Atomic-Scale Structural and Magnetic Coupling Properties of Twin Boundaries in Lithium Ferrite (Li_0.5Fe_2.5O₄) Film

Abstract

It is of great academic significance to understand the influence that the atomic-scale structure of interfaces and boundaries within materials has on magnetic coupling characteristics and promote the innovation of advanced magnetic devices. Here, we carried out a systematic investigation of the atomic and electronic structures of twin boundaries (TBs) in Li_0.5Fe_2.5O₄ (LFO) thin films and determined their concurrent magnetic couplings using atomic-resolution transmission electron microscopy and first-principle calculations at the atomic scale. The results show that ferromagnetic or antiferromagnetic coupling can exist across the different TBs in LFO thin films, and electrical structures within a few atomic layers directly rely on the atom arrangement across the TB. Uncovering one-to-one relationships between the magnetic coupling properties of individual TBs and atomic-scale structures can clarify a thorough comprehension of numerous fascinating magnetic properties of commonly utilized magnetic materials, which will undoubtedly encourage the progress of sophisticated magnetic materials and devices.

1. Introduction

A wide range of magnetic properties can be found in spinel ferrites, which have drawn attention due to their potential utilization in sensors, transformers, antennas, high-frequency inductors, microwave devices, and spintronic devices [1]. Magnetic coupling across boundaries in spinel ferrites plays a critical role in both fundamental research significance and magnetic application. For instance, antiphase boundaries (APBs) have been frequently observed in spinel-type ferrite thin films, such as NiFe₂O₄, Fe₃O₄, and LFO [2,3,4]. Atomic models and magnetic coupling across APBs have been extensively determined using high-resolution scanning transmission electron microscopy (STEM) and density function theory (DFT) in spinel-type materials [5,6,7]. Antiferromagnetic interactions arise across the APBs, resulting in a larger coercive field for magnetization saturation and increased magnetoresistance within the ferromagnetic film, which can be harmful for applications [8,9,10]. In contrast, engineering the formation of APBs has emerged as a promising approach to effectively modulate the functionality in solid oxide fuel applications [11]. Therefore, it is vital to understand atomic arrangements and magnetic coupling across individual boundaries to tailor the magnetic properties. However, the challenges of simultaneously and accurately determining the atomic structure and magnetic coupling of individual boundaries significantly impede investigations into the relationship between local atomic arrangements and magnetic coupling at boundaries. This is a fascinating but difficult research topic in interface and boundary science.

Besides APBs, it was found that TBs also occur in spinel-type materials, e.g., Fe₃O₄ and MnAl₂O₄, which display unusual magnetic characteristics [12,13]. The controllable formation of TBs in spinel lithium manganate helps to obtain a higher rate of performance [14]. In particular, Chen et al. [15] reported on the atomic configuration and magnetic coupling of TBs in Fe₃O₄ single crystal by combining STEM and the differential phase contrast (DPC) imaging technique, suggesting that the magnetic coupling nature of TBs in Fe₃O₄, whether ferromagnetic (FM) or antiferromagnetic (AFM), is intimately tied to the atomic configurations at their cores. Specifically, antiferromagnetic interactions can arise across non-stoichiometric TBs. Atomic structure models of TBs have been constructed on the basis of crystallographic relationships and verified experimentally using a high-resolution STEM in LFO films grown on the SrTiO₃ (STO) (001) substrate [16]. LFO, as an abundant magnetic material, garners significant interest because of its fascinating electronic and magnetic properties. In defect-free LFO crystal, the magnetic moments of Fe³⁺ ions interact through super-exchange interactions mediated by oxygen ions, leading to the antiparallel alignment of Fe³⁺ ion’s magnetic moments on tetrahedral and octahedral sites, which results in the subferromagnetic ground state with a high saturation magnetization of 2.5 μB per formula unit [17,18]. Compared to Fe₃O₄ materials, non-magnetic Li ions instead of magnetic Fe ions are half occupied at octahedral sites; hence, the magnetic couplings associated with the TBs in LFO film remain unclear.

In the present work, atomic structure configuration and magnetic coupling across TBs in LFO thin film fabricated on the STO (001) substrate were probed by combining high-resolution STEM imaging techniques and first-principle calculations, demonstrating how the nature of magnetic coupling across TBs can vary between antiferromagnetic and ferromagnetic coupling, contingent upon the atomic structures and resulting electronic configurations of the TBs.

