Structural, Elastic, Electronic, and Magnetic Properties of Full-Heusler Alloys Sc₂TiAl and Sc₂TiSi Using the FP-LAPW Method

Round 1

Reviewer 1 Report

Report on manuscript magnetochemistry-2219926

Title "Structural, Elastic, Electronic, and Magnetic Properties of the 2 Full-
Heusler Alloys: Sc2TiAl, Sc2TiSi Using FP-LAPW Method"

by Khadejah M. Al-Masri et al.

The authors report a theoretical study of two Sc based Heusler compounds.

Most of the basic findings are already published in reference [Y. Han,  et al.
Results in Physics 12 (2019) 435]. New are the elastic properties and the use of
the Tran-Blaha modified Becke-Johnson functional, which has no effect as
realized by the authors.

The presentation and discussion of the results is substandard, therefore, I
can not recommend that the manuscript is published in its present status. The
manuscript may be published in Magnetochemistry after some major revisions as
given in the following.

1) Referencing: Comprehensive reviews on Heusler compounds can be easily found
using Google scholar or Web of Science or the journals search engines. The major
work on Heusler compounds by the groups of C. Felser (Theory and Experiment) and
I. Galanakis (Theory) is not even mentioned. As a starting point see the
following books and references there, as well as the reviewing articles by these
groups.
[1] I. Galanakis, P.H. Dederichs (Eds.) "Half-Metallic Alloys", Springer Lecture Notes in Physics 676
[2] C. Felser, G. H. Fecher (Eds.) "Spintronics", Springer (2013)
[3] C. Felser, A. Hirohata (Eds.), "Heusler alloys", Springer Series in Materials Science 222

2) Figure 1 has a very bad quality and has to be improved. Further, it is
sufficient to show only the correct (L2_1) structure for one of the compounds
(e.g. Fig.1(a) in high quality).

3) From the calculations it is obvious that the regular L2_1 structure is the
stable ground state (assuming a cubic structure), as was already found in the
work of Han et al.. Therefore, all results concerning the "wrong" inverse X_a
structure are superfluous and have to be removed.

4) The element specific magnetic moments are ambiguous. Most probably they were
calculated using the haphazardly chosen size of the atoms (muffin-tin radii).
The authors need to perform Bader's quantum theory of atoms in molecules (QTAIM)
analysis to find valuable element specific charges and magnetic moments. This
removes also the magnetic moment of the "interstitial" which is just a result of
the used method. The AIM analysis can be done easy and fast with the computer
program used by the authors.

It is not clear why the total magnetic spin moments reported here differ from
those reported by Han et al.. by about 10%. Most probably the number of k-points
(1000 in the full Brillouin zone) is much to low. The authors should increase
this number (up to at least 32000) to find well converged values for the
magnetic moments.
The authors may further discuss or at least comment on the difference between
pseudo-potential (Castep) and all electron (Wien2k) codes, in case the 10%
deviation is still present after converging the spin moments.

5) Figures 4 to 11, show 50% of empty space. I recommend to use only the enegy
range from -7eV to 4eV. There are no bands below about -7eV and the occupied
states reached by optical spectroscopy with visible light are restricted.
As mentioned above, there is no need to repeat the results for the X_a structure,
these plots have to be omitted.
The same is true for the plots of the density of states.

The use of different colors in the band structure plots is highly misleading as
they are completely arbitrary. The authors need to use either single colors
(maybe red for majority and blue for minority states) or they should use the
colors to distinguish bands with different irreducible representations.

6) The discussion of the electronic and magnetic structure leaves several points
open that need to be discussed.

a) Why are this two compounds simple metallic ferromagnets and not half-
metallic? Compare the binding schemes of Galanakis ([1] page 17 Fig.9), Felser
([2] page 135 Fig.7.9), and Han (Ref 9 Fig. 4) (see and cite also the original
works of the different groups!). The authors may include the irreducible
representations at Gamma at least in the band strutures of one of the compounds.

b) According to the Slater-Pauling rule, the Si compound should have a magnetic
moment that is 1 mu_B higher than that of the Al compound. Why is this not
fulfilled here ? Compare Galanakis ([1] page 19 Fig.11) Felser ([2] pages 120,
121 equations 7.4, 7.5 ) and Han who cites (J. Appl. Phys., 99 (2006)).

c) Why become the compounds ferromagnetic even though they are built from
"light" 3d transition metals only ? What are the results of non-spin polarized
calculations ? Is the ferromagnetism a result of the used exchange-correlation
functional ?

