High-Frequency Magnetic Field Energy Imaging of Magnetic Recording Head by Alternating Magnetic Force Microscopy (A-MFM) with Superparamagnetic Tip

Round 1

Reviewer 1 Report

In this paper, authors report the use of A-MFM with superparamagnetic tips for imaging HF magnetic fields from PMR poles in a broad frequency range. The study is clearly presented and easy to follow. Specific comments can be found below:

1. Could the authors more clearly elaborate the applicability of this system (the last paragraph of introduction)? Is it only useful for PMR systems or could it be used for other magnetic materials?

2. Have the author been able to generate images using this technique or is this technique still purely theoretical? Although a broad frequency range has been investigated, could the claims that losses in image quality don't occur be supported by actual images? The only images are the ones of the out-of-plane signal near the main pole. Is this enough to draw such conclusion?

3. Is this technique applicable only for imaging or could some local magnetic properties at the nanoscale be determined? For example, MFM is already used for determination of magnetic momentum. Could something similar be achieved with this system?

4. In the final chapter of the introduction, the authors claim that this experiment could be important in other fields. Particularly, they mention magnetic resonance. However, it's known that too high magnetic fields can be harmful for human health. Thus, could you draw a connection between the conditions used here and the ones that would be safe for wider use?

5. Please provide relevant references in the paragraph 37-41.

Some spell-check notes:
- The last figure before the conclusion should be Fig 4, but is denoted Fig 1.
- Check for double spaces throughout the article
- In the funding section the sentence is not finished.
- Line 31: abbreviation SP is already introduced, so there's no need to introduce it again

 

Author Response

We are happy to thank the reviewers for their attention and valuable comments. We believe that these remarks can help us to correct errors and clarify the unclear points and make the paper better and more readable.

 

Reviewer 1:

In this paper, authors report the use of A-MFM with superparamagnetic tips for imaging HF magnetic fields from PMR poles in a broad frequency range. The study is clearly presented and easy to follow. Specific comments can be found below:

 

1. Could the authors more clearly elaborate the applicability of this system (the last paragraph of introduction)? Is it only useful for PMR systems or could it be used for other magnetic materials?

Authors: This system of A-MFM with superparamagnetic tip is useful not only to detect AC magnetic field but also to detect DC magnetic field of the sample, when the source of external AC magnetic field is placed beneath the sample for measurement. For hard magnets, DC magnetic field was imaged with high spatial resolution while measuring AC magnetic field was applied perpendicularly to a sample surface. The system enables the magnetic domain observation for a hard magnet with rough sample surface.  [Y. Cao, Y. Zhao, J. Tang, H. Du, Y. Zhou, H. Saito, Ultramicroscopy 212 (2020) 112980]

Here the important point of SP tip is that its magnetization is parallel to AC magnetic field. In this case, we applied uniform AC magnetic field to SP tip and thus the direction of AC magnetic field in SP tip is the same. On the other hand, magnetic recording head in the present study generates nonuniform AC magnetic field in the tip.  The intensity and the direction of the head magnetic field varies along the SP tip, with the maximal vertical magnetization in the tip end, because of the head element is very small.

 

2. Have the author been able to generate images using this technique or is this technique still purely theoretical? Although a broad frequency range has been investigated, could the claims that losses in image quality don't occur be supported by actual images? The only images are the ones of the out-of-plane signal near the main pole. Is this enough to draw such conclusion?

Authors: The images of Fig.3 a-e are the data processed images by using measured spatial Lock-in X signal image and Lock-in Y signal image according to the equations in the manuscript [2]. Of course, the manual adjustment of phase in Lock-in amplifier is possible. These two methods give the same image.

The losses in image quality in high frequency was generated by decreasing the AC current to the head due to the mismatch of electrical impedance in distributed parameter circuit. That is also described in the text (lines 169 and 170), so the images were normalized for comparison.

The present images in Fig.3 a-e correspond to magnetic field energy images, which is the square of magnetic field. So, the information of magnetic field direction is lost. But the center of the main pole of perpendicular magnetic recording head is expected to generate out-of-plane field by the configuration and device purpose. Our observed in-plane signal images were also very weak.

