Effect of the Core–Shell Exchange Coupling on the Approach to Magnetic Saturation in a Ferrimagnetic Nanoparticle
, Sergey V. Stolyar 3, Alexey A. Mokhov 3, Vladimir A. Fel’k 2, Dmitriy A. Velikanov 1 and Rauf S. Iskhakov 1Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The submitted manuscript provides a theoretical basis for analyzing the approach to magnetic saturation for a rather complicated system - an ensemble of core-shell nanoparticles with a magnetically blocked core and a spin-disordered shell. The proposed equation for this (Eq. 2) is well explained in the text and validated with micromagnetic simulations. This work will be appreciated by many scientific groups dealing with magnetic nanoparticles and will help to evaluate their effective magnetic anisotropy constant, characteristic length scales, and the strength of the core-shell exchange coupling. Thus, the manuscript can be accepted for publication in Magnetochemistry after addressing a minor comment below.
The saturation magnetization of the magnetite is written as "Ms = 480 G". Please refer to the magnetic units listed on the NIST website: https://www.nist.gov/system/files/documents/pml/electromagnetics/magnetics/magnetic_units.pdf. There is a 4Pi times difference between magnetization expressed in [G] and [emu/cm3]. I assume that authors actually meant "Ms = 480 emu/cm3". The conformation for this confusion can be found at page 7, where a specific magnetization of 92 emu/g is given. Considering magnetite density of about 5.2 g/cm3, saturation magnetization of about 480 emu/cm3 is expected with [emu/cm3] as appropriate units.
Author Response
Comment: The saturation magnetization of the magnetite is written as "Ms = 480 G". Please refer to the magnetic units listed on the NIST website: https://www.nist.gov/system/files/documents/pml/electromagnetics/magnetics/magnetic_units.pdf. There is a 4Pi times difference between magnetization expressed in [G] and [emu/cm3]. I assume that authors actually meant "Ms = 480 emu/cm3". The conformation for this confusion can be found at page 7, where a specific magnetization of 92 emu/g is given. Considering magnetite density of about 5.2 g/cm3, saturation magnetization of about 480 emu/cm3 is expected with [emu/cm3] as appropriate units.
Response: It is fixed. According to academic editor comment it was converted to SI units also. Thank you!
Reviewer 2 Report
Comments and Suggestions for Authors
This article presents a magnetic saturation equation applied to core-shell iron oxide structures and cites sufficient experimental data to confirm the universality of the equation. The experimental design of the article is scientifically sound. It is instructive for the synthesis of biocompatible core-shell iron oxide materials. It is worth noting that the biocompatible core-shell iron oxide materials cited by the authors are all non-metallic shells, but in recent years a large portion of the research has been on metallic shells such as Au, Ag, and MoS2. It is intriguing whether these materials are still applicable to this equation?
Author Response
Comment: This article presents a magnetic saturation equation applied to core-shell iron oxide structures and cites sufficient experimental data to confirm the universality of the equation. The experimental design of the article is scientifically sound. It is instructive for the synthesis of biocompatible core-shell iron oxide materials. It is worth noting that the biocompatible core-shell iron oxide materials cited by the authors are all non-metallic shells, but in recent years a large portion of the research has been on metallic shells such as Au, Ag, and MoS2. It is intriguing whether these materials are still applicable to this equation?
Response: We have no idea why limit the use of the findings of this work for particles with metal shells. Although this issue requires additional research. Given that this is quite an interesting comment, we have added the following text to the discussion.
“The data shown in Fig. 5-7 concern particles with non-metallic shells. Considering that in recent years a lot of the research has been devoted to metallic shells such as Au, Ag, it will be interesting to test the applicability and universality of equations (2) and (4) to such objects in the future.”
Thank you!
Reviewer 3 Report
Comments and Suggestions for Authors
The manuscript presented by Komogortsev et al. is an interesting work relating the LAMS with the surface effects found in magnetic nanoparticles. Overall, the organization of the manuscript is commendable, however, a few significant observations become apparent upon closer examination:
1-In line 38 and further, superparamagnetism is a regime, not a state; I would uniformize this term in the whole manuscript. Any case is incorrect. The regime, of course, will depend on competition among magnetic anisotropy and thermal energy. Please see the review Bedanta, Subhankar, and Wolfgang Kleemann. "Supermagnetism."Journal of Physics D: Applied Physics 42.1 (2008): 013001.
2-Collective magnetic nanoparticles often present narrow and broad particle size distributions; hence, it is expected to have a distribution of blocking temperatures and not only one blocking temperature, as assumed in the introduction (see line 40).
3-The micromagnetic testing section has a lack of mathematical background, plots are useful for representation of the magnetic phenomena, but details of the software packages, input files, and mathematical construction need to be added.
4-I recommend uniformizing the units for the magnetic field and saturation magnetization to kOe and emu/g. Some parts use G, while others use Oe.
Please, in lines 198, add the units for the a and b parameters.
6-Regarding the previous comment, what are these values for fit in Figure 5? Including the one for chiSG.
7- Could you please provide the correlation parameter that best fits Figure 6? R2? or chi2? Add this information to the manuscript.
Author Response
Comment 1: In line 38 and further, superparamagnetism is a regime, not a state; I would uniformize this term in the whole manuscript. Any case is incorrect. The regime, of course, will depend on competition among magnetic anisotropy and thermal energy. Please see the review Bedanta, Subhankar, and Wolfgang Kleemann. "Supermagnetism."Journal of Physics D: Applied Physics 42.1 (2008): 013001.
Response: It is fixed throughout the whole text and the good reference you mentioned was added to the review. Thank you!
Comment 2: Collective magnetic nanoparticles often present narrow and broad particle size distributions; hence, it is expected to have a distribution of blocking temperatures and not only one blocking temperature, as assumed in the introduction (see line 40).
Response: In line 40 we mean the average value of blocking temperature, as the academic editor correctly noted. We have modified this sentence by replacing "blocking temperature" with "mean blocking temperature". In this work, we do not place any emphasis on the importance of monodispersity of the particles. However, it is natural that in an experiment we always deal with an ensemble of particles, and, therefore, we measure average values.
Comment 3: The micromagnetic testing section has a lack of mathematical background, plots are useful for representation of the magnetic phenomena, but details of the software packages, input files, and mathematical construction need to be added.
Response: To fill this deficiency, the following text was added: “The total energy of the particle was presented as: , where is the exchange energy, is the magnetic anisotropy energy, is the Zeeman energy, is the magneto-dipole energy. The total energy of the system is calculated as the sum of the magnetic moments of the cells. Each equilibrium state of the magnetic system corresponds to a local minimum of the total energy functional. The exchange energy contribution from cell i is given by , where is the set consisting of the 6 nearest cells to cell i, is the exchange coefficient between cells i and j, and is the discretization step size, between cell i and cell j, is the component of reduced (normalized) magnetization vector . The anisotropy energy for cell i is given by , where , , , for reduced (normalized) magnetization and orthonormal anisotropy axes , , and . The Zeeman energy for cell i is given by , where is saturation magnetization and is an applied field. The Standard demagnetization energy term in OOMMF package, built upon the assumption that the magnetization is constant in each cell. It computes the average demagnetization field in each cell using formulae from [50,51] and convolution via the Fast Fourier Transform.”
Comment 4: I recommend uniformizing the units for the magnetic field and saturation magnetization to kOe and emu/g. Some parts use G, while others use Oe.
Response: It is fixed. According to academic editor comment it was converted to SI units also. Thank you!
Comment 5: Please, in lines 198, add the units for the a and b parameters.
Response: The information was added: “…the both and in [A/m] units”.
Comment 6: Regarding the previous comment, what are these values for fit in Figure 5? Including the one for chiSG.
Response: The information has added: “The parameters used for fitting in Fig. 5 are , , and (according to academic editor comment it was changed from ).”
Comment 7: Could you please provide the correlation parameter that best fits Figure 6? R2? or chi2? Add this information to the manuscript.
Response: The information was added: “The correlation best fit parameter R2 is 0.988.”
Author Response File: 
Author Response.pdf
Round 2
Reviewer 3 Report
Comments and Suggestions for Authors
The authors have addressed all my amendments and the article is now acceptable.