2. Materials and Methods

Materials and TEM/STEM experiments: The LFO ceramic target for film growth was prepared by a standard solid-state reaction method with the initial reactants Fe₂O₃ and LiCO₃ using a molar ratio of 5:2 for Fe₂O₃ and LiCO₃, respectively [19]. The LFO films were deposited on single-crystalline (001)-oriented STO substrates using a high-pressure sputtering system at a substrate temperature of 800 °C and in an ambient atmosphere consisting of Ar and O₂ at a 1:1 ratio with a pressure of 0.5 mbar. To facilitate TEM/STEM analysis, cross-sectional lamella specimens were produced via the focused ion beam (FIB) lift-out technique using an FEI Helios600i Dualbeam system (Thermo Fisher Scientific, Waltham, MA, USA), and the flowchart photo of TEM /STEM sample preparation by the instrument is shown in Supplementary Figure S1. The lamellae were sectioned in STO <110> crystallographic directions. Bright-field (BF) TEM images and selected-area electron diffraction (SAED) patterns were acquired using a JEOL JEM-2100 microscope. Atomic-resolution high-angle annular dark field (HAADF) and annular bright field (ABF) imaging were carried out on a JEOL ARM200F (JEOL Ltd., Tokyo, Japan), and the specific parameters attributed to HAADF and ABF STEM imaging are documented in our previous research [16].

HAADF and ABF image simulation: The HAADF STEM images were simulated using the abTEM package with the PRISM algorithm [20]. The electron energy was set at 200 keV, the radial cutoff of the plane-wave expansion was set as 30 mrad, and the defocus parameter was 30 Å. The detector angles for HAADF and ABF image simulations were 70–180 mrad and 12–24 mrad, respectively, and the other parameters for ABF image simulation were identical to those for HAADF image simulation.

The calculation for DFT: Density functional theory calculations were performed using the projector augmented plane-wave (PAW) basis set, implemented within the Vienna ab initio simulation package (VASP) [21]. And the plane waves were cut off at 400 eV. The exchange-correlation effects of electrons were modeled using the generalized gradient approximation (GGA), as proposed by Perdew, Burke, and Ernzerhof [22]. The energy convergence criterion for solving the self-consistent Kohn–Sham equations was set at 10⁻⁵ eV. The Brillouin zone was sampled using the Monkhorst-Pack scheme with a resolution finer than 0.03 Å⁻¹ [23]. To enhance the modeling of strong electron–electron interactions within d-shells, we employed the DFT + U approach [24], setting Ueff = 3.8 eV for the d-shells of Fe ion. All structures considered in this study were fully relaxed until a Hellman–Feynman value less than 0.05 eV/Å was obtained. The formation energy of twin boundaries is defined as follows [15]:

$$E_f={\displaystyle \frac{1}{2A}}\left(E_{TB}-n_O{\mu }_O-n_{Fe}{\mu }_{Fe}-n_{Li}{\mu }_{Li}\right)$$

(1)

where E_TB is the total energy of the supercell model with two identical twin boundaries, n_O, n_Fe, and n_Li are the quantities of O, Fe, and Li ions in the supercell model, μ_Fe and μ_Li denote the chemical potentials of Fe and Li ions, respectively, defined as the energy per atom in pure metal body-centered crystals, μ_O is the chemical potential of O ions and is calculated via the Equation 8μ_O + 5μ_Fe + μ_Li = μ(LiFe₅O₈) in which μ(LiFe₅O₈) is the energy of the cell of Li-doped Fe₃O₄, and A denotes the area of each twin boundary.

3. Results and Discussions

Figure 1a displays the low magnification bright field TEM images of LFO thin film with a thickness of 30 nm, showing a cross-sectional overview of the LFO/STO (001) heterosystem. The contrast difference between the film and substrate is clearly visible, and the interface between the film and substrate is indicated by a horizontal arrow. The oblique contrast lines indicated by the yellow arrow are discerned in the film, and the contrasting lines result from the twin boundaries situated in the (111) habit plane.

