as thermal energy profitably usable in hyperthermia was evaluated by the means of ac-hysteresis loops and thermometric measurements. Among the studied samples, the mixed LiZn-ferrite structure matches in a better way the practical requirements of heat-assisted applications than those of the mixed ferrite structure constituted by the highly anisotropic Co2<sup>+</sup> ions. In the entire investigated field range, the LiZn-ferrite sample displayed the highest SLP values indicating how the low anisotropic divalent species [Li<sup>+</sup>0.5Fe3<sup>+</sup>0.5] favor the heat release by hysteresis losses with respect to the high anisotropic divalent Co2<sup>+</sup> ions.

In conclusion, the SLP evaluation and the structural and magnetic characterizations of ferrite samples in dry form or dispersed in the liquid solution were calculated. This represents a preliminary and important step towards the understanding of the physical properties for their perspective use in magnetic hyperthermia and heat-assisted biomedical applications. Obviously, for prospective in vitro and in vivo studies, several other aspects should be carefully taken into account such as the size and charge of the NPs and their degree of aggregation in the magnetic solution.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1424-8220/20/7/2151/s1, Figure S1: A selection of the ac-hysteresis loops acquired at the selected vertex fields for all samples.

**Author Contributions:** Conceptualization, P.T. (Paola Tiberto), M.C. F.M. and S.N.K.; preparation of the samples, P.T. (Priyanka Tiwari) and R.V.; XRD characterization and structural data analysis, P.T. (Priyanka Tiwari), R.V. and S.N.K.; DC-magnetic measurements and data analysis, G.B., M.C., F.C. and F.M.; AC-magnetic measurements and data analysis, G.B., M.C., F.C. and L.M.; SLP evaluation, G.B., M.C., F.C and L.M.; supervision, P.T. (Paola Tiberto), M.C. and S.N.K.; writing the manuscript, G.B., M.C. and S.N.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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