3. Is this technique applicable only for imaging or could some local magnetic properties at the nanoscale be determined? For example, MFM is already used for determination of magnetic momentum. Could something similar be achieved with this system?

Authors: For magnetic materials, MFM detects magnetic field from magnetic charges which generate from the discontinuity of magnetization, such as at a sample surface, inside a sample.

Conventional MFM detects magnetic field in the form of magnetic field derivative. But MFM signal depends on the direction of tip magnetization, which is hard to control for ferromagnetic tip. Therefore, the interpretation of magnetic domain structure is sometimes not easy without the information of tip moment.

The present system also detects magnetic field in the form of magnetic field energy derivative. But the signal has maximum and good reliability because the tip has no hysteresis and the tip moment direction is always parallel to AC magnetic field in SP tip. The well-conditioned images seem to be helpful to interpret the domain structure of magnetic materials.

 

4. In the final chapter of the introduction, the authors claim that this experiment could be important in other fields. Particularly, they mention magnetic resonance. However, it's known that too high magnetic fields can be harmful for human health. Thus, could you draw a connection between the conditions used here and the ones that would be safe for wider use?

Authors:  We used standard PMR head from commercial HDD. Indeed, magnetic recording requires strong fields. However, these fields are localized and decay with distance  as 1/r function, which makes them safe enough for people. Too high fields require large currents, which could burn the PMR head itself. Moreover, amplitude modulation used in our experiment decreases the total power and makes the conditions safer.

5. Please provide relevant references in the paragraph 37-41.

Authors: We added the following references:

8. Balaev, D.A.; Stolyarc, S.V.; Knyazev, Yu.V; Yaroslavtsev, R.N.; Pankrats, A.I.; Vorotynov, A.M.; Krasikov, A.A.; Velikanov, ; Bayukov, O.A.; Ladygina, V.P.; Iskhakov, R.S. Role of the surface effects and interparticle magnetic interactions in the temperature evolution of magnetic resonance spectra of ferrihydrite nanoparticle ensembles. Results Phys. 2022, 35, 105340.
9. Sadat, M.E.; Bud’ko, S.L.; Ewing, R.C.; Xu, H.; Pauletti, G.M.; Mast, D.B.; Shi, D. Effect of dipole interactions on blocking temperature and relaxation dynamics of superparamagnetic iron-oxide (Fe₃O₄) nanoparticle systems. Materials 2023, 16(2), 496.
10. Slay, D.; Cao, D.; Ferré, E.C.; Charilaou, M. Ferromagnetic resonance of superparamagnetic nanoparticles: The effect of dipole–dipole interactions. Appl. Phys. 2021, 130, 113902.
11. Song, N.N.; Yang, H.T.; Liu, H.L.;. Ren, X.; Ding, H.F.; Zhang, X.Q.; Cheng, Z.H. Exceeding natural resonance frequency limit of monodisperse Fe3O4 nanoparticles via superparamagnetic relaxation. Rep., 2013, 3, 3161.

 

Reviewer 2 Report

1. The submitted paper reports an incremental advance over the papers bunch published by the authors, see Refs. [1-6] in the citation. Moreover, whereas Refs. [1-3] describe using ferromagnetic tips, Refs. [4,5] consider the use of superparamagnetic ones. Under this circumstance, authors should thoroughly reconsider the Introduction to substantiate the article's novelty.

2. The math exposed in the paper, viz. Eqs. (1), and (2) appear in most of the self-cited papers, so what is new in this regard?

3. The experimental setup, Figure 1., is principally the same as in the previous works.

4. There are a few rather physically meaningless sentences in the text,e.g., in line 40: "Particle size, shape and orientation dispersion, additionally broadens the ferromagnetic resonance area." This is concurrently vague and wrong in terms of the English language. Another example is seen in line 37: "In SP materials, ferromagnetic resonance occurs in a wide region of HF ..." In the article, HF is the abbreviation of "high frequency", so again the sentence is a bit vague.

5. In line 95, "... near sample surface..." would be "... near the sample surface...". In line 127, "... PLL (phase locked loop circuit) ..." the abbreviation goes before that it abbreviated but it should be vice versa

6. The specificity of the magnetic resonance in the superparamagnets should be outlined in more detail. 

Author Response

We are happy to thank the reviewers for their attention and valuable comments. We believe that these remarks can help us to correct errors and clarify the unclear points and make the paper better and more readable.

 

Reviewer 2:

1. The submitted paper reports an incremental advance over the papers bunch published by the authors, see Refs. [1-6] in the citation. Moreover, whereas Refs. [1-3] describe using ferromagnetic tips, Refs. [4,5] consider the use of superparamagnetic ones. Under this circumstance, authors should thoroughly reconsider the Introduction to substantiate the article's novelty.

Authors: Previous A-MFM studies were performed at low frequency current, while this work studies high frequency ones. We changed the 2^nd paragraph to specify the novel points.

“However, A—MFM has been previously used only at low frequencies, because frequency modulation occurs in a limited frequency interval. To circumvent this limitation, here we propose the low frequency amplitude modulation of high-frequency (HF) current. The SP tip is expected to have a particular advantage for detecting HF magnetic field, because SP materials have better magnetic response in HF magnetic field region, comparing with that of ferromagnetic tips [7].”

2. The math exposed in the paper, viz. Eqs. (1), and (2) appear in most of the self-cited papers, so what is new in this regard?

Authors: They might look similar, however, previously we used magnetic field without amplitude modulation H=H₀cos(ωt), while now we use amplitude modulated field H=H₀(1+αcos(ω_mt))cos(ω_ct)  with the modulation depth α. Thus, the Eq (1) is new. Some other equations, such as Eq (2), were often used previously, but they are needed to understand the calculations using the new formula.

3. The experimental setup, Figure 1., is principally the same as in the previous works.

Authors: The setup is based on previous works, but here it includes amplitude modulation system. We added it to this work to avoid confusion.

4. There are a few rather physically meaningless sentences in the text,e.g., in line 40: "Particle size, shape and orientation dispersion, additionally broadens the ferromagnetic resonance area." This is concurrently vague and wrong in terms of the English language. Another example is seen in line 37: "In SP materials, ferromagnetic resonance occurs in a wide region of HF ..." In the article, HF is the abbreviation of "high frequency", so again the sentence is a bit vague.

Authors: We thank the reviewer for valuable comment. We removed the sentence in line 40 and modified that in 37 as:

“In SP materials, ferromagnetic resonance occurs in a broad frequency region because nanoparticles contain significant amount of surface atoms with distorted coordination and different properties [8], compared to the bulk. Next reason is that each nanoparticle inside SP tip coating is affected by nonuniform magnetic field from thermally agitated neighboring nanoparticles, which affects resonance frequency [9,10]. This reason is especially important in our case because of the significantly high content of superparamagnetic particles inside the matrix [6].”

5. In line 95, "... near sample surface..." would be "... near the sample surface...". In line 127, "... PLL (phase locked loop circuit) ..." the abbreviation goes before that it abbreviated but it should be vice versa

Authors: We corrected it, thanks for attention.

6. The specificity of the magnetic resonance in the superparamagnets should be outlined in more detail.

Authors: We changed the lines 37-50 as following:

“The SP tip is expected to have a particular advantage for detecting HF magnetic field, because SP materials have better magnetic response in HF magnetic field region, comparing with that of ferromagnetic tips [7]. In SP materials, ferromagnetic resonance occurs in a broad frequency region because nanoparticles contain significant amount of surface atoms with distorted coordination [8], compared to the bulk. Next reason is that each nanoparticle inside SP tip coating is affected by nonuniform magnetic field from thermally agitated neighboring nanoparticles, which affects resonance frequency [9.10]. This reason is especially important in our case because of the significantly high content of superparamagnetic particles inside the matrix [6]. The total magnetic response is a superposition of all nanoparticle contributions. In the SP materials, the blocking resonance frequency can exceed the ferromagnetic resonance frequency, which is caused by the intrinsic magnetocrystalline anisotropy. So, with the particle size decrease, SP susceptibility may be kept in GHz range  [7–11].”

 

 

 

Round 2

Reviewer 2 Report

In my opinion, in the revised manuscript the authors have met all items of my critique. I think that the paper can be published in the present revised form