FMR Damping in Thin Films with Exchange Bias

Round 1

Reviewer 1 Report

Chechenin et al. in this manuscript discuss different mechanisms which determine FMR damping in bilayer ferromagnetic/antiferromagnetic (F/AF and AF/F) exchange bias systems. Authors conclude that samples have the different LW because of a significant difference in microstructure of F-layer. Overall, it is an interesting study and is fit for the journal. Following are the some of my concerns:

1. derivative of the microwave absorption spectra should be reported.
2. If possible, linewidths should be obtained by fitting the derivative of the microwave absorption spectra
3. Line 141 “AFM study of our samples….” Which ones? Mention the figure number.
4. Authors should report AFM
5. Why were these film thicknesses chosen? What about the microstructures at other film thicknesses?

Author Response

Response to the Referee1

Dear Referee,

Thank you for your valuable remarks. We hope that we answered all your remark. Below we listed the answers. 

1. derivative of the microwave absorption spectra should be reported.

A: We have included experimental FMR spectrum fitted by Lorentzian  in Fig. 2 of revised MS.

2. If possible, linewidths should be obtained by fitting the derivative of the microwave absorption spectra

A: LW was obtained from fitting of derivative of FMR lines. The text was added/modified in Sec. 2:

“…The resonance magnetic field, Hr, and LW, ΔH_FMR, were obtained from the Lorentzian function fit of derivative of the microwave absorption spectra, a representative curve is given in Figure 2. The other magnetic characteristics of the samples entered in Eq. (4), the uniaxial anisotropy field, the exchange bias field and geometry angles shown in Figure 1 were obtained from the fitting of the angular dependences (AD) of the resonant magnetic field, Hr(j_H). A more complete account of the results is given in [13].

3. Line 141 “AFM study of our samples….” Which ones? Mention the figure number.

А: We included the AFM scan picture as a Fig. 3, and corresponding text below this figure:

“…The topography of the sample surface is measured using the atomic-force micro-scope. The representative picture of the surface scan is given in Figure 3…”

We also refer to Fig. 3 in the text in Line 142 of the original MS. The results of AFM study are shown in fig.4(c) (2(c) in original MS).

4. Authors should report AFM

A: See answer to remark 3.

5. Why were these film thicknesses chosen? What about the microstructures at other film thicknesses?

A: Our purpose was to to compare properties of two sets of samples with ferromagnetic/antiferromagnetic layers with opposite order of F and AF layers deposition with the AF thickness as the only variable.  The reasoning was given also in the piece of added text in Sec.4.

“…The choice of t_AF thickness was dictated by an interest of practical devices, like GMR sensors. Smaller t_AF give normally lower exchange bias. Besides, our experience shows a much more frustrated properties of F/AF system at t_AF below 10 nm [3].

Best regards,

Nikolay Chechenin

e-mail: [email protected]

Author Response File: Author Response.docx

Reviewer 2 Report

Reviewer remarks

On Manuscript ID: magnetochemistry-1188269,

Title: FMR Damping in Thin Films with Exchange Bias

Authors: Nikolay G. Chechenin *, Irina O. Dzhun, Georgy V. Babaytsev, Mikhail

1. Kozin, Alexey V. Makunin, Irina L. Romashkina

Dear authors.

I studied your manuscript, and I have comments on the text and content of the material you submitted.

First of all, the introduction lacks the motivation for novelty and the purpose of this work. Secondly, the text, some formulas and references should be corrected.

Some of the comments are presented below:

Line 35. This formula does not contain the contribution to the effective field from the demagnetizing fields of the sample, which is important for thin ferromagnetic films. However, it appears in formula (3)!

Line 38. Dear Authors! If we remove this contribution (H_MS) from the effective field (2), then the precession will still be damped due to the second dissipative term in the equation (1).

Line 47. Dear Authors! "Greater than" or "less than" ratios are typically used for scalars rather than vectors.

Line 52. A sign correction is required in front of the anisotopy field H_K.

Line 191. There are no Figures with this number in the manuscript.

Line 199. There is an error in formula (7)! See ref. [33] - Hoffmann, H. Theory of Magnetization Ripple IEEE Trans on Mag 1968, MAG-4, 32-38

Line 201. There is no such symbol (α) in formula (7)!