7) There are possibly misinterpretations of the calculated elastic properties:

a) The last line of equation (3)  (c12 < B < C11) does not belong to the Born-
Huang stability criteria.

b) The ductile-brittle criterion given by the authors is incomplete. A more
modern interpretation was given by Christensen (see R. M. Christensen, "The
Theory of Materials Failure", Oxford University Press (2013) or S.-C. Wu J.
Appl. Phys. 125, 082523 (2019) for cubic Heusler compounds and references
there.) The authors should make use of it.

c) A comparison to the elastic constants of other cubic Heusler compounds is
missing.

d) It needs to be mentioned that the stability criteria from the elastic
constants are static ones. In general, the dynamic lattice stability should also
be tested using phonon calculations.

8) From the simple total energy argument it is not clear whether or not these
cubic compounds exist. This would need to compare not only to different crystal
structures with lower symmetry, but also to the total energies of the ternaries
to different mixtures of binaries and elements.

Author Response

Response to the Reviewer 1

 

Dear Professor,

Thank you for your fruitful and helpful comments and suggestions sent to us for improving our manuscript. We have revised the manuscript accordingly, and the detailed corrections are given below.

-----------------------------------------------------------------------------------------------------------------

 

1) Referencing: Comprehensive reviews on Heusler compounds can be easily found
using Google scholar or Web of Science or the journals search engines. The major
work on Heusler compounds by the groups of C. Felser (Theory and Experiment) and
I. Galanakis (Theory) is not even mentioned. As a starting point see the
following books and references there, as well as the reviewing articles by these
groups.
[1] I. Galanakis, P.H. Dederichs (Eds.) "Half-Metallic Alloys", Springer Lecture Notes in Physics 676
[2] C. Felser, G. H. Fecher (Eds.) "Spintronics", Springer (2013)
[3] C. Felser, A. Hirohata (Eds.), "Heusler alloys", Springer Series in Materials Science 222

 

• Thank you very much for the suggested references. We cited 12 new references in the introduction section.

 

 

2) Figure 1 has a very bad quality and has to be improved. Further, it is
sufficient to show only the correct (L2_1) structure for one of the compounds
(e.g. Fig.1(a) in high quality).

 

 

•  

 

3) From the calculations it is obvious that the regular L2_1 structure is the
stable ground state (assuming a cubic structure), as was already found in the
work of Han et al.. Therefore, all results concerning the "wrong" inverse X_a
structure are superfluous and have to be removed.

• We have omitted the band structures & DOS for the Xa structure only and kept the structure, magnetic & elastic results for the purpose of completeness study for Xa structure in addition to the L21 structure.

 

 

4) The element specific magnetic moments are ambiguous. Most probably they were
calculated using the haphazardly chosen size of the atoms (muffin-tin radii).
The authors need to perform Bader's quantum theory of atoms in molecules (QTAIM)
analysis to find valuable element specific charges and magnetic moments. This
removes also the magnetic moment of the "interstitial" which is just a result of
the used method. The AIM analysis can be done easy and fast with the computer
program used by the authors.

It is not clear why the total magnetic spin moments reported here differ from
those reported by Han et al.. by about 10%. Most probably the number of k-points
(1000 in the full Brillouin zone) is much to low. The authors should increase
this number (up to at least 32000) to find well converged values for the
magnetic moments.
The authors may further discuss or at least comment on the difference between
pseudo-potential (Castep) and all electron (Wien2k) codes, in case the 10%
deviation is still present after converging the spin moments.

 

• Thanks a lot for paying our attention to this point. We have increased the number of k-points to 50,000 in the full Brillouin zone and found the values of the magnetic moment are improved & become close to the available theoretical results.

 

 

5) Figures 4 to 11, show 50% of empty space. I recommend to use only the enegy
range from -7eV to 4eV. There are no bands below about -7eV and the occupied
states reached by optical spectroscopy with visible light are restricted.
As mentioned above, there is no need to repeat the results for the X_a structure,
these plots have to be omitted.
The same is true for the plots of the density of states.

The use of different colors in the band structure plots is highly misleading as
they are completely arbitrary. The authors need to use either single colors
(maybe red for majority and blue for minority states) or they should use the
colors to distinguish bands with different irreducible representations.

• The figures of the Xa(inverse) band structures & DOS are omitted for both compounds.

 

 

6) The discussion of the electronic and magnetic structure leaves several points
open that need to be discussed.

a) Why are this two compounds simple metallic ferromagnets and not half-
metallic? Compare the binding schemes of Galanakis ([1] page 17 Fig.9), Felser
([2] page 135 Fig.7.9), and Han (Ref 9 Fig. 4) (see and cite also the original
works of the different groups!). The authors may include the irreducible
representations at Gamma at least in the band strutures of one of the compounds.

• The two compounds are ferromagnetic metallic for two reasons:

1- The band structure calculations show metallic behaviors for both compounds in the spin up & spin down.

2- The values of the magnetic moments are non-integer. The non-integral total magnetic moments confirm their metallic nature & consistence with the results of their band structures & DOS.

