Refrigeration in Adiabatically Confined Anisotropic Transition Metal Complexes Induced by Sudden Magnetic Field Quenching

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript

Refrigeration in adiabatically confined anisotropic transition metal complexes induced by sudden magnetic field quenching

by Andrew Palii, Valeria Belonovich, and Boris Tsukerblat

is an excellent issue from top scientists in the field. This opens new area of applications of transition metal complexes with predicted properties. 

The manuscript needs a rapid publication in the form as it is.

 

Author Response

Mr. Steve Yan

Managing Editor

E-Mail: steve.yan@mdpi.com

                                                                                                                       09 August,2025

Dear Mr. Yan,

Thank you for your kind letter Wed 6 Aug 2025 and your work on  our manuscript

 “magnetochemistry-3812376”

Title: Refrigeration in adiabatically confined anisotropic transition metal complexes induced by sudden magnetic field quenching

Authors: Andrew Palii, Valeria Belonovich, Boris Tsukerblat  

We greatly appreciate the reviewer's comments, which are undoubtedly valuable, and thank them for their assessment of the work.  All this comments are taken into account when preparing a revised version of the manuscript. The following modification have been made (they are marked in red in the highlighted revised version, responses listed in this letter are also red)):

Reviewer 1

We thank the Reviewer for his assessment of the work.

Reviewer 2

• Is there any experimental determination on the similar system? Does these theoretically predicated results consistent with those by experimental determined?

Response: In this paper we propose the theoretical development for a new  mechanism of molecular refrigeration. Although presently we do not have yet the experimental data confirming efficiency of the suggested mechanism we discuss the systems that are expected to exhibit an appreciable refrigeration effect. In reply to this comment the text has been modified in order to emphasize this important issue (pages 2,3 , revised text).

• Some RE-based materials, especially of Gd-based ones, are reported to show prominent cryogenic magnetocaloric performances, such as, like, J. Magn. Magn. Mater. (2025), https://doi.org/10.1016/j.jmmm.2025.173107; Magnetochemistry (2024), https://doi.org/10.3390/magnetochemistry10080053; J. Mater. Chem. A (2025), https://doi.org/10.1039/D5TA00892A, etc., some comments are suggested to avoid the misleading to the readers.

Response: We agree, the reader should get the updated and more complete information about the results in this area. In response to the Reviewer’s we have added the following text (page 2):

have been achieved by using crystalline systems. Very recently the low-temperature magnetocaloric responses in solid-state magnets have been extensively studied, aimed to developing high-performing MC materials for magnetic refrigeration and in-depth understanding of their magneto physical characteristics [ 32-34]. Thus in Ref. [32] a remarkable low-temperature magnetocaloric response    in GdNaGeO₄ oxide has been discovered oxide and this system was found to be an excellent candidate for the application in low-temperature magnetic refrigeration. The influence of  substitutions (Fe, Mn, Cu, Al) on the magnetic properties and magnetocaloric effect of the GdCo₂ compounds has been revealed in Ref. [33]. Finally, the new material  Gd₁₁O₁₀(SiO₄)(PO₄)₃ for cryogenic magnetic refrigeration application  have been  synthesized and its structure , magnetic properties, and cryogenic magnetocaloric performances have been studied in detail [34].

       Noting the achievements achieved in the field of solid-state magnetic resonance, it is also necessary to mention the undoubted advantages of nanomagnets, which include the possibility of chemical control of their structure and properties (especially magnetic anisotropy, [5-7]) to achieve maximum effect. Although high anisotropy is generally considered....

We have also added the references (page 13) indicated by the Reviewer:

32. Zhang, Y. Na, Y. Xie, Y. Zhao, Unveiling the structural and magnetic properties of RENaGeO4 (RE = Gd, Dy, and Ho) oxides and remarkable low-temperature magnetocaloric responses in GdNaGeO4 oxide, J. Mater. Chem. A,2025, 13, 19923–19932.
33. Souca, G. Dudric, R. Küpper, K. Tiusan, C. Tetean, R. Band Structure Calculations, Magnetic Properties and Magneto- caloric Effect of GdCo1.8M0.2 Compounds with M = Fe, Mn, Cu, A, Magnetochemistry 2024, 10, 53-73.
34. Chen, W. Lin, J. Wang, X. Li, L. Structural, magnetic, and cryogenic magnetocaloric properties of Gd11O10(SiO4)(PO4)3 phosphosilicate, J. Magnetism and Magnetic Materials 626 (2025) 173107-173113.

 

• The magnetic field change should be from zero to a certain field, e. g., 0-5 T, not only 5 T.

Response: It is underlined

• The conclusion is too long; I think, it is better to compress it.