Line 216. Dear Authors! You should pay attention to newer and more detailed numerical studies of the effect of crystallite size on the magnetic microstructure and high-frequency properties of nanocrystalline thin ferromagnetic films. They are published in the works:

1. A.V. Izotov, B.A. Belyaev, P.N. Solovev, N.M. Boev, Grain-size dependence of magnetic microstructure and high-frequency susceptibility of nanocrystalline thin films: A micromagnetic simulation study, J. Magn. Magn. Mater., 529 (2021), 167856. https://doi.org/10.1016/j.jmmm.2021.167856
2. A.V. Izotov, B.A. Belyaev, P.N. Solovev, N.M. Boev, Numerical calculation of high frequency magnetic susceptibility in thin nanocrystalline magnetic films, Physica B 556 (2019) 42–47, https://doi.org/10.1016/j.physb.2018.12.006.
3. B.A. Belyaev, N.M. Boev, A.V. Izotov, P.N. Solovev, Study of peculiarities of the microwave absorption spectrum of nanocrystalline thin magnetic films, Russ. Phys. J. 61 (2019) 1798-1805, https://doi.org/10.1007/s11182-019-01603-4.
4. A. Bachleitner-Hofmann, B. Bergmair, T. Schrefl, A. Satz, D. Suess, Soft magnetic properties of thin nanocrystalline particles due to the interplay of random and coherent anisotropies, IEEE Trans. Magn. 53 (2017) 1-6, https://doi.org/10.1109/ TMAG.2017.2695580.
5. S.V. Komogortsev, V.A. Fel'k, R.S. Iskhakov, G.V. Shadrina, Micromagnetism in a planar system with a random magnetic anisotropy and two-dimensional magnetic correlations, J. Exp. Theor. Phys. 125 (2017) 323-332, https://doi.org/10.1134/S1063776117070196.

Line 230.  Error in the formula! See ref. [22] - Hoffmann, H. Magnetic properties of thin ferromagnetic films in relation to their structure. Thin Solid Films 1979, 58, 223-233.

Line 237. In this place of the manuscript, the previously not introduced designation N_Z first appeared.

Line 266. Dear Authors! Your explanation looks plausible enough. However, the work does not provide any evidence in favor of this conclusion. Figures 3 and 4 show the results from completely different works, as well as for other samples. Therefore, either a more weighty argument in favor of this conclusion is required, or in the conclusion it is necessary to rely on an assumption, and not on a statement.

In conclusion, I believe that the manuscript requires a major correction.

Comments for author File: Comments.pdf

Author Response

Response to the Referee2

Dear Referee,

Thank you very much for your valuable remarks. Below there is a list of your remarks and our answers. I hope that we answered all your remarks.

R: First of all, the introduction lacks the motivation for novelty and the purpose of this work.

A: Thank you for your remark. We added the text to the Introduction:

“Motivation of the paper was to compare properties of two sets of samples with ferromagnetic/antiferromagnetic layers with opposite order of F and AF layers deposition. A single variable of deposition was the thickness of the AF layers. In spite of identical other conditions of deposition, we could expect different growth mechanisms and different resulting magnetic and structural properties of the F-layers, even for the same layer thickness. The FMR is an excellent probe to test these properties. Below we present the results and the analysis of the data. Specially, we concentrate on the variation of LW because it contains an important information on dynamics of the high frequency response of the tested structure, and important information about influence of different factors on the FMR LW.”

R: Secondly, the text, some formulas and references should be corrected.

A: The corrections are commented below

Some of the comments are presented below:

R: Line 35. This formula does not contain the contribution to the effective field from the demagnetizing fields of the sample, which is important for thin ferromagnetic films. However, it appears in formula (3)!

A: Thank you! Certainly, we have taken into account demagnetizing field, following well known derivation of FMR equations to obtain resonance condition parameters. We have modified eq. (2) in the revised MS to include demagnetizing field:

„H_eff = H_D + H + H_K + H_EB + H_MS ,                                 (2)

where H_D is a demagnetizing field, H is an applied DC-field …..”

R: Line 38. Dear Authors! If we remove this contribution (H ) from the effective field (2), then the precession will still be damped due to the second dissipative term in the equation (1).

A: Certainly, we agree with the referee’s statement. It was also stated in the paragraph, starting with the Line 54 of original MS. For better understanding what we wanted to say we have modified the text in Lines 38, 39 as

“The H_MS is usually neglected when considering the collective spin dynamics. In our case, the geometry of the FMR experiment…”

R: Line 47. Dear Authors! "Greater than" or "less than" ratios are typically used for scalars rather than vectors.

A: Thank you! We have set the absolute magnitudes of vectors to compare in Lines 47, 48

“…for weak fields |H_EB+H_K+ H_MS| <H<<4pMs gives the relation…”

R: Line 52. A sign correction is required in front of the anisotropy field H .

A: Thank you! It was misprint. The plus sign before H_K was changed to minus in Eq. (4)

“….Hr= (w/g)² /(4pM_S) - H_EB cos(j_H - β) - H_Kcos2j_H    (4)…”

R: Line 191. There are no Figures with this number in the manuscript.

A: Thank you, it was misprint! The text was corrected to

“…Figures 4(a) and (b),…”

R: Line 199. There is an error in formula (7)! See ref. [33] -

Hoffmann, H. Theory of Magnetization Ripple IEEE Trans on Mag 1968, MAG-4, 32-38

A: No, the eq.(7) in the MS is the same as eq. (10) in ref. [33] with some small arithmetic transformation and substitutions of variables notations in consistence with those used in the MS text.

