Origin of Multiferroism of β-NaFeO₂

Round 1

Reviewer 1 Report

Understanding the mechanism behind the multiferroicity of a particular material, at room temperature, is of great relevance for the development of functional materials for practical applications.  b-NaFeO₂  compound, which is a ferroelectric and weak ferromagnetic compound with ordering temperatures above room temperature,  has the potential to become a good candidate for applications in spintronics.

I consider this work as relevant for the materials science community, as the first theoretical study of the magnetoelectric (ME) coupling in  b-NaFeO₂  which nicely correlates the ME properties with its crystalline structure. The low stability against humidity and CO₂ could be a drawback that has to be considered for the performance of experimental measurements.

Author Response

Thanks for the the positive review

Reviewer 2 Report

This manuscript is a theoretical work on multiferroism in β-NaFeO₂, reporting simulation results on the temperature and magnetic field dependences of magnetisation and polarization. The manuscript can be considered for publication if its text is clarified for general reader.

 

Term dielectric constant should be changed for relative dielectric permittivity, since it is not constant indeed.

Sentences like “Only the α and β phases show ferroelectricity [4] and [1], respectively.” and “β-NFO thin films are growth on ZnO substrates by Bakaimi et al. [9].” should be rephrased to make their message more clear.

Definition of such parameters of Eq. 1 as J, K, g and μ_B should be also clarified.

References are needed for sentences like “This means that at TFEC =1372 K there is a structural phase transition from a paraelectric P41212 centrosymmetric tetragonal phase into a non-centrosymmetric orthorhombic structure Pn21a. This is a phase transition of displacive type.” Moreover, it looks contradictory that the FE Curie temperature jumps from 1373 to 1372 K and back along the manuscript.

Definition of parameter β in Eq. 8 is missing as well, while it is also unclear whether the parameter β keep the same definition in Eqs. 12 and 15. Definitions of parameter k_B in Eq. 10 and parameter N in Eq. 11 should be also provided.

It is also unclear what are the meanings, values and units used by the authors for parameters k_B, z and Tc in equation Jx = 3kBTC=(zS(S +1)). Additionally, using Jx, a, b, and c values listed in the manuscript, Jy and Jz values should be rather 17.49 and 9.97, respectively, but not 17.46 and 9.72.

In sentence “With τ = 0.003°, i.e. sin τ ~ τ we observe d = -√2 τ J = 0.27 K.”, the authors have to indicate the reference for τ = 0.003° and to provide used value for J.

In the next sentence, definitions and values for β_c and E_i are missing as well.

Parameters k, E, α, β, γ, δ of Eq. 15 need to be defined also.

Finally, English of the manuscript has to be improved.

 

As a result, current manuscript can be considered for publications only when revised in precise way with all the requested details and clarifications.

Author Response

Reviewer 2:

Dear Reviewer

We are very grateful for the positive referee’s report and the helpful comments. The changes which are made in the revised version according to you (marked red in the text) are the following:

 

1. “Term dielectric constant should be changed for relative dielectric permittivity, since it is not constant indeed.” We have changed dielectric constant with relative dielectric permittivity. 2. “Sentences like “Only the α and β phases show ferroelectricity [4] and [1], respectively.” and “β-NFO thin films are growth on ZnO substrates by Bakaimi et al. [9].” should be rephrased to make their message more clear.” The two sentences are rephrased as “Only the α and β phases show ferroelectricity [1,4].”,  “β-NFO thin films growth on ZnO substrates are studied by Bakaimi et al. [9].” and we hope that they are now clearer. 3. “Definition of such parameters of Eq. 1 as J, K, g and μ_B should be also clarified.” The parameters are defined on p. 3: “J is the symmetric exchange interaction, K - the constant of the single-ion magnetic anisotropy, g - the gyromagnetic factor, \mu_B - the Bohr magneton.” 4. “References are needed for sentences like “This means that at TFEC =1372 K there is a structural phase transition from a paraelectric P41212 centrosymmetric tetragonal phase into a non-centrosymmetric orthorhombic structure Pn21a. This is a phase transition of displacive type.” Moreover, it looks contradictory that the FE Curie temperature jumps from 1373 to 1372 K and back along the manuscript.” The reference [1] is added after this sentence. We thank the reviewer for this remark, sorry for these mistakes, TFEC is now corrected to 1373 K. 5) “Definition of parameter β in Eq. 8 is missing as well, while it is also unclear whether the parameter β keep the same definition in Eqs. 12 and 15. Definitions of parameter k_B in Eq. 10 and parameter N in Eq. 11 should be also provided.” Thank you for this remark. We have added the definition of \beta in Eq. 8, it is (x,y,z). After Eq. 12 is clarified that \beta = 1/k_BT, k_B is the Boltzmann constant, and after Eq. 15 it is added that \alpha,\beta,\gamma = (x,y,z). 6) “It is also unclear what are the meanings, values and units used by the authors for parameters k_B, z and Tc in equation Jx = 3kBTC=(zS(S +1)). Additionally, using Jx, a, b, and c values listed in the manuscript, Jy and Jz values should be rather 17.49 and 9.97, respectively, but not 17.46 and 9.72.” We have clarified the parameters: k_B is the Boltzmann constant, z=4 is the number of nearest neigbours, S=5/2 is the spin value and TCFM is the ferromagnetic critical temperature.So far as in the literature for the crystal lattice constants there are different values we have taken averaged values for Jy and Jz. By citing the constants, we have taken those from the cited literature. The reviewer is right. For clarity of the article, the values for Jy and Jz are changed to those indicated by the reviewer - 17.49 and 9.97. 7) “In sentence “With τ = 0.003°, i.e. sin τ ~ τ we observe d = -√2 τ J = 0.27 K.”, the authors have to indicate the reference for τ = 0.003° and to provide used value for J.” We have added the reference, it is [1], and the value of J, it is J^x=-62.74 K. 8) “In the next sentence, definitions and values for β_c and E_i are missing as well.” On p. 7 are given the definitions of β_c=1/(k_B T_C^FE), k_B is the Boltzmann constant, and E_i are the ferroelectric energies of the system above T_C^FE. T_C^FE=1373 K is given by the model parameters. Ei are observed within our model to be \approx 40-45 K. 9) “Parameters k, E, α, β, γ, δ of Eq. 15 need to be defined also.” These parameters are now also defined on p. 9: \bf k is the wave vector, E is energy or frequency, \alpha,\beta,\gamma = (x,y,z), \delta is the delta function. 10) “Finally, English of the manuscript has to be improved.” We have tried to improve the English of the manuscript. 11) Moreover, we are sending a new Figure 3, where is changed according to the reviewer remark Dielectric constant to Relative Dielectric Permittivity in the inset.  

We hope that all comments of the second reviewer are taken into account and the manuscript is now acceptable for publication in Magnetochemistry.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper by Apostolova et al. reports theoretical calculations for temperature dependence of magnetization and electric polarization of beta-NaFeO2, which shows multiferroic behavior at room temperature. Moreover, dependence of the polarization on the magnetic field along different axes is also calculated. 

The calculation seems to be carefully carried out ant the obtained results are reasonably interpreted in terms of Magnetoelectric (ME) interactions including the magnetostriction (MS) and Zyaloshinsky-Moriya (DM) interactions. 

The paper is well organized and it is expected to encourage experimental studies to further understand the multiferroic behavior of NaFeO2, which has potential application in the spintronics technology. Therefore, I recommend the publication of this paper. 

Author Response

Thaks for the positive review

Round 2

Reviewer 2 Report

The authors addressed major part of the previous report comments. However, there are still several issues addressed not completely or properly.

