- PII
- S1028096025010102-1
- DOI
- 10.31857/S1028096025010102
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 1
- Pages
- 71-77
- Abstract
- In the framework of the phenomenological approach, we obtained a non-uniform vortex distribution of magnetization and the associated non-uniform electric polarization in small magnetic particles in the shape of cylinders. The microscopic mechanism of this connection between magnetization and polarization is due to spin-orbit interaction. Within the framework of the phenomenological approach, the emergence of an inhomogeneous magnetic state and the associated appearance of inhomogeneous electric polarization in the volume of small magnetic particles have been studied. The specific form for magnetization and polarization is determined by the shape and size of the cylindrical particles. Using the free energy expression for magnetization, we obtained a nonuniform distribution of magnetization in the form of three-dimensional magnetic vortices. A vortex state occurs only for cylinders with a radius greater than a certain critical value, and for particles with a smaller radius a uniform magnetic state arises. In a vortex state, non-uniform electric polarization occurs, directed in the form of rays from the cylinder axis. The region of existence of such inhomogeneous states has been determined. The change in local electric polarization of small magnetic particles in an external magnetic field is considered. An expression for the magnetoelectric susceptibility is obtained.
- Keywords
- магнитные частицы электрическая поляризация феноменологическая теория фазовых переходов спин-орбитальное взаимодействие магнитоэлектрический эффект
- Date of publication
- 14.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 4
References
- 1. Hehn M., Ounadjela K., Bucher J-P et al. // Science. 1996. V. 272. No. 5269. P. 1782. https://doi.org/10.1126/science.272.5269.1782
- 2. Cowburn R.P., Koltsov D.K., Adeyeye A.O., Welland M. E., and Tricker D. M. // Phys. Rev. Lett. 1999. V. 83. No. 5. P. 1042. https://doi.org/10.1103/PhysRevLett.83.1042
- 3. Stapper Jr. C.H. // J. Appl. Phys. 1969. V. 40. No. 2. P. 798. https://doi.org/10.1063/1.1657466
- 4. Usov N.A., Nesmeyanov M.S. // Scientific Reports. 2020. V. 10. Art. No. 10173. https://doi.org/10.1038/s41598-020-67173-5
- 5. Peixoto L., Magalhaes R., Navas D. et al. // Appl. Phys. Rev. 2020. V. 7. Art. No. 011310. https://doi.org/10.1063/1.5121702
- 6. Sergienko I.A., Dagotto E. // Phys. Rev. B. 2006. V. 73, № 9, P. 094434. https://doi.org/ 10.1103/PhysRevB.73.094434
- 7. Cheong S.-W., Mostovoy M. // Nat. Mater. 2007. V. 6. № 1, P. 13. https://doi.org/ 10.1038/nmat1804
- 8. Roßler U. K., Bogdanov A. N., Pfleiderer C. // Nature. 2006. V. 442. P. 17. https://doi.org/10.1038/nature05056
- 9. Levanyuk A.P., Blinc R. // Phys. Rev. Lett. 2013. V. 111. No. 9. Art. No. 097601. https://doi.org/10.1103/PhysRevLett.111.097601
- 10. Hill N.A. // J. Phys. Chem. B. 2000. V. 104. No. 29. P. 6694. https://doi.org/10.1021/jp000114x
- 11. Khanh N.D., Abe N., Sagayama H., Nakao A., Hanashima T., Kiyanagi R., Tokunaga Y., Arima T. // Phys. Rev. B. 2016. V. 93. № 7. P. 075117. https://doi.org/10.1103/PhysRevB.93.075117
- 12. Ma C., Zhang X., Xia J., Ezawa M., Jiang W., Ono T., Piramanayagam S. N., Morisako A., Zhou Y., Liu X. // Nano Lett. 2019. V. 19, P. 353. https://doi.org/ 10.1021/acs.nanolett.8b03983
- 13. Zheng F., Rybakov F.N., Borisov A.B., Song D., Wang S., Li Zi-An, Du H., Kiselev N.S., Caron J., Kovacs A., Tian M., Zhang Y., Brugel S., Dunin-Borkowski R.E. // Nature Nanotechnology. 2018. V. 13. P. 451. https://doi.org/10.1038/s41565-018-0093-3
- 14. Гуревич Л. Э., Филиппов Д. А. // Физика твердого тела. 1986. Т. 28. № 9. С. 2696.
- 15. Zhang X., Zhou Y., Song K.M., Park T.-E., Xia J., Ezawa M., Liu X., Zhao W., Zhao G., Woo S. // J. Phys.: Condens. Matter. 2020. V. 32. P. 143001. https://doi.org/10.1088/1361-648X/ab5488
- 16. Mostovoy M. // Phys. Rev. Lett. 2006. V. 96. № 6. P. 067601. https://doi.org/10.1103/PhysRevLett.96.067601.
- 17. Логгинов А.С., Мешков Г.А., Николаев А.В., Пятаков А.П. // Письма в ЖЭТФ. 2007. Т. 86. № 2. С. 124; (Logginov A.S., Meshkov G.A., Nikolaev A.V., Pyatakov A.P. // JETP Letters. 2007. V. 86. No. 2. P. 115). https://doi.org/10.1134/S0021364007140093
- 18. Levanyuk A.P., Blinc R. // Phys. Rev. Lett. 2013. V. 111. No. 9. Art. No. 097601. https://doi.org/10.1103/PhysRevLett.111.097601
- 19. Дзялошинский И.Е. // ЖЭТФ. 1960. Т. 37. № 3. С. 881; Dzyaloshinskii I.E. // JETP. 1960. V. 10. No. 3. P. 628.
- 20. Moriya T. // Phys. Rev. 1960. V. 120. No. 1. P. 91. https://doi.org/10.1103/PhysRev.120.91
- 21. Звездин А.К., Пятаков А.П. // УФН. 2009. Т. 179. № 8. С. 897. https://doi.org/10.3367/UFNr.0179.200908i.0897
- 22. Пятаков А.П., Звездин А.К. // УФН. 2012. Т. 182. № 6. С. 593. https://doi.org/10.3367/UFNr.0182.201206b.0593
- 23. Pyatakov A.P., Sergeev A.S., Mikailzade F.A., Zvezdin A.K. // JMMM. 2015. V. 383. P. 255. https://doi.org/ 10.1016/j.jmmm.2014.11.035
- 24. Шапошникова Т.С., Мамин Р.Ф. // Поверхность. Рентгеновские, синхротронные и нейтронные исследования. 2021. № 12. С. 31. https://doi.org/10.31857/S1028096021120190; (Shaposhnikova T.C., Mamin R.F. // J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech. 2021. V. 15. № 6. P. 1282). https://doi.org/10.1134/S1027451021060434
- 25. Шапошникова Т.С., Мамин Р.Ф. // Изв. РАН. Сер. физ. 2024. Т. 88. № 5; (Shaposhnikova T.C., Mamin R.F. // Bull. Russ. Acad. Sci. Phys. 2024. V. 88. No. 5. P. 783. https://doi.org/10.1134/S1062873824706597
- 26. Ландау Л.Д., Лифшиц Е.М. Электродинамика сплошных сред. Москва: Наука, 1982, 620 с.
- 27. Sato M., Ishii Y. // J. Appl. Phys. 1989. V. 66. P. 983. https://doi.org/10.1063/1.343481