7. 
   b) According to the Slater-Pauling rule, the Si compound should have a magnetic
   moment that is 1 mu_B higher than that of the Al compound. Why is this not
   fulfilled here ? Compare Galanakis ([1] page 19 Fig.11) Felser ([2] pages 120,
   121 equations 7.4, 7.5 ) and Han who cites (J. Appl. Phys., 99 (2006)).

 

• Slater-Pauling rule is inapplicable since our two compounds are metallic in both spin up & spin down. Slater-Pauling rule is applicable for the half-metallic compounds & our compounds are metallic.

1. 
   
   c) 1- Why become the compounds ferromagnetic even though they are built from
   "light" 3d transition metals only ?

 

• Even though 3d transition metals are relatively light, they can still have unpaired electrons in their d orbitals, and these electrons can contribute to ferromagnetism in compounds containing these metals. Additionally, the strength of the ferromagnetism can be enhanced by factors such as crystal structure, doping with other elements, and the presence of magnetic impurities. As a result, light 3d transition metals can still exhibit ferromagnetism in certain compounds due to the way their electrons are arranged.

 

 

 

 

     2- What are the results of non-spin polarized
calculations ?

    

• The results of non-spin polarized calculations are displayed in Figures 2 & 3. It is found that the ground state energy is for the L21 regular structure for both compounds.

 

 

    3- Is the ferromagnetism a result of the used exchange-correlation
functional ?

 

 

• No, ferromagnetism is not a result of the exchange-correlation functional used in density functional theory (DFT) calculations. Ferromagnetism is an intrinsic property of certain materials that arises from the alignment of the magnetic moments of the atoms in the material. However, the choice of exchange-correlation functional can affect the accuracy of DFT calculations of magnetic properties. The exchange-correlation functional is a mathematical expression that accounts for the interactions between electrons in a material, and different functionals can give different results for the same system. Some functionals are better suited for calculating magnetic properties than others, and the choice of functional can affect the accuracy of calculated magnetic moments, magnetic anisotropy, and other magnetic properties. Overall, while the choice of exchange-correlation functional can affect the accuracy of DFT calculations of magnetic properties, it does not determine whether a material exhibits ferromagnetic behavior or not.

 

 

7) There are possibly misinterpretations of the calculated elastic properties:

a) The last line of equation (3)  (c12 < B < C11) does not belong to the Born-
Huang stability criteria.

 

• You are right. Thanks a lot. The equation has been corrected. It was a mistake. The correct one is as follows .

1. 
   
   b) The ductile-brittle criterion given by the authors is incomplete. A more
   modern interpretation was given by Christensen (see R. M. Christensen, "The
   Theory of Materials Failure", Oxford University Press (2013) or S.-C. Wu J.
   Phys. 125, 082523 (2019) for cubic Heusler compounds and references
   there.) The authors should make use of it.

 

• The elastic section has been modified according to the Ref. 19. Blackman’s diagram and Every’s diagram are used to compare the elastic properties of the studied compounds, whereas Pugh’s and Poisson’s ratios are used in the analysis of the relationship between interatomic bonding type and physical properties.

 The results are in good agreement.

1. 
   
   c) A comparison to the elastic constants of other cubic Heusler compounds is

 

• Other elastic experimental & theoretical results for Cubic Heusler compounds are not available in the literature to compare with.

1. 
   
   d) It needs to be mentioned that the stability criteria from the elastic
   constants are static ones. In general, the dynamic lattice stability should also
   be tested using phonon calculations.

 

• Instead of doing the dynamical calculations we have done the formation energy calculations as in section 3.2. The formation energies for the whole structures are negative. This means that the compound could be formed.

 

 

8) From the simple total energy argument it is not clear whether or not these
cubic compounds exist. This would need to compare not only to different crystal
structures with lower symmetry, but also to the total energies of the ternaries
to different mixtures of binaries and elements.

• It is found from the calculations that the compound is mechanically stable which means that the compound could be exist. In addition to that the formation energy shows that the compound is also stable by getting the negative values of energies which means that the compound could be formed.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The work is very intersting and well organised and I see it is suitable to publish at magnetochemistry journal. 

only view points the authors should have to care about in the final version.

1- adding a new references related to the topic.

2- Adding in the introduction with clear way the important to the out come results.

3-the references should follow the journal recommendation, such adding the DIO of all cited references.

 

Author Response

Response to the Reviewer 2

 

Dear Professor,

Thank you for your fruitful and helpful comments and suggestions sent to us for improving our manuscript. We have revised the manuscript accordingly, and the detailed corrections are given below.

-----------------------------------------------------------------------------------------------------------------

 

 

The work is very intersting and well organised and I see it is suitable to publish at magnetochemistry journal. 

only view points the authors should have to care about in the final version.

1- adding a new references related to the topic.

• We have added 12 new references in the introduction section.

 

2- Adding in the introduction with clear way the important to the out come results.

• It is highlighted with red color.

 

3-the references should follow the journal recommendation, such adding the DIO of all cited references.

•  

 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The submitted article is a numerical study of structural, elastic, electronic, and magnetic characteristics of both normal and inverse Heusler alloys Sc2TiAl and Sc2TiSi. This study is motivated by the authors themselves as an investigation of potential candidates for "electronics" or "spintronics".

The study is conducted using a quite usual flavor of DFT, based on full potential linearly augmented plane waves basis and GGA approximation implemented in "Wien2k". The ground state properties and structure relaxation are performed in this setting, and are then completed by using the so-called mBJ-GGA, that is a modified version of the usual PBE functional coupled with GGA.

Apart form the fact that the choice of the method is not discussed too much, the study seems to be well conducted, and the ground states properties computed here are almost equal to those perfomed by other authors with essentially the same method. This at least demonstrate no obvious error in the definition of the structure and the GGA part of this study, but is not original.

The main purpose is "a study consisting of investigating and predicting structural, magnetic, electronic, and elastic properties of Sc2TiAl and Sc2TiSi in the cubic phase for possible spintronic applications". Since, the electronic and magnetic properties where essentially already in the (ref [9]), this leaves the elastic properties part, which in se is interesting for the study of the stability and potentially useful mechanical properties.

A possible motivation of this article could have been to redo this computation in hope of finding a different result, using mBJ-GGA. One could argue that the hope was very small from the beginning, as some authors already noticed that the mBJ-GGA mostly correct the numerical values of an existing gap, but rarely create one when it is not already present in the GGA computation. As noticed by the authors themselves : "the mBJ method does not improve the energy band gap in metals, but can only be used in semiconductors and insulators", so what motivates the choice of mBJ-GGA?

My main concern is thus that the conclusion of the work is essentially the same as a in the ref. [9] of the article, that already determined the electronic properties using a very similar approach (implemented in the "CASTEP" code). The studied compounds seem both to be metallic, so essentially not good potential candidates for spintronics applications. So what could be the motivation of redoing a structural study of these compounds for spintronics applications? The novelty is thus reduced to elastic properties, so the accent should be on this part.

More on the form, some self-citations in the introduction seem quite unadapted : different compounds, half-metallic, ... At the same time, a recent review paper (such as [*], for instance) could be relevant in a general introduction to the "Heusler Alloys", along the same lines of the very broad studies such as the ref [9] and [13] of this article.  In general, a rapid search in the litterature reveals a lot of not cited works that could have been relevant. I strongly insist on the pertinence of a more detailed bibliography.

In conclusion, I don't recommend the publication in the present form. As a minimum, the work should clearly precise :

 - a more detailed bibliography, to locate the study in a certain context and a clear motivation, adressing the novelty of the approach, in particular compared to the results of ref [9] on 171 alloys, including the 2 studied here.

 - A reason to pick these particular 2 alloys would be nice too: for instance, which property is seeked for the 2 metallic compounds, that motivates the choice of the numerical method (more adapted to non metallic materials)?

 

[*] Kelvin Elphick, William Frost, Marjan Samiepour, Takahide Kubota, Koki Takanashi, Hiroaki Sukegawa, Seiji Mitani & Atsufumi Hirohata (2021) Heusler alloys for spintronic devices: review on recent development and future perspectives, Science and Technology of Advanced Materials, 22:1, 235-271, DOI: 10.1080/14686996.2020.1812364

Author Response

Response to the Reviewer 3

 

Dear Professor,

Thank you for your fruitful and helpful comments and suggestions sent to us for improving our manuscript. We have revised the manuscript accordingly, and the detailed corrections are given below.

-----------------------------------------------------------------------------------------------------------------

 Reviewer 3

 

The submitted article is a numerical study of structural, elastic, electronic, and magnetic characteristics of both normal and inverse Heusler alloys Sc2TiAl and Sc2TiSi. This study is motivated by the authors themselves as an investigation of potential candidates for "electronics" or "spintronics".

The study is conducted using a quite usual flavor of DFT, based on full potential linearly augmented plane waves basis and GGA approximation implemented in "Wien2k". The ground state properties and structure relaxation are performed in this setting, and are then completed by using the so-called mBJ-GGA, that is a modified version of the usual PBE functional coupled with GGA.

Apart form the fact that the choice of the method is not discussed too much, the study seems to be well conducted, and the ground states properties computed here are almost equal to those perfomed by other authors with essentially the same method. This at least demonstrate no obvious error in the definition of the structure and the GGA part of this study, but is not original.

1- The main purpose is "a study consisting of investigating and predicting structural, magnetic, electronic, and elastic properties of Sc2TiAl and Sc2TiSi in the cubic phase for possible spintronic applications". Since, the electronic and magnetic properties where essentially already in the (ref [9]), this leaves the elastic properties part, which in se is interesting for the study of the stability and potentially useful mechanical properties.

