Microstructural Modeling of the Magnetization Process in Ni2MnGa Alloy Polytwin Crystals
Round 1
Reviewer 1 Report
In this paper it is developed a microstructural model based on a micromagnetic analysis using a finite element method able to describe the physical behavior of a Ni2MnGa Heusler alloy in the presence of an applied magnetic field. The authors start from the well-known Landau-Lifshitz-Gilbert equations, write down the boundary conditions in terms of the scalar potential and finally express the weak variational problem in the Eqs.(7-8). These are the key equations to start the micromagnetic analysis that first is devoted to the study of the magnetization process of a single grain and then to the study of polycrystalline samples. This part is quite complex being considered the dependence of the average value of the magnetization for different directions of the applied magnetic field. Even though most of the formalism comes from the one developed in Ref [13], results obtained according to the micromagnetic model are novel. For the topics treated which match the aims and scopes of the journal and for the interesting results obtained, in my opinion, this manuscript could potentially deserve publication.
However, some amendments are necessary with special regard to the following comments and questions:
1 1) In the expression of the effective field it is defined a total field given by the sum of the external magnetic field and a contribution resulting from the gradient of the scalar potential: is this field the magnetostatic field generated by the volume and surface magnetic charges? It is not specified in the text but it would be helpful for an average reader.
2 2) What are the advantages of starting from the Landau-Lifshitz-Gilbert equations of motion (and not solving directly them together with the boundary conditions) but then solving the variational problem? Generally, micromagnetic models directly solve the equations of motion. Is this done only in terms of the smoothness of the problem solution? This aspect should be underlined better in the discussion.
3 3) A few more information about the simulation parameters employed in the finite element method (e.g. time step, mesh size and so on) is needed.
4 4) What do the authors mean by weak variational problem within this context?
5 5) It should be outlined in the Introduction the novelty of this work with respect to the results obtained in Ref.[13] by the same authors.
6 6) Why in Fig.2 there is a slow down of the magnetization for angles in the range between 45 and 90 angles of the external magnetic field? Is this related to the anisotropy properties?
7 7) The discussion of Figure 3 is given after the comments to Figure 4-7. I think that this could create confusion in a reader and I would suggest to move up it before those comments. Moreover, the contents of Figure 3 are mainly discussed in the relative caption and less in the main text. It is not clear to me what is really represented in Figure 3 either only the results of Ref.[21] or those results together with the ones of this work? This should be clarified.
8 8) Before Eq.(9) it is mentioned the generalized Frohlich-Kenelly formula but there is no reference to it.
9 9) Could the authors justify why in Figure 10 the best fitting magnetization via the generalized Frohlich-Kenelly formula is obtained for p = 2 and gamma = 2.6? Is there a reason for this?
1 10) How the results of the magnetization of the single grain is then used to simulate the polycrystalline phase?
1 11) What would the authors expect from a qualitative point of view if the process of detwinning is included?
12) The role of magnetoelasticity is relevant in certain structures. What would occur qualitatively if the magneto-elastic effect is not neglected?
1 13) Could the model developed be applied to other types of Heusler alloys?
Author Response
First of all, we express our great gratitude to the reviewer for the work done and the high appreciation of the manuscript of the article.
Please see the attachment with responses to comments.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
An original paper on description of behaviour of magnetic shape memory alloy Ni2MnGa in realistic polytwin configuration. As it develops the methodology I think it can be useful for all researchers interested in magnetic shape memory alloys and its publication can be recommended. The language is well understandable, I just propose several minor corrections to smoothen up.
Introduction, line 3…you can skip “occurs”, cooling will be gerund and not substantive.
Line 41, Néel (accent)
Line 43….use rather “that” if it relates to the cited work
L. 44, with the Landau…
L. 58…..in the present paper….(instead of “in this paper”)
L. 59 skip “the” before the chemical formula
l. 66 and 67 avoid using “constant” for “parameter” at exchange. I think at anisotropy it is so common that it can stay. Mju_zero in permeability of vacuum, I never heard “magnetic constant”.
Author Response
First of all, we express our great gratitude to the reviewer for the work done and the high appreciation of the manuscript of the article. We have made all the proposed corrections to the text of the article. All changes made to the new version of the article are highlighted in color.
Round 2
Reviewer 1 Report
First, I would like to thank the authors for carefully addressing all my previous comments and questions. In the present form, the manuscript is even more readable and the novelty with respect to previous works is more evident. The manuscript deserves publication in Magnetochemistry.
