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Nature of spin-lattice coupling in two-dimensional CrI3 and CrGeTe3

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Abstract

Spin-lattice (SL) coupling plays an important role in spintronic applications given its effects on magnetic, ferroelectric, optical, and thermodynamic properties. Experiments and theoretical calculations have revealed a large SL coupling effect in CrGeTe3 and CrI3 monolayers. However, the microscopic origin of SL coupling in these systems is still unclear. In this work, we develop a systematic method to explore the atomistic mechanism of SL coupling based on the density functional theory. We find that the first- and second-order SL couplings in ternary system CrGeTe3 are considerably stronger than those in binary system CrI3. For the first-order SL coupling, the Cr ions of the magnetic pair and Ge ions positively contribute to the strain enhancement of ferromagnetism in CrGeTe3. However, the Cr ions provide a negative contribution in CrI3. Furthermore, our tight-binding analysis suggests that the p-d hopping in CrGeTe3 gradually decreases with the tensile strain, rapidly enhancing the ferromagnetism under the tensile strain. The large frequency shifts in CrGeTe3 are caused by the large second-order exchange derivatives (one type of second-order SL coupling) of the Cr ions of the magnetic pair.

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References

  1. J. W. Seo, W. Prellier, P. Padhan, P. Boullay, J. Y. Kim, H. Lee, C. D. Batista, I. Martin, E. E. M. Chia, T. Wu, B. G. Cho, and C. Panagopoulos, Phys. Rev. Lett. 105, 167206 (2010), arXiv: 1006.3603.

    Article  ADS  Google Scholar 

  2. B. Dupé, S. Prosandeev, G. Geneste, B. Dkhil, and L. Bellaiche, Phys. Rev. Lett. 106, 237601 (2011).

    Article  ADS  Google Scholar 

  3. C. Escorihuela-Sayalero, O. Diéguez, and J. Íñiguez, Phys. Rev. Lett. 109, 247202 (2012), arXiv: 1207.6859.

    Article  ADS  Google Scholar 

  4. Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, ACS Nano 6, 1695 (2012).

    Article  Google Scholar 

  5. J. S. White, M. Bator, Y. Hu, H. Luetkens, J. Stahn, S. Capelli, S. Das, M. Döbeli, T. Lippert, V. K. Malik, J. Martynczuk, A. Wokaun, M. Kenzelmann, C. Niedermayer, and C. W. Schneider, Phys. Rev. Lett. 111, 037201 (2013), arXiv: 1304.7200.

    Article  ADS  Google Scholar 

  6. A. Lupascu, J. P. Clancy, H. Gretarsson, Z. Nie, J. Nichols, J. Terzic, G. Cao, S. S. A. Seo, Z. Islam, M. H. Upton, J. Kim, D. Casa, T. Gog, A. H. Said, V. M. Katukuri, H. Stoll, L. Hozoi, J. van den Brink, and Y. J. Kim, Phys. Rev. Lett. 112, 147201 (2014), arXiv: 1312.4005.

    Article  ADS  Google Scholar 

  7. H. Zheng, B. Yang, D. Wang, R. Han, X. Du, and Y. Yan, Appl. Phys. Lett. 104, 132403 (2014).

    Article  ADS  Google Scholar 

  8. Y. Song, D. Yuan, X. Lu, Z. Xu, E. Bourret-Courchesne, and R. J. Birgeneau, Phys. Rev. Lett. 123, 247205 (2019), arXiv: 1911.06492.

    Article  ADS  Google Scholar 

  9. J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. Jung, L. F. Kourkoutis, J. W. Kim, P. J. Ryan, T. Heeg, M. Roeckerath, V. Goian, M. Bernhagen, R. Uecker, P. C. Hammel, K. M. Rabe, S. Kamba, J. Schubert, J. W. Freeland, D. A. Muller, C. J. Fennie, P. Schiffer, V. Gopalan, E. Johnston-Halperin, and D. G. Schlom, Nature 466, 954 (2010).

    Article  ADS  Google Scholar 

  10. Y. Feng, C. Wang, S. L. Tian, Y. Zhou, C. Ge, H. Z. Guo, M. He, K. J. Jin, and G. Z. Yang, Sci. China-Phys. Mech. Astron. 60, 067711 (2017).

    Article  ADS  Google Scholar 

  11. A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Phys. Rev. Lett. 108, 197601 (2012), arXiv: 1112.5936.

    Article  ADS  Google Scholar 

  12. S. J. Allen, and H. J. Guggenheim, Phys. Rev. Lett. 21, 1807 (1968).

    Article  ADS  Google Scholar 

  13. M. J. Massey, R. Merlin, and S. M. Girvin, Phys. Rev. Lett. 69, 2299 (1992).

    Article  ADS  Google Scholar 

  14. A. B. Souchkov, J. R. Simpson, M. Quijada, H. Ishibashi, N. Hur, J. S. Ahn, S. W. Cheong, A. J. Millis, and H. D. Drew, Phys. Rev. Lett. 91, 027203 (2003), arXiv: cond-mat/0212644.