Response: We agree with this comment, we have compressed the Concluding remarks (see highlighted text in revised article).

4) The style of references was not uniform; if possible, please include the DOI information.

 

Reviewer 3

- The authors should highlight the advantages of the proposed refrigeration concept over conventional MCE method in the background.

The advantages of the proposed approach lies in the technological and physical issues which regards to the options of the control the size and chemical control of the composition of the refrigeration carriers and the main physical parameters such as magnetic anisotropy.

 

- Based on the theoretical results of S = 1 model, the authors should give some inferences about other spin systems in the conclusion.

Response:  we agree with this comment. The following comment has been added to the text (page 3,

Although we consider only the fairly simple  S=1 systems have been considered to illustrate the background of the proposed concept, the main results seem admit extension to complexes possessing arbitrary spin values. In fact, the basic Hamiltonian describing anisotropy, Eq. (1), is applicable to any spin value, while the remaining evaluations for the high spin values remain the same, but of course, the expressions become more complex. In particular, the expressions for the energy levels , Eq. (2), admits  simple generalization. At the same time, for  the spin-Hamiltonian involves high order terms () but the corresponding contributions are usually small and should be taken into account when the experimental data (for instance, EPR)  clearly indicate their presence.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The magnetocaloric (MC) properties in various materials have been extensively investigated recently, not only due to their potential applications for magnetic refrigeration but also for better understanding their magneto-physical properties. In this work, the authors theoretically propose the concept of magnetothermal effect in magnetically anisotropic complexes of 3d-metal ions. The results are reasonable and interesting. The quality of this manuscript is good. I recommend it for publication after some minor revision. Some of my comments are given as below: 1) Is there any experimental determination on the similar system? Does these theoretically predicated results consistent with those by experimental determined? 2) Some RE-based materials, especially of Gd-based ones, are reported to show prominent cryogenic magnetocaloric performances, such as, like, J. Magn. Magn. Mater. (2025), https://doi.org/10.1016/j.jmmm.2025.173107; Magnetochemistry (2024), https://doi.org/10.3390/magnetochemistry10080053; J. Mater. Chem. A (2025), https://doi.org/10.1039/D5TA00892A, etc., some comments are suggested to avoid the misleading to the readers. 3) The magnetic field change should be from zero to a certain field, e. g., 0-5 T, not only 5 T. 4) The conclusion is too long; I think, it is better to compress it. 5) The style of references was not uniform; if possible, please include the DOI information.

Author Response

Mr. Steve Yan

Managing Editor

E-Mail: steve.yan@mdpi.com

                                                                                                                       09 August,2025

Dear Mr. Yan,

Thank you for your kind letter Wed 6 Aug 2025 and your work on  our manuscript

 “magnetochemistry-3812376”

Title: Refrigeration in adiabatically confined anisotropic transition metal complexes induced by sudden magnetic field quenching

Authors: Andrew Palii, Valeria Belonovich, Boris Tsukerblat  

We greatly appreciate the reviewer's comments, which are undoubtedly valuable, and thank them for their assessment of the work.  All this comments are taken into account when preparing a revised version of the manuscript. The following modification have been made (they are marked in red in the highlighted revised version, responses listed in this letter are also red)):

Reviewer 1

We thank the Reviewer for his assessment of the work.

Reviewer 2

• Is there any experimental determination on the similar system? Does these theoretically predicated results consistent with those by experimental determined?

Response: In this paper we propose the theoretical development for a new  mechanism of molecular refrigeration. Although presently we do not have yet the experimental data confirming efficiency of the suggested mechanism we discuss the systems that are expected to exhibit an appreciable refrigeration effect. In reply to this comment the text has been modified in order to emphasize this important issue (pages 2,3 , revised text).

• Some RE-based materials, especially of Gd-based ones, are reported to show prominent cryogenic magnetocaloric performances, such as, like, J. Magn. Magn. Mater. (2025), https://doi.org/10.1016/j.jmmm.2025.173107; Magnetochemistry (2024), https://doi.org/10.3390/magnetochemistry10080053; J. Mater. Chem. A (2025), https://doi.org/10.1039/D5TA00892A, etc., some comments are suggested to avoid the misleading to the readers.