R: Line 201. There is no such symbol (α) in formula (7)!

A: Thank you, it was misprint. The a was changed to j_H, as in eq. (7);

“…j_H is the angle…”

R: Line 216. Dear Authors! You should pay attention to newer and more detailed numerical studies of the effect of crystallite size on the magnetic microstructure and high-frequency properties of nanocrystalline thin ferromagnetic films. They are published in the works:

1. A.V. Izotov, B.A. Belyaev, P.N. Solovev, N.M. Boev, Grainsize dependence of magnetic microstructure and highfrequency susceptibility of nanocrystalline thin films: A micromagnetic simulation study, J. Magn. Magn. Mater., 529 (2021), 167856. https://doi.org/10.1016/j.jmmm.2021.167856
2. A.V. Izotov, B.A. Belyaev, P.N. Solovev, N.M. Boev, Numerical calculation of high frequency magnetic susceptibility in thin nanocrystalline magnetic films, Physica B 556 (2019) 42–47, https://doi.org/10.1016/j.physb.2018.12.006.
3. B.A. Belyaev, N.M. Boev, A.V. Izotov, P.N. Solovev, Study of peculiarities of the microwave absorption spectrum of nanocrystalline thin magnetic films, Russ. Phys. J. 61 (2019) 1798-1805, https://doi.org/10.1007/s11182-019-01603-4.
4. A. Bachleitner-Hofmann, B. Bergmair, T. Schrefl, A. Satz, D. Suess, Soft magnetic properties of thin nanocrystalline particles due to the interplay of random and coherent anisotropies, IEEE Trans. Magn. 53 (2017) 1-6, https://doi.org/10.1109/ TMAG.2017.2695580.
5. S.V. Komogortsev, V.A. Fel'k, R.S. Iskhakov, G.V. Shadrina, Micromagnetism in a planar system with a random magnetic anisotropy and two-dimensional magnetic correlations, J. Exp. Theor. Phys. 125 (2017) 323-332, https://doi.org/10.1134/S1063776117070196.

A: Thank you for your information. Some of references are fresh and useful, indeed. We have inserted two references, more relevant to the MS:

” 35. Izotov, A.V.; Belyaev, B.A.; Solovev, P.N.; Boev, N.M. Grain-size dependence of magnetic microstructure and high-frequency susceptibility of nanocrystalline thin films: A micromagnetic simulation study. J. Magn. and Magn. Mat. 2021, 529, 167856, https://doi.org/10.1016/j.jmmm.2021.167856

36. Belyaev, B.A.; Boev, N.M.; Izotov, A.V.; Solovev, P.N. Study of peculiarities of the microwave absorption spectrum of nanocrystalline thin magnetic films, Russ. Phys. J. 61 (2019) 1798-1805, https://doi.org/10.1007/s11182-019-01603-4”

R: Line 230. Error in the formula! See ref. [22] - Hoffmann, H. Magnetic properties of thin ferromagnetic films in relation to their structure. Thin Solid Films 1979, 58, 223-233.

A: No, the eq. (9) is correct! The eq. (8) in [22], you refer to, is a particular case of (9) in the MS for the case of j_H = 0 and 90⁰.

R: Line 237. In this place of the manuscript, the previously not introduced designation N first appeared.

A: Thank you! The Nz value is introduced in the following line as

“where N_z=4p is the demagnetizing factor for thin film, H_eff can be generalized…”

R: Line 266. Dear Authors! Your explanation looks plausible enough. However, the work does not provide any evidence in favor of this conclusion. Figures 3 and 4 show the results from  completely different works, as well as for other samples. Therefore, either a more weighty argument in favor of this conclusion is required, or in the conclusion it is necessary to rely on an assumption, and not on a statement.

A: You are right, thank you! We changed the conclusion to assumption. It is more correct, we agree.

“…. We proposed that the TS and BS samples…”

In conclusion, we would like to thank you for their useful remarks.

Best regards,

Nikolay Chechenin

e-mail: [email protected]

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I have no comments on the revised version of the manuscript.

Author Response

Reply to Remark2
R: at lines 51,52 an equality is written as the  condition   "for weak fields". If the fields are positive, the module sign is not necessary. If the fields may be negative, then the conditions should be written for each field with module sign.  
A: Thank you for the remark! The inequality in the MS in the left side is written for absolute values of the sum of vector fields to compare with absolute values of H and 4piMs. You are right, in our case the fields are weak enough to be written as the sum of their absolute values. Nevertheless, it would give a confusion with Eqs. (3,4) where vector nature of magnetic fields is reflected in cosines terms. So I would prefer to keep the inequality in its original form.   

Author Response File: Author Response.pdf