    Article  ADS  Google Scholar 

  15. P. A. Sharma, J. S. Ahn, N. Hur, S. Park, S. B. Kim, S. Lee, J. G. Park, S. Guha, and S. W. Cheong, Phys. Rev. Lett. 93, 177202 (2004).

    Article  ADS  Google Scholar 

  16. S. Petit, F. Moussa, M. Hennion, S. Pailhès, L. Pinsard-Gaudart, and A. Ivanov, Phys. Rev. Lett. 99, 266604 (2007).

    Article  ADS  Google Scholar 

  17. F. Wang, and A. Vishwanath, Phys. Rev. Lett. 100, 077201 (2008), arXiv: 0709.3546.

    Article  ADS  Google Scholar 

  18. C. H. Sohn, C. H. Kim, L. J. Sandilands, N. T. M. Hien, S. Y. Kim, H. J. Park, K. W. Kim, S. J. Moon, J. Yamaura, Z. Hiroi, and T. W. Noh, Phys. Rev. Lett. 118, 117201 (2017).

    Article  ADS  Google Scholar 

  19. I. Stockem, A. Bergman, A. Glensk, T. Hickel, F. Körmann, B. Grabowski, J. Neugebauer, and B. Alling, Phys. Rev. Lett. 121, 125902 (2018), arXiv: 1802.02934.

    Article  ADS  Google Scholar 

  20. E. Aytan, B. Debnath, F. Kargar, Y. Barlas, M. M. Lacerda, J. X. Li, R. K. Lake, J. Shi, and A. A. Balandin, Appl. Phys. Lett. 111, 252402 (2017), arXiv: 1710.06386.

    Article  ADS  Google Scholar 

  21. M. N. Iliev, H. Guo, and A. Gupta, Appl. Phys. Lett. 90, 151914 (2007).

    Article  ADS  Google Scholar 

  22. J. F. Robillard, O. B. Matar, J. O. Vasseur, P. A. Deymier, M. Stippinger, A. C. Hladky-Hennion, Y. Pennec, and B. Djafari-Rouhani, Appl. Phys. Lett. 95, 124104 (2009).

    Article  ADS  Google Scholar 

  23. C. X. Quintela, F. Rivadulla, and J. Rivas, Appl. Phys. Lett. 94, 152103 (2009).

    Article  ADS  Google Scholar 

  24. J. Hemberger, T. Rudolf, H. A. Krug von Nidda, F. Mayr, A. Pimenov, V. Tsurkan, and A. Loidl, Phys. Rev. Lett. 97, 087204 (2006), arXiv: cond-mat/0603627.

    Article  ADS  Google Scholar 

  25. J. H. Lee, and K. M. Rabe, Phys. Rev. Lett. 104, 207204 (2010), arXiv: 0910.5438.

    Article  ADS  Google Scholar 

  26. R. Pradip, P. Piekarz, A. Bosak, D. Merkel, O. Waller, A. Seiler, A. Chumakov, R. Rüffer, A. Oleś, K. Parlinski, M. Krisch, T. Baumbach, and S. Stankov, Phys. Rev. Lett. 116, 185501 (2016).

    Article  ADS  Google Scholar 

  27. S. Lee, A. Pirogov, M. Kang, K. H. Jang, M. Yonemura, T. Kamiyama, S. W. Cheong, F. Gozzo, N. Shin, H. Kimura, Y. Noda, and J. G. Park, Nature 451, 805 (2008).

    Article  ADS  Google Scholar 

  28. S. Dong, H. Xiang, and E. Dagotto, Natl. Sci. Rev. 6, 629 (2019).

    Article  Google Scholar 

  29. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature 546, 265 (2017), arXiv: 1703.05753.

    Article  ADS  Google Scholar 

  30. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature 546, 270 (2017), arXiv: 1703.05892.

    Article  ADS  Google Scholar 

  31. H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, and K. Ohtani, Nature 408, 944 (2000).

    Article  ADS  Google Scholar 

  32. C. Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, Y. Wang, L. Lu, X. C. Ma, and Q. K. Xue, Science 340, 167 (2013), arXiv: 1605.08829.

    Article  ADS  Google Scholar 

  33. W. Han, R. K. Kawakami, M. Gmitra, and J. Fabian, Nat. Nanotech. 9, 794 (2014), arXiv: 1503.02743.

    Article  ADS  Google Scholar 

  34. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M. H. Phan, and M. Batzill, Nat. Nanotech. 13, 289 (2018).

    Article  ADS  Google Scholar 

  35. N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Cepellotti, G. Pizzi, and N. Marzari, Nat. Nanotech. 13, 246 (2018), arXiv: 1611.05234.