Response: We agree, the reader should get the updated and more complete information about the results in this area. In response to the Reviewer’s we have added the following text (page 2):

have been achieved by using crystalline systems. Very recently the low-temperature magnetocaloric responses in solid-state magnets have been extensively studied, aimed to developing high-performing MC materials for magnetic refrigeration and in-depth understanding of their magneto physical characteristics [ 32-34]. Thus in Ref. [32] a remarkable low-temperature magnetocaloric response    in GdNaGeO₄ oxide has been discovered oxide and this system was found to be an excellent candidate for the application in low-temperature magnetic refrigeration. The influence of  substitutions (Fe, Mn, Cu, Al) on the magnetic properties and magnetocaloric effect of the GdCo₂ compounds has been revealed in Ref. [33]. Finally, the new material  Gd₁₁O₁₀(SiO₄)(PO₄)₃ for cryogenic magnetic refrigeration application  have been  synthesized and its structure , magnetic properties, and cryogenic magnetocaloric performances have been studied in detail [34].

       Noting the achievements achieved in the field of solid-state magnetic resonance, it is also necessary to mention the undoubted advantages of nanomagnets, which include the possibility of chemical control of their structure and properties (especially magnetic anisotropy, [5-7]) to achieve maximum effect. Although high anisotropy is generally considered....

We have also added the references (page 13) indicated by the Reviewer:

32. Zhang, Y. Na, Y. Xie, Y. Zhao, Unveiling the structural and magnetic properties of RENaGeO4 (RE = Gd, Dy, and Ho) oxides and remarkable low-temperature magnetocaloric responses in GdNaGeO4 oxide, J. Mater. Chem. A,2025, 13, 19923–19932.
33. Souca, G. Dudric, R. Küpper, K. Tiusan, C. Tetean, R. Band Structure Calculations, Magnetic Properties and Magneto- caloric Effect of GdCo1.8M0.2 Compounds with M = Fe, Mn, Cu, A, Magnetochemistry 2024, 10, 53-73.
34. Chen, W. Lin, J. Wang, X. Li, L. Structural, magnetic, and cryogenic magnetocaloric properties of Gd11O10(SiO4)(PO4)3 phosphosilicate, J. Magnetism and Magnetic Materials 626 (2025) 173107-173113.

 

• The magnetic field change should be from zero to a certain field, e. g., 0-5 T, not only 5 T.

Response: It is underlined

• The conclusion is too long; I think, it is better to compress it.

Response: We agree with this comment, we have compressed the Concluding remarks (see highlighted text in revised article).

4) The style of references was not uniform; if possible, please include the DOI information.

 

Reviewer 3

- The authors should highlight the advantages of the proposed refrigeration concept over conventional MCE method in the background.

The advantages of the proposed approach lies in the technological and physical issues which regards to the options of the control the size and chemical control of the composition of the refrigeration carriers and the main physical parameters such as magnetic anisotropy.

 

- Based on the theoretical results of S = 1 model, the authors should give some inferences about other spin systems in the conclusion.

Response:  we agree with this comment. The following comment has been added to the text (page 3,

Although we consider only the fairly simple  S=1 systems have been considered to illustrate the background of the proposed concept, the main results seem admit extension to complexes possessing arbitrary spin values. In fact, the basic Hamiltonian describing anisotropy, Eq. (1), is applicable to any spin value, while the remaining evaluations for the high spin values remain the same, but of course, the expressions become more complex. In particular, the expressions for the energy levels , Eq. (2), admits  simple generalization. At the same time, for  the spin-Hamiltonian involves high order terms () but the corresponding contributions are usually small and should be taken into account when the experimental data (for instance, EPR)  clearly indicate their presence.

 

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This is an interesting work. The authors propose a new concept of the magnetothermal effect which could be achieved by sudden magnetic field quenching in axially magnetically anisotropic 3d complexes. In the manuscript, they take the S = 1 simple model to elucidate their thoughts, and the theoretical derivation seems to be appropriate. Such a visualized physical model should be important to develop novel magnetic refrigerants for material scientists and chemists. Overall, the work is of some novelty and significance, so it could be accepted for publication after a minor revision is made by the authors.

I suggest the authors to consider the following points:

- The authors should highlight the advantages of the proposed refrigeration concept over conventional MCE method in the background.

- Based on the theoretical results of S = 1 model, the authors should give some inferences about other spin systems in the conclusion.

Author Response

Mr. Steve Yan

Managing Editor

E-Mail: steve.yan@mdpi.com

                                                                                                                       09 August,2025

Dear Mr. Yan,

Thank you for your kind letter Wed 6 Aug 2025 and your work on  our manuscript

 “magnetochemistry-3812376”

Title: Refrigeration in adiabatically confined anisotropic transition metal complexes induced by sudden magnetic field quenching

Authors: Andrew Palii, Valeria Belonovich, Boris Tsukerblat  

We greatly appreciate the reviewer's comments, which are undoubtedly valuable, and thank them for their assessment of the work.  All this comments are taken into account when preparing a revised version of the manuscript. The following modification have been made (they are marked in red in the highlighted revised version, responses listed in this letter are also red)):

Reviewer 1

We thank the Reviewer for his assessment of the work.

Reviewer 2

• Is there any experimental determination on the similar system? Does these theoretically predicated results consistent with those by experimental determined?

Response: In this paper we propose the theoretical development for a new  mechanism of molecular refrigeration. Although presently we do not have yet the experimental data confirming efficiency of the suggested mechanism we discuss the systems that are expected to exhibit an appreciable refrigeration effect. In reply to this comment the text has been modified in order to emphasize this important issue (pages 2,3 , revised text).

• Some RE-based materials, especially of Gd-based ones, are reported to show prominent cryogenic magnetocaloric performances, such as, like, J. Magn. Magn. Mater. (2025), https://doi.org/10.1016/j.jmmm.2025.173107; Magnetochemistry (2024), https://doi.org/10.3390/magnetochemistry10080053; J. Mater. Chem. A (2025), https://doi.org/10.1039/D5TA00892A, etc., some comments are suggested to avoid the misleading to the readers.

Response: We agree, the reader should get the updated and more complete information about the results in this area. In response to the Reviewer’s we have added the following text (page 2):

have been achieved by using crystalline systems. Very recently the low-temperature magnetocaloric responses in solid-state magnets have been extensively studied, aimed to developing high-performing MC materials for magnetic refrigeration and in-depth understanding of their magneto physical characteristics [ 32-34]. Thus in Ref. [32] a remarkable low-temperature magnetocaloric response    in GdNaGeO₄ oxide has been discovered oxide and this system was found to be an excellent candidate for the application in low-temperature magnetic refrigeration. The influence of  substitutions (Fe, Mn, Cu, Al) on the magnetic properties and magnetocaloric effect of the GdCo₂ compounds has been revealed in Ref. [33]. Finally, the new material  Gd₁₁O₁₀(SiO₄)(PO₄)₃ for cryogenic magnetic refrigeration application  have been  synthesized and its structure , magnetic properties, and cryogenic magnetocaloric performances have been studied in detail [34].

       Noting the achievements achieved in the field of solid-state magnetic resonance, it is also necessary to mention the undoubted advantages of nanomagnets, which include the possibility of chemical control of their structure and properties (especially magnetic anisotropy, [5-7]) to achieve maximum effect. Although high anisotropy is generally considered....

We have also added the references (page 13) indicated by the Reviewer:

32. Zhang, Y. Na, Y. Xie, Y. Zhao, Unveiling the structural and magnetic properties of RENaGeO4 (RE = Gd, Dy, and Ho) oxides and remarkable low-temperature magnetocaloric responses in GdNaGeO4 oxide, J. Mater. Chem. A,2025, 13, 19923–19932.
33. Souca, G. Dudric, R. Küpper, K. Tiusan, C. Tetean, R. Band Structure Calculations, Magnetic Properties and Magneto- caloric Effect of GdCo1.8M0.2 Compounds with M = Fe, Mn, Cu, A, Magnetochemistry 2024, 10, 53-73.
34. Chen, W. Lin, J. Wang, X. Li, L. Structural, magnetic, and cryogenic magnetocaloric properties of Gd11O10(SiO4)(PO4)3 phosphosilicate, J. Magnetism and Magnetic Materials 626 (2025) 173107-173113.

 

• The magnetic field change should be from zero to a certain field, e. g., 0-5 T, not only 5 T.

Response: It is underlined

• The conclusion is too long; I think, it is better to compress it.

Response: We agree with this comment, we have compressed the Concluding remarks (see highlighted text in revised article).

4) The style of references was not uniform; if possible, please include the DOI information.

 

Reviewer 3

- The authors should highlight the advantages of the proposed refrigeration concept over conventional MCE method in the background.

The advantages of the proposed approach lies in the technological and physical issues which regards to the options of the control the size and chemical control of the composition of the refrigeration carriers and the main physical parameters such as magnetic anisotropy.

 

- Based on the theoretical results of S = 1 model, the authors should give some inferences about other spin systems in the conclusion.

Response:  we agree with this comment. The following comment has been added to the text (page 3,

Although we consider only the fairly simple  S=1 systems have been considered to illustrate the background of the proposed concept, the main results seem admit extension to complexes possessing arbitrary spin values. In fact, the basic Hamiltonian describing anisotropy, Eq. (1), is applicable to any spin value, while the remaining evaluations for the high spin values remain the same, but of course, the expressions become more complex. In particular, the expressions for the energy levels , Eq. (2), admits  simple generalization. At the same time, for  the spin-Hamiltonian involves high order terms () but the corresponding contributions are usually small and should be taken into account when the experimental data (for instance, EPR)  clearly indicate their presence.

 

Author Response File: Author Response.docx