• The electronic properties are not calculated for our compounds in Ref.(9). In Ref.(9), the studied compounds for electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Studying the magnetic properties is very important to know whether the compound is metallic or half-metallic. The integral value of the magnetic moment means that the compound is half-metallic while the non-integral value means that the compound is metallic which is in our case.

2- A possible motivation of this article could have been to redo this computation in hope of finding a different result, using mBJ-GGA. One could argue that the hope was very small from the beginning, as some authors already noticed that the mBJ-GGA mostly correct the numerical values of an existing gap, but rarely create one when it is not already present in the GGA computation. As noticed by the authors themselves : "the mBJ method does not improve the energy band gap in metals, but can only be used in semiconductors and insulators", so what motivates the choice of mBJ-GGA?

• It is well known that GGA method gives incorrect energy band gap with an error of about 30-40% compared with the experimental results. mBJ-GGA method is an efficient for improving the band structure for semiconductors and insulators. Sometimes the compound is metallic using GGA while it is semiconductor using mBJ-GGA. If the compound is metallic then mBJ-GGA is inefficient. Since we have no idea whether the compound is metallic or semiconductor, we have to make a test to make sure that the compound couldn’t change its behavior.

 

3- My main concern is thus that the conclusion of the work is essentially the same as a in the ref. [9] of the article, that already determined the electronic properties using a very similar approach (implemented in the "CASTEP" code). The studied compounds seem both to be metallic, so essentially not good potential candidates for spintronics applications. So what could be the motivation of redoing a structural study of these compounds for spintronics applications? The novelty is thus reduced to elastic properties, so the accent should be on this part.

 

• Electronic properties are not calculated in Ref. 9. In Ref.(9), the studied compounds for electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Structural properties are very important to be calculated since the physical properties can be calculated at the optimized lattice parameter and this step is very important to determine the ground state energy. mBJ-GGA method is used to confirm the metallicity behavior in both spin up & spin down. To check if our compounds are suitable for spintronics, we have studied the various properties of our compounds with the help of the FP-LAPW method.

 

4- More on the form, some self-citations in the introduction seem quite unadapted : different compounds, half-metallic, ... At the same time, a recent review paper (such as [*], for instance) could be relevant in a general introduction to the "Heusler Alloys", along the same lines of the very broad studies such as the ref [9] and [13] of this article.  In general, a rapid search in the litterature reveals a lot of not cited works that could have been relevant. I strongly insist on the pertinence of a more detailed bibliography.

• We have added 12 new references including the suggested reference.

 

5- In conclusion, I don't recommend the publication in the present form. As a minimum, the work should clearly precise :

 a-  a more detailed bibliography, to locate the study in a certain context and a clear motivation, adressing the novelty of the approach, in particular compared to the results of ref [9] on 171 alloys, including the 2 studied here.

• Electronic , elastic & formation energy of the two compounds are studied for the first time.

 b- A reason to pick these particular 2 alloys would be nice too: for instance, which property is seeked for the 2 metallic compounds, that motivates the choice of the numerical method (more adapted to non metallic materials)?

• The lack of information in the stability of the compounds motivates us to study the mechanical properties in addition to the formation energy. Knowing the mechanical stability from the elastic properties means that the compound could be exist. Getting negative value of the formation energy allows the compound to be formed. Elastic constants provide important information concerning the strength of materials and often act as stability criteria or order parameters in the study of the problem of structural transformation. From the study we could say that the compounds could be formed since the calculated negative value of the formation energy predicts that the present compounds are thermodynamically stable. In additionto that the elastic parameters show that the compounds are mechanically stable and could be created.

[*] Kelvin Elphick, William Frost, Marjan Samiepour, Takahide Kubota, Koki Takanashi, Hiroaki Sukegawa, Seiji Mitani & Atsufumi Hirohata (2021) Heusler alloys for spintronic devices: review on recent development and future perspectives, Science and Technology of Advanced Materials, 22:1, 235-271, DOI: 10.1080/14686996.2020.1812364

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Report on manuscript magnetochemistry-2219926

Title "Structural, Elastic, Electronic, and Magnetic Properties of the 2 Full-
Heusler Alloys: Sc2TiAl, Sc2TiSi Using FP-LAPW Method"

by Khadejah M. Al-Masri et al.

The authors resubmitted their manuscript on a theoretical study of two Sc based Heusler compounds. The revised manuscript is improved, however, the presentation of the results -- in particular the figures-- are still not satisfying.

Therefore, I recommend that the manuscript is published after improving the
figures. In Figures 4, 5, and 6, the energy range has to be restricted to -9eV
(bottom of the valence bad) to +2eV. For Figure 5, -5eV to +2eV may be
sufficient. In addition, the white space between the panels needs to be
minimized in Figures 5 and 6.

Further, all typographical mistakes should be removed (e.g.: "creteria" and
"stablity" in line 317).