First, the authors have not provided values and units used by them for parameter k_B in equation Jx = 3kBTC(zS(S + 1))=-62.74K. They just wrote that k_B is the Boltzmann constant. However, 3TC(zS(S + 1))=61.97K. Therefore, from the equation provided by the authors k_B can be deduced as dimensionless value of -1.0124, while the Boltzmann constant is known to be of 1.3806452 x 10^-23 J/K. Thus, there is either evident contradiction both in sign and value with the common knowledge or mistake by the authors in definition of the key parameter Jx. In both cases, all further simulations done by the authors do not look reliable.

Reliability does not appear as well when the authors change Jy and Jz values at page 7, but keep old values for these parameters at the end of page 6 – beginning of page 7, introducing another contradiction. Moreover, the simulation figures look to be also the same.

Second, multiple definition of parameter β introduces confusion as well. In Eqs. 8 and 9 it is (x,y,z), in Eq. 12 it is 1/k_BT, in Eq. 15 it is just y, besides the phase definition along the manuscript.

Additionally, sentences like “β-NFO thin films growth on ZnO substrates are studied by Bakaimi et al. [9].” do not bring any scientific message to the reader. What is importance of the fact that films were studied? Furthermore, there still many grammar mistakes along the manuscript.

 

As a result, contradictions and confusions still present in the revised manuscript make its reliability doubtful and hence its publication useless for readers.

Author Response

Dear Reviewer,

We are very grateful for the positive referee’s reports and the helpful comments. The changes which are made in the re-revised version according to Reviewer 2 (marked red in the text) are the following:

 

Reviewer 2:

 

1. “First, the authors have not provided values and units used by them for parameter k_B in equation Jx = 3kBTC(zS(S + 1))=-62.74K. They just wrote that k_B is the Boltzmann constant. However, 3TC(zS(S + 1))=61.97K. Therefore, from the equation provided by the authors k_B can be deduced as dimensionless value of -1.0124, while the Boltzmann constant is known to be of 1.3806452 x 10^-23 J/K. Thus, there Reis either evident contradiction both in sign and value with the common knowledge or mistake by the authors in definition of the key parameter Jx. In both cases, all further simulations done by the authors do not look reliable.Reliability does not appear as well when the authors change Jy and Jz values at page 7, but keep old values for these parameters at the end of page 6 – beginning of page 7, introducing another contradiction. Moreover, the simulation figures look to be also the same.”                The exchange interaction  is observed approximately from the equation in the mean field approximation . The expression for determines the magnitude of the exchange interaction value while the magnetic configuration its sign. Unfortunately, there is no measured value of the paramagnetic Curie temperature in the literature. When its value would be known the sign of the antiferromagnetic interactions could be determined by calculations.

Now we will calculate the expression for  with the following parameters: :

We will use the relation that converts J units to K units: 1J = 0.724.10²³ K. Then for the magnitude of  we get  (see Soshin Chikazumi, “Physics of Ferromagnetism”, Oxford University Press, page 631, ISBN 0-19-851776-9).  But  there is an antiferromagnetic arrangement along the x-axis (see Fig. 1b). This means that the sign of   is negative. After fitting with the experimental data in order to obtain the , where the magnetization vanishes, it is corrected to  = -62.74 K, which is used by the numerical calculations.

            We will note again that the sign is determined by the magnetic order under  from experimental studies. For precision (where the reviewer is right about and for which we thank him/her) the expression  will be replaced by  .  In this way, we think that the misunderstandings on this point are resolved.

            Let us emphasize that this is a qualitative theory built on the basis of the analysis of a small amount of experimental data, and the theory must reproduce indisputable data such as the Curie temperature. The fitting of   is done by varying the value of  . Thanks for this clarifying question. We added some explanations on page 7.

It must be noted that the changes in the values of the constants and  presented in revision 1 are after the decimal point. Therefore, they insignificantly affect the numerical calculations and the presented figures. We checked this.

Obviously, these are stupid technical errors made by the authors. Please accept our sincere apologies

 

2. “Second, multiple definition of parameter β introduces confusion as well. In Eqs. 8 and 9 it is (x,y,z), in Eq. 12 it is 1/k_BT, in Eq. 15 it is just y, besides the phase definition along the manuscript.”