Figure 1b displays the typical diffraction patterns covering the LFO film and part of the STO substrate recorded along the [1$\overline{1}$0] zone of the axis of STO. The diffraction pattern of the STO substrate is marked by a solid white rectangle, and the diffraction patterns marked by a solid yellow and dashed yellow rectangle have a 70.5° rotation, which results from the LFO matrix region and twin domain area, respectively. The film–substrate orientation relationship in LFO matrix regions is represented by [1$\overline{1}$0](001)_film//[1$\overline{1}$0](001)_substrate. The results of diffraction patterns also confirm that the twin boundaries form in the LFO film. It was observed that the reflection spots split between film and substrate along the in-plane and out-of-plane, indicating that misfit strain relaxation occurs. Using the lattice parameter of the STO substrate (0.3905 nm) [25] as the calibration standard, we determined the in-plane and out-of-plane lattice parameters of the film to be 0.8301 nm and 0.8359 nm, respectively.

High-resolution STEM experiments were conducted in order to definitively discern the atomic structure of TBs viewed along [1$\overline{1}$0] the zone of the axis of the STO substrate. Numerous STEM measurements show the simultaneous presence of three distinct types of TBs in the LFO film. Figure 2 displays three groups of STEM-HAADF and ABF images of TBs; Figure 2a,b show the HAADF image and ABF image of TB I, indicated by green arrows; and Figure 2c,d display the HAADF image and ABF image of TB II, indicated by blue arrows; also, Figure 2e,f show the HAADF image and ABF image of TB III, indicated by red arrows. The film was separated into domain I and domain II by the TBs. It was found that domains I and II display a reflection symmetry across the TB I in Figure 2a, indicated by orange dashed lines. On the contrary, domains I and II, separated by either a TB II or a TB III, exhibit a combination of a glide transformation and reflection symmetry, which is also indicated by orange dashed lines in Figure 2b,c. Based on the STEM-HAADF imaging principle, the intensity in the HAADF image directly correlates with the atomic number (Z) [26]; as a result, the heavier atoms appear brighter, and, additionally, the higher atomic density also generates a brighter contrast. Only the Fe atomic columns are visible in the HAADF images in Figure 2, while oxygen columns remain undetectable due to significantly weaker scattering. The contrast variation in cation columns arises from the varying density of Fe atoms in [1$\overline{1}$0] the projection direction. It is clear that the cation arrangement of TB I is symmetric, in contrast with those of TB II and TB III, which are asymmetric, and the three types of TBs all lie in (111) habit planes. Remarkably, TB III presents cation deficiency, which induces intensity variation in the atomic columns, as marked by a red arrow in Figure 2e. The white arrow demonstrates the atomic column with cation deficiency in Figure 2e.

Figure 2b,d,f display ABF images of three types of TBs, which were acquired simultaneously alongside their corresponding HAADF image to immediately resolve O atom columns. According to ABF images, the oxygen sublattices in three types of TBs appear a feature of ∑3[111] coherent TBs. In particular, the planes between twin domains, namely TBs, lie at the O atom plane marked by green, blue, and red arrows, respectively. Different cation arrangements within the O sublattices lead to the formation of three distinct types of TBs.

To identify the magnetic properties of three types of TBs, DFT computations were performed. On the basis of the experimental STEM images, the potential candidate atomic models of TBs were established, and the most energetically stable atomic structures were acquired in which formation energy was adopted. The formation energies for TB I, TB II, and TB III were determined to be 1.67 J/m², 0.75 J/m², and 2.80 J/m², respectively. However, TB III was frequently observed in the LFO film, which is contradictory to the calculated formation energy. In fact, the APBs also form in the LFO film, and APBs interact with TB I and TB II, further generating abundant TB III., which have been frequently observed in previous work [16]. The density distribution of the three types of TBs is different from that in Fe₃O₄ single crystals [15]. The lowest-energy optimal atomic configuration after relaxation is shown in Figure 3a,c,e; STEM simulations were undertaken by the use of the relaxed atomic models displayed in Figure 3b,d,f, which match well with the experimental counterparts.

In order to identify the magnetic configuration that is the most stable for each type of TB, we compared the energy of the FM and AFM coupling configurations. The results indicate how TB I prefers to configure AFM coupling across the boundary with an interface formation energy 0.39 J/m² lower than that of FM coupling. Also, TB II configures preferably as AFM coupling across the boundary with interface formation energy 0.47 J/m² lower than that of FM coupling. In contrast, TB III typically develops FM couplings across boundaries with an interface formation energy −0.06 J/m² lower than that of AFM coupling. The weak FM coupling at TB III is likely to result from the Fe cation deficiency, which leads to the decreased density of super-exchange interactions between cations via oxygen [27]. The results of formation energy for TBs, exchange coupling energy, and the magnetic coupling of three types of TBs are summarized and presented in

Table 1. Formation energy, exchange coupling energy and magnetic coupling of TBI, TB II, and TB III.