The sentence "The optimized structural parameters were determined by generalized gradient approximation (GGA) for the exchange-correlation potential, Vxc" in the abstract makes no sense. The optimized structure is found from a minimization of the total energy.
I strongly recommend to ask a native speaker (or a commercial editing service) to improve the grammar and meaning of sentences.

Comments for author File: Comments.pdf

Author Response

Response to the Reviewer 1

Dear Professor,

Thank you again for your fruitful and helpful comments and suggestions sent to us for improving our manuscript. We have revised the manuscript accordingly, and the detailed corrections are given below.

Top of Form

 

1) The authors resubmitted their manuscript on a theoretical study of two Sc based Heusler compounds. The revised manuscript is improved, however, the presentation of the results -- in particular the figures-- are still not satisfying.

Therefore, I recommend that the manuscript is published after improving the
figures. In Figures 4, 5, and 6, the energy range has to be restricted to -9eV
(bottom of the valence bad) to +2eV. For Figure 5, -5eV to +2eV may be
sufficient. In addition, the white space between the panels needs to be
minimized in Figures 5 and 6.

Response 1:        Done.

2) Further, all typographical mistakes should be removed (e.g.: "creteria" and
"stablity" in line 317).

Response 1:        Done.

 
3) The sentence "The optimized structural parameters were determined by generalized gradient approximation (GGA) for the exchange-correlation potential, Vxc" in the abstract makes no sense. The optimized structure is found from a minimization of the total energy.

Response 1:    Done. It is corrected in the manuscript.

4) I strongly recommend to ask a native speaker (or a commercial editing service) to improve the grammar and meaning of sentences.

Response 1:  

   Done. The manuscript has been polished by an expert in English language. The typographical and

    grammatical errors have been corrected and highlighted in red color.

Author Response File: Author Response.pdf

Reviewer 3 Report

 

Dear Author,

I would like to comment on your reply about some of my remarks:

Answer to remark 1:

• The electronic properties are not calculated for our compounds in Ref.(9). In Ref.(9), the studied compounds for electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Studying the magnetic properties is very important to know whether the compound is metallic or half-metallic. The integral value of the magnetic moment means that the compound is half-metallic while the non-integral value means that the compound is metallic which is in our case.

We maybe have different interpretations of the results presented in the ref 9. It seems to me that the properties were calculated a stated in this sentence quoted from Ref[9] :
"Electronic structure of 171 scandium-based full Heusler alloys:
The band structures of 171 SB FH alloys are calculated using the first-principles calculation. The calculated electronic structures indicate that all alloys with L21-type structure are just common nonmagnetic or magnetic metals. However, some of the XA-type SB FH alloys have spintronic properties".

My interpretation of this sentence is that the Sc2TiAl and Sc2TiSi were calculated as normal metals. From the results presented at line 1 and 4 on the table A1, it was quite clear that the SP rule wasn't fulfilled, and that was another indication that they weren't half metallic.

Indeed, your results seem to confirm this, and my remark was more to give the reader a motivation to the present study. I also said that the mechanical properties used to discuss the stability of these alloys was a sufficient motivation for the paper. But I still consider that you should make clear from the beginning that you don't expect them to be half-metals.

Answer to remark 2:

• It is well known that GGA method gives incorrect energy band gap with an error of about 30-40% compared with the experimental results. mBJ-GGA method is an efficient for improving the band structure for semiconductors and insulators. Sometimes the compound is metallic using GGA while it is semiconductor using mBJ-GGA. If the compound is metallic then mBJ-GGA is inefficient. Since we have no idea whether the compound is metallic or semiconductor, we have to make a test to make sure that the compound couldn’t change its behavior.

It is also noted by several authors that in general, the mBJ-GGA does not open a gap when it is not already present in the GGA computation. As you say yourself, it improves the value that is computed with an error of about 30-40%. My remark was more that you could expect from the beginning that mBJ-GGA would not be really useful in this case, and I thought that you had some ulterior motivations. Maybe, you could comment on the possible improvement in the the computation of other properties, since, as you say yourself, it doesn't improve the quality of the computation of "energy band gap" for metals: "Therefore, the mBJ method does not improve the energy band gap in metals."

In fact, I have some difficulties to understand what is this "energy band gap in metals" you refer to in the conclusion.   Answer to remark 3:  

 

• Electronic properties are not calculated in Ref. 9. In Ref.(9), the studied compounds for electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Structural properties are very important to be calculated since the physical properties can be calculated at the optimized lattice parameter and this step is very important to determine the ground state energy. mBJ-GGA method is used to confirm the metallicity behavior in both spin up & spin down. To check if our compounds are suitable for spintronics, we have studied the various properties of our compounds with the help of the FP-LAPW method.

You refer to the ref [9] as the article in which you can find the already computed quantities (magnetic moments and energies), and you reproduce partially the lines 1 and 4 of the table A1.