    Article  ADS  Google Scholar 

  36. K. S. Burch, D. Mandrus, and J. G. Park, Nature 563, 47 (2018).

    Article  ADS  Google Scholar 

  37. Y. Liu, and C. Petrovic, Phys. Rev. B 97, 174418 (2018), arXiv: 1805.08203.

    Article  ADS  Google Scholar 

  38. Y. Tian, M. J. Gray, H. Ji, R. J. Cava, and K. S. Burch, 2D Mater. 3, 025035 (2016), arXiv: 1604.08745.

    Article  Google Scholar 

  39. X. Li, and J. Yang, J. Mater. Chem. C 2, 7071 (2014).

    Article  Google Scholar 

  40. L. Webster, and J. A. Yan, Phys. Rev. B 98, 144411 (2018), arXiv: 1809.08725.

    Article  ADS  Google Scholar 

  41. C. Xu, J. Feng, H. Xiang, and L. Bellaiche, npj Comput. Mater. 4, 57 (2018), arXiv: 1811.05413.

    Article  ADS  Google Scholar 

  42. Y. Sun, R. C. Xiao, G. T. Lin, R. R. Zhang, L. S. Ling, Z. W. Ma, X. Luo, W. J. Lu, Y. P. Sun, and Z. G. Sheng, Appl. Phys. Lett. 112, 072409 (2018).

    Article  ADS  Google Scholar 

  43. L. Webster, L. Liang, and J. A. Yan, Phys. Chem. Chem. Phys. 20, 23546 (2018), arXiv: 1805.10479.

    Article  Google Scholar 

  44. L. D. Casto, A. J. Clune, M. O. Yokosuk, J. L. Musfeldt, T. J. Williams, H. L. Zhuang, M. W. Lin, K. Xiao, R. G. Hennig, B. C. Sales, J. Q. Yan, and D. Mandrus, APL Mater. 3, 041515 (2015).

    Article  ADS  Google Scholar 

  45. M. A. McGuire, G. Clark, S. Kc, W. M. Chance, G. E. Jellison, V. R. Cooper, X. Xu, and B. C. Sales, Phys. Rev. Mater. 1, 014001 (2017), arXiv: 1706.01796.

    Article  Google Scholar 

  46. X. Z. Lu, X. Wu, and H. J. Xiang, Phys. Rev. B 91, 100405 (2015), arXiv: 1503.03565.

    Article  ADS  Google Scholar 

  47. C. J. Fennie, and K. M. Rabe, Phys. Rev. Lett. 96, 205505 (2006), arXiv: cond-mat/0602503.

    Article  ADS  Google Scholar 

  48. H. J. Xiang, E. J. Kan, S. H. Wei, M. H. Whangbo, and X. G. Gong, Phys. Rev. B 84, 224429 (2011), arXiv: 1106.5549.

    Article  ADS  Google Scholar 

  49. H. Xiang, C. Lee, H. J. Koo, X. Gong, and M. H. Whangbo, Dalton Trans. 42, 823 (2013).

    Article  Google Scholar 

  50. W. Baltensperger, and J. Helman, Helv. Phys. Acta 41, 668 (1968).

    Google Scholar 

  51. W. Baltensperger, J. Appl. Phys. 41, 1052 (1970).

    Article  ADS  Google Scholar 

  52. J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959).

    Article  ADS  Google Scholar 

  53. J. B. Goodenough, Magnetism and the Chemical Bond (Interscience Publishers, New York, 1963), Vol. 1.

    Google Scholar 

  54. A. A. Mostofi, J. R. Yates, G. Pizzi, Y. S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 185, 2309 (2014).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai, 200433, China

    Jing Li, JunSheng Feng, PanShuo Wang & HongJun Xiang

  2. Shanghai Qi Zhi Institute, Shanghai, 200232, China

    Jing Li & HongJun Xiang

  3. School of Physics and Materials Engineering, Hefei Normal University, Hefei, 230601, China

    JunSheng Feng

  4. Department of Applied Physics and Institution of Energy and Microstructure, Nanjing University of Science and Technology, Nanjing, 210094, China

    ErJun Kan

  5. Collaborative Innovation Center of Advanced Microstructures, Nanjing, 210093, China

    HongJun Xiang

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  1. Jing Li
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  2. JunSheng Feng
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  3. PanShuo Wang
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Correspondence to ErJun Kan or HongJun Xiang.

Additional information

The work at Fudan was supported by the National Natural Science Foundation of China (Grant Nos. 11825403, and 11804138), and the Program for Professor of Special Appointment (Eastern Scholar). JunSheng Feng was supported by Anhui Provincial Natural Science Foundation (Grant No. 1908085MA10), and the Opening Foundation of State Key Laboratory of Surface Physics Fudan University (Grant No. KF2019_07).

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Li, J., Feng, J., Wang, P. et al. Nature of spin-lattice coupling in two-dimensional CrI3 and CrGeTe3. Sci. China Phys. Mech. Astron. 64, 286811 (2021). https://doi.org/10.1007/s11433-021-1717-9

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