Type of TBs	Formation Energy (J/m2)	Exchange Coupling Energy (EFM-EAFM) (J/m2)	Magnetic Coupling
TB I	1.67	0.39	AFM
TB II	0.75	0.47	AFM
TB III	2.80	−0.06	FM

.

The results of the spin-polarized density of states (DOS) provide additional evidence of these magnetic coupling for TBs, as shown in Figure 4. The LFO film was separated by the TBs as domain I, shaded by transparent yellow, and domain II, shaded by transparent blue, and the spin-polarized DOSs for domain I and domain II are plotted in the left and right part in Figure 4a–c. As shown in Figure 4a, the spin polarization flips direction across the boundary planes of TB I, which suggests AFM coupling between two twin domains separated by TB I. The same situation appears in Figure 4b, demonstrating the AFM coupling nature at TB II. In contrast to the DOS results of TB I and II, the spin polarization remains in the same direction across the boundary plane of TB III in Figure 4c. Noticeably, the spin-polarized DOS at the three different types of TBs is directly depicted in Supplementary Figure S2; spin polarization eventually inverts over the core area of TB I and II, revealing their AFM coupling nature, while the direction of spin polarization remains unaltered across the core area of TB III, and consistent with its FM coupling characteristics.

The atomic structures of three types of TBs in the LFO film are similar to that of the Fe₃O₄ crystal, whereas magnetic couplings across the TBs are quite different from the results in Fe₃O₄ crystal, where TB I and II both exhibit FM coupling and TB III undergoes AFM coupling [15]. It is recognized that in the spinel structure AB₂O₄, the magnetic spins align in an antiparallel manner between the tetrahedral and octahedral sites. Concerning magnetic coupling, depending on the super-exchange interaction via cation-oxygen-cation, the bond angle should be considered. For the case of TBs in LFO films, the bond angles of 131.6°, 133.5°, and 89.7° between A-O-B atoms dominate across TB I, TB II, and TBIII, respectively, when acquired from relaxed atomic models. Particularly, for B-site Li ions, which are not magnetic ions in LFO, the B-site occupation of Li ions at TB I and II is inclined to decrease FM exchange interactions between B-O-B atoms, which may result in AFM coupling across TB I and II. On the contrary, Fe deficiency exists at TB III, and the antiferromagnetic super-exchange interactions between A-O-B atoms decrease, which results in weak FM coupling dominated at TB III. In the present work, we anticipated the ferromagnetic or antiferromagnetic coupling of TBs in LFO film by first-principle calculations; furthermore, the experimental evidence to directly support magnetic coupling will be provided in future work to verify the DFT results. The occurrence of TBs with AFM coupling will weaken the saturation magnetization of the film, and the pinning of the magnetic domain walls effect induced by those antiferromagnetic TBs are likely to arise in the LFO film, resulting in a larger coercive field in the film [28]. Also, the presence and density of antiferromagnetic TBs can manipulate the effective magnetic anisotropy of magnetic film. In contrast, the TBs with ferromagnetic coupling do not decrease the spin polarization of the film [7,29]. Taking into account the magnetic coupling nature occurring across TBs in LFO film, the nano-scale TBs present intriguing prospects for utilization in advanced nano-spintronic devices, such as spin torque magnetic random-access memory.

4. Conclusions

In conclusion, understanding the interaction mechanisms of atomic structure and magnetic coupling is crucial for the field of materials science. By combining atomic-resolution STEM measurements and atomistic first-principles computations, we successfully determined the atomic structure and magnetic coupling of different TBs in LFO films. It was discovered that three types of TBs form in the LFO/STO film system, which exhibit a different atomic core structure. The atomic core structure of TBs directly affects whether the magnetic coupling across the TBs is antiferromagnetic or ferromagnetic. DFT results indicate that magnetic couplings across TB I and TB II are antiferromagnetic and that across TB III exhibit ferromagnetic. Revealing the nature of magnetic coupling across grain boundaries, as well as material interfaces can help with the development of improved magnetic materials and technologies.