The structure relaxation is said to be accomplished in ref. 9:

"By using the total energy as a function of the lattice constants (i.e., unit volume), the geometry of the 171 SB FH alloys is optimized to study their ground states"

I understand to you may compare your results with those in ref 9, but in that case, you should clearly tell the reader that the computation as already been performed, and justify even with minimal arguments why you are redoing it. Probably some comments on small the discrepancies between your results and those of ref. 9 in particular concerning the atom-resolved spin magnetic moments that were already in ref 9.

That was essentially the nature of my remark 3: what is a justification of redoing a computation ? Most of the time, it is because you expect an improvement, so I would appreciate to have an idea of what could be expected and even better, some comments on the obtained results. Now that your table as evolved between the 2 submissions and it is getting closer to the results in ref 9, you maybe have an argument to explain the differences, in particular why the magnetic moment of the Al atom is 10 times smaller than the one in ref 9 ? 

In conclusion, the quality of the manuscript has improved with this second version, but I still think that the article would gain in clarity if you put the accent on what is the novelty and what is a confirmation of already published results. As a plus, a motivation for the choice of this method would be a nice addition, since, it is always a good idea to justify an increase in the computing effort. In particular, is there an improvement on the mechanical properties estimations ? You argue that the gap is better computed, but I am not sure that it plays any role in the computation of elastic coefficients.

 

 

Author Response

Response to the Reviewer 3

 

Dear Professor,

Thank you again for your fruitful and helpful comments and suggestions sent to us for improving our manuscript. We have revised the manuscript accordingly, and the detailed corrections are given below.

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1- Remark 1:

• The electronic properties are not calculated for our compounds in Ref.(9). In Ref.(9), the studied compounds for electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Studying the magnetic properties is very important to know whether the compound is metallic or half-metallic. The integral value of the magnetic moment means that the compound is half-metallic while the non-integral value means that the compound is metallic which is in our case.

We maybe have different interpretations of the results presented in the ref 9. It seems to me that the properties were calculated a stated in this sentence quoted from Ref[9] :
"Electronic structure of 171 scandium-based full Heusler alloys:
The band structures of 171 SB FH alloys are calculated using the first-principles calculation. The calculated electronic structures indicate that all alloys with L21-type structure are just common nonmagnetic or magnetic metals. However, some of the XA-type SB FH alloys have spintronic properties".

My interpretation of this sentence is that the Sc2TiAl and Sc2TiSi were calculated as normal metals. From the results presented at line 1 and 4 on the table A1, it was quite clear that the SP rule wasn't fulfilled, and that was another indication that they weren't half metallic.

Indeed, your results seem to confirm this, and my remark was more to give the reader a motivation to the present study. I also said that the mechanical properties used to discuss the stability of these alloys was a sufficient motivation for the paper. But I still consider that you should make clear from the beginning that you don't expect them to be half-metals.

Response 1:  

The motivation of the present study is to examine the mechanical properties of the compounds and analyze their stability by investigating its behavior. Given the limited availability of theoretical and experimental data on this topic, it is crucial to validate the findings reported in Ref. 9.It was initially anticipated that both compounds would exhibit a half-metallic L21 structure, as their total magnetic moments were in proximity to an integral number (2.92 for Sc2TiAl and 2.96 for Sc2TiSi). However, we only confirmed their metallic behavior after conducting comprehensive magnetic and electronic calculations.

                                       

2- Remark 2:

• It is well known that GGA method gives incorrect energy band gap with an error of about 30-40% compared with the experimental results. mBJ-GGA method is an efficient for improving the band structure for semiconductors and insulators. Sometimes the compound is metallic using GGA while it is semiconductor using mBJ-GGA. If the compound is metallic then mBJ-GGA is ineffi cient. Since we have no idea whether the compound is metallic or semiconductor, we have to make a test to make sure that the compound couldn’t change its behavior.

It is also noted by several authors that in general, the mBJ-GGA does not open a gap when it is not already present in the GGA computation. As you say yourself, it improves the value that is computed with an error of about 30-40%. My remark was more that you could expect from the beginning that mBJ-GGA would not be really useful in this case, and I thought that you had some ulterior motivations. Maybe, you could comment on the possible improvement in the the computation of other properties, since, as you say yourself, it doesn't improve the quality of the computation of "energy band gap" for metals: "Therefore, the mBJ method does not improve the energy band gap in metals."

In fact, I have some difficulties to understand what is this "energy band gap in metals" you refer to in the conclusion.   

 

 

Response 2: 

I agree with your viewpoint. Upon careful consideration, it appears that the inclusion of

the phrase 'energy band gap in metals' within the conclusion section is unnecessary

Therefore, I have eliminated the statement from the conclusion section.

                                                                                     

 

3- Remark 3:  

 

9. A) Electronic properties are not calculated in Ref. 9. In Ref.(9), the studied compounds for

  electronic structures are: Sc2CoGe, Sc2CrGa, Sc2MnSn, Sc2PdIn, Sc2VGe and Sc2RhSn. Structural properties are very important to be calculated since the physical properties can be calculated at the optimized lattice parameter and this step is very important to determine the ground state energy. mBJ-GGA method is used to confirm the metallicity behavior in both spin up & spin down. To check if our compounds are suitable for spintronics, we have studied the various properties of our compounds with the help of the FP-LAPW method.

You refer to the ref [9] as the article in which you can find the already computed quantities (magnetic moments and energies), and you reproduce partially the lines 1 and 4 of the table A1.

The structure relaxation is said to be accomplished in ref. 9:

"By using the total energy as a function of the lattice constants (i.e., unit volume), the geometry of the 171 SB FH alloys is optimized to study their ground states"

I understand to you may compare your results with those in ref 9, but in that case, you should clearly tell the reader that the computation as already been performed, and justify even with minimal arguments why you are redoing it. Probably some comments on small the discrepancies between your results and those of ref. 9 in particular concerning the atom-resolved spin magnetic moments that were already in ref 9.

That was essentially the nature of my remark 3: what is a justification of redoing a computation ? Most of the time, it is because you expect an improvement, so I would appreciate to have an idea of what could be expected and even better, some comments on the obtained results.

Response 3a:     

I would like to emphasize that the data presented in Reference 9 pertains to the magnetic properties of all the compounds discussed therein, whereas electronic structure calculations have been performed for many of these compounds except for the ones we are investigating. We believe it is necessary to repeat the calculations to validate the magnetic results and fill the gap in electronic structure calculations for our compounds, as there are no available experimental results for our system. This would complement the existing theoretical calculations and provide a more comprehensive understanding of our system.

 

1. B) Now that your table as evolved between the 2 submissions and it is getting closer to the results in ref 9, you maybe have an argument to explain the differences, in particular why the magnetic moment of the Al atom is 10 times smaller than the one in ref 9 ? 

Response 3b:     

It has been observed that in the Sc2TiAl inverse compound, the magnetic moment of the Al atom is 10 times smaller than that in ref (9). However, in the regular compound, it is only 6 times smaller than that in ref (9), which is approximately the same percentage as in Si compounds. In our opinion, this suggests that the reduced magnetic moment is not solely attributed to the Al atom. To our knowledge, this decrease could be due to either the intrinsic properties of the calculational method used in our work (Wien2k) or in ref (9). Looking at the table, we notice differences in the magnetic moment for each atom between our present work and that in ref (9). Notably, the Ti atom exhibits a significant difference, ranging from 0.53-0.69 µB or 50% in the studied compounds. However, the differences in the magnetic moment of the z=Al or Si atom are minor, ranging from 0.17-0.21 µB. The crucial point is that both methods yield total magnetic moments that are comparable for the same compound, making these methods equally reliable for studying any compound. Since we lack experimental data, we cannot determine which method is preferable for calculating the magnetic moment of each atom. In the FPLAPW method used in Wien2k, the space around the atoms in the unit cell is divided into two regions. The first region is a spherical muffin tin (MT) around the nuclei, where radial solutions of the Schrödinger equation and their energy derivatives are used as basic functions. The second region is the interstitial region between the MTs, where the basis set consists of plane waves [13-15].

The formula for the FPLAPW method is as follows:

     (1)

 

Where Y_lm(r) is Spherical harmonic, u_l(r,E_l) is the regular solution of the radial Schrödinger equation for energy E_l and the spherical part of the potential inside the sphere, andis the energy derivative of u_l taken at the same energy E_l. Therefore, the interstitial region in our study has a magnetic moment that leads to differences in the magnetic moment of each atom in the studied compounds compared to that in ref (9).

 

 

1. C) In conclusion, the quality of the manuscript has improved with this second version, but I still think that the article would gain in clarity if you put the accent on what is the novelty and what is a confirmation of already published results. As a plus, a motivation for the choice of this method would be a nice addition, since, it is always a good idea to justify an increase in the computing effort. In particular, is there an improvement on the mechanical properties estimations ? You argue that the gap is better computed, but I am not sure that it plays any role in the computation of elastic coefficients.

Response 3c:     

 The rationale behind selecting the FP-LAPW method is two-fold: it is an all-electron method and boasts high accuracy in its calculations. Given the lack of theoretical and experimental results in the literature, confirming our findings is of utmost importance. The electronic structure calculations demonstrate the metallic behavior of the compounds, which is crucial for computing their elastic constants. Our primary motivation is to investigate the stability of the compounds, as well as other characteristics such as formation energy. We are confident that the FP-LAPW method is ideal for calculating the elastic properties, owing to its all-electron nature and efficient performance

Author Response File: Author Response.pdf