Skyrmion phases in ground state of magnetoelectric bilayer induced by planar Dzyaloshinskii-Moriya interaction

A.G. Nugumanov ORCID logo , I.F. Sharafullin, M.K. Kharrasov show affiliations and emails
Received 31 May 2023; Accepted 31 July 2023;
Citation: A.G. Nugumanov, I.F. Sharafullin, M.K. Kharrasov. Skyrmion phases in ground state of magnetoelectric bilayer induced by planar Dzyaloshinskii-Moriya interaction. Lett. Mater., 2023, 13(4) 317-322


3D view of topological charge phase diagram. Axes are parameters of exchange and magnetoelectric interaction, height is absolute value of topological charge in ground state.Composite multiferroic films allow the existence of a wide range of stable magnetic skyrmion structures in the phase diagram, which can be used to create next-generation ultra-dense memory units. In this paper, we investigate the processes of formation of skyrmion lattice phases and continuously distributed skyrmion phases in the ground state of a magnetoelectric film consisting of a magnetic layer surrounded by two ferroelectric layers with a triangular lattice and Dzyaloshinskii-Moriya interfacial magnetoelectric interaction. The ground state is calculated using an artificial neural network, which approximates the ground state of the film as a function of macroscopic parameters. The proposed method for calculating the ground state has a number of advantages compared to classic gradient descent and allows one to construct a phase diagram of the dependence of the topological charge on the parameters of magnetic and magnetoelectric interaction. Using a combined method including gradient descent and an artificial neural network, we have mapped the phase diagram of the skyrmion topological charge for different combinations of exchange and magnetoelectric interaction parameters. Using a neural network to predict first approximations of the ground states allowed us to avoid the excessive computational costs required in the case of direct gradient descent with random initialization for the system of 3600 interdependent nonlinear equations for each spin and dipole component.

References (28)

1. A. Rosch. Nat. Nanotechnol. 12, 103 (2017). Crossref
2. A. Fert, V. Cros, J. Sampaio. Nat. Nanotechnol. 8, 152 (2013). Crossref
3. W. Koshibae, Y. Kaneko, J. Iwasaki, M. Kawasaki, Y. Tokura, N. Nagaosa. