The Influence of Thickness on the Magnetic Properties of Nanocrystalline Thin Films: A Computational Approach
Round 1
Reviewer 1 Report
Please see the attached file.
Comments for author File: 
Comments.pdf
Author Response
Reviewer: Is the computational part based on a model equation? If yes,
– which equations have been solved?
– Is it linear or nonlinear?
– which technique is used to solve the equation?
Authors: Suggestions were accepted. A more detailed introduction to model equation was added in the Materials and Methods section:
The model equation used is known as the Hamiltonian and it corresponds to the observable Energy. This function describes the state of an element (spin moment) in the physical system in terms of its magnetic parameters, under the temperature constrain. The solution of the system is a linear combination of individual states for each element of the system.
The Monte Carlo method is used to generate spin fluctuations in the system; these are accepted or rejected according to the Metropolis algorithm. The range of energy fluctuations is given by transitions between states of minimum energy or by the probabilities of changing to higher energy given by the expression exp(ΔE/ KBT) compared to a random number between 0 and 1. Here, ΔE is the energy change given by the spin fluctuation and KB is the Boltzmann constant. These fluctuations cause the system to transit through the configuration space.
Reviewer: The authors mentioned using Monte Carlo simulation.
– which distribution of random variables (with which range) is used?
– what is the effect of the variation?
The range of fluctuations depends on the magnitude of the exchange, dipole, anisotropy, and external field parameters in competition with temperature. However, in our simulations these parameters remain constant according to the experimental range. In our case, the variation has been made on the thickness of the film. This variation implies changes in the structural configuration of the system that affects its energy, and consequently magnetic behavior.
Reviewer: If not, how the mentioned boundary condition (period) is applied?
Authors: A more detailed explanation about PBC was added in the Materials and Methods section.
Periodic boundary conditions (PBC) were implemented in the xy plane where spin copies are located by means of replicas of the sample, then, the spins are placed at the edges consider interactions in all directions under the limits of the thickness.
Reviewer: The authors are asked to suggest recently published papers in nanomaterials and nanostructure that used Monte Carlo simulation. It will help the readers to have more idea regarding the computations. The following related papers should be discussed in the manuscript.
Authors: Suggestion was accepted. More recent references were introduced with the next paragraph:
on the other hand, the Monte Carlo method continues to be used successfully to explain and predict the properties of materials at the nanoscale. For example, in [27] [28] a Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system is evaluated and in [29] a computational technique based on Bayesian estimation is used to determine the physical parameters of the nanowire field-effect sensors and the properties of the analyte molecules.
Between them:
[27] AmirrezaKhodadadian, MaryamParvizi, and ClemensHeitzinger, “An adaptive multilevel Monte Carlo algorithm for the stochastic drift–diffusion–Poisson system,” vol. 368, p. 113163, 2020.
[28] Amirreza Khodadadian, Leila Taghizadeh, and Clemens Heitzinger, “Three-dimensional optimal multi-level Monte–Carlo approximation of the stochastic drift–diffusion–Poisson system in nanoscale devices,” Journal of Computational Electronics, vol. 17, pp. 76–89, 2018.
[29] Amirreza Khodadadian, Benjamin Stadlbauer, and Clemens Heitzinger, “Bayesian inversion for nanowire field-effect sensors,” Journal of Computational Electronics, vol. 19, pp. 147–159, 2019.
Reviewer 2 Report
The paper is interesting and, with some additions, it certainly deserves to be published. In particular:
1) Some formulas are not original, so I ask that each of them be associated with a relevant bibliographic reference.
2) The punctuation close to the mathematical formulas is not entirely correct. Please read the text carefully and correct any inaccuracies.
3) (6) is it experimental or is it mathematically obtainable? Please specify.
4) Perhaps a supplementary comment to (9) would be desirable.
5) The work presented in the paper is certainly well done and well structured. However, I suggest to the authors to insert at least one sentence in the text that highlights the problem of the behavior of the material in the vicinity of the pre-yield zone of the material where solid and fluid phases could co-exist in which the rheology of the material undergoes evident behavioral changes. Furthermore, I suggest that the authors include the following relevant works in the bibliography:
doi: 10.1515/jnetdy.2002.023.1
doi: 10.1109/TMAG.2020.3032892
doi: 10.1007/s00161-004-0185-1
doi: 10.1016/j.jestch.2018.07.019
doi: 10.1016/j.ijnonlinmec.2019.103288
Author Response
Reviewer: Some formulas are not original, so I ask that each of them be associated with a relevant bibliographic reference.
Authors: Suggestion was accepted. The next references were introduced:
[8] Ralph Skomski, Simple Models of Magnetism. Oxford University Press, 2008.
[24] P. Bruno, “Physical origins and theorical models of magnetic anisotropy,” in IFF-Ferienkurse, Edited by P.H. Dederichs, P. Grünberg, and W. Zinn., Forschungszentrum Jülich, 1993, p. 24.1-24.28.
[26] C. Santamaria and H. T. Diep, “Effect of Dipolar Interactions in Magnetic Thin Films,” IEEE Trans. Magn., vol. 34, no. 4, 1998.
Reviewer: The punctuation close to the mathematical formulas is not entirely correct. Please read the text carefully and correct any inaccuracies.
Authors: Suggestion was accepted. We found some mistakes in punctuation.
Reviewer: (6) is it experimental or is it mathematically obtainable? Please specify.
Authors: The referee is right. A clarification is necessary, the equation is proposed by us like a general description according to reports of the most common magnetic elements, Ni, Fe and Co. The phrase in this paragraph was changed by:
The relationship given by eq. (6) is proposed in this work, considered in agreement with experimental reports
Reviewer: Perhaps a supplementary comment to (9) would be desirable.
Authors: Suggestion was accepted. The next phrases were introduced:
Dipole interactions are too weak at short range to explain spontaneous magnetization in a material. However, they are important to defining demagnetization effects due to sample shape. In the case of systems compose by particles, dipolar interaction becomes relevant due to the correlation by exchange interaction is interrupted. In some cases, is enough to obtaining alignments of vortex type in isolated nanodisks
Reviewer: The work presented in the paper is certainly well done and well structured. However, I suggest to the authors to insert at least one sentence in the text that highlights the problem of the behavior of the material in the vicinity of the pre-yield zone of the material where solid and fluid phases could co-exist in which the rheology of the material undergoes evident behavioral changes. Furthermore,
Authors: Suggestion was accepted. The next phrases were introduced:
Magneto-rheological fluids are a set of soft magnetic particles whose elastic limit increases in the presence of an external magnetic field. In the focus of this study, the dipole interaction plays an important role, mainly in the transition from the absence of fields, where the rearrangement is spontaneous, to redirection by the dynamics of moments with external effects. Some important works on the subject can be consulted at[27] [28] [29] [30] [31]
The next references were introduced:
[27] K. C. Chen and C. S. Yeh, “Extended Irreversible Thermodynamics Approach to Magnetorheological Fluids,” J. Non-Equilib. Thermodyn., vol. 26, pp. 355–372, 2001.
[28] Mario Versaci, Antonino Cutrupi, and Annunziata Palumbo, “A Magneto-Thermo-Static Study of a Magneto-Rheological Fluid Damper: A Finite Element Analysis,” IEEE Transactions on Magnetics, vol. 57, p. 4600210, 2021.
[29] I. A. Brigadnov and A. Dorfmann, “Mathematical modeling of magnetorheological fluids,” Continuum Mechanics and Thermodynamics, vol. 17, pp. 29–42, 2005.
[30] KorayÖzsoy, “A mathematical model for the magnetorheological materials and magneto reheological devices.”
[31] MarioVersaci and AnnunziataPalumbo, “Magnetorheological Fluids: Qualitative comparison between a mixture model in the Extended Irreversible Thermodynamics framework and an Herschel–Bulkley experimental elastoviscoplastic model,” International Journal of Non-Linear Mechanics, vol. 118, p. 103288, 2020.
Round 2
Reviewer 1 Report
The authors adequately considered the requested comments by the reviewer. The paper is recommended for publication.