 We have clarified and changed the different \betas with different denotations. In Eqs. 8 and 9 “\beta” is changed with “d” which gives the components of \Delta P. In Eq. 12 it remains \beta. The indices ?, ?, ? are the components of the related spins. 3. “Additionally, sentences like “β-NFO thin films growth on ZnO substrates are studied by Bakaimi et al. [9].” do not bring any scientific message to the reader. What is importance of the fact that films were studied? Furthermore, there still many grammar mistakes along the manuscript.” We have removed the sentence “β-NFO thin films growth on ZnO substrates are studied by Bakaimi et al. [9].” 4. “Finally, English of the manuscript has to be improved.” The article has been checked by a certified English translator and all inaccuracies have been removed.  

We hope that all comments of the second reviewer are taken into account and the manuscript is now acceptable for publication in Magnetochemistry.

Round 3

Reviewer 2 Report

Response submitted by the authors has many missing symbols and perhaps equations, not allowing one to understand it well.

Regarding the revised manuscript, the raised issues are again addressed there not completely.

English in sentences like “Let us emphasize that in ABO2 compounds where A = Cu, Ag, Na, Li and B = Fe, Cr is observed a strong spin-phonon interaction [14].” and “We will give a shortly description how are observed some model parameters.” still does not look to be correct.

Parameter beta is Eqs. 12 and 15 still has very different definitions.

Most important, the key parameter Jx written now as “| Jx |= 3k_BT^FM_C/(zS(S + 1)), k_B is the Boltzmann constant, z = 4 is the number of nearest neighbors, S = 5/2 is the spin value, T^FM_C is the magnetic critical temperature” (723 K) is still claimed by the authors to be of 62.74 K by absolute value. However, simple calculations using the provided numbers and the relation that converts J units to K units as 1 J = 0.724^.10²³ K, results in no more than just 62.00 K.

Thus, it is still not clear how one can believe in numerical simulations reported in this manuscript, while simple math checking shows fault.

Author Response

Dear Reviewer,

We are very grateful for the remarks of Reviewer 2 which helped to clarify and improve our article. The changes which are made in the re-re-revised version (marked red in the text) are the following:

 

Reviewer 2:

 

1. “English in sentences like “Let us emphasize that in ABO2 compounds (A = Cu, Ag, Na, Li and B = Fe, Cr) is observed a strong spin-phonon interaction [14].” and “We will give a shortly description how are observed some model parameters.” still does not look to be corrected.” We have rewritten the two sentences as: “Let us emphasize that a strong spin-phonon interaction is reported in ABO2 compounds (A = Cu, Ag, Na, Li and B = Fe, Cr) [14].” and “We will give a shortly description for the calculation of some model parameters.” 2. “Parameter beta is Eqs. 12 and 15 still has very different definitions.” Parameter \beta in Eq. 12 is removed. 1/k_BT is included in the equation. 3. “Most important, the key parameter Jx written now as “| Jx |= 3k_BT^FM_C/(zS(S + 1)), k_B is the Boltzmann constant, z = 4 is the number of nearest neighbors, S = 5/2 is the spin value, T^FM_C is the magnetic critical temperature” (723 K) is still claimed by the authors to be of 62.74 K by absolute value. However, simple calculations using the provided numbers and the relation that converts J units to K units as 1 J = 0.724^.10²³ K, results in no more than just 62.00 K.” Following strictly the reviewer's request we calculated the value of J_x and get J_x = -61.94K. Then, on the basis of this value, we calculated all the remaining interaction constants as: J_z=17,27K, J_y=-9,84K; d=0,26K_. With these new interaction constants, we have done again all numerical calculations. The new figures are presented in the re-re-revised paper.  

We hope that all comments of the second reviewer are taken into account and the manuscript is now acceptable for publication in Magnetochemistry.

Author Response File: Author Response.pdf

Round 4

Reviewer 2 Report

Well, now the manuscript looks correct and hence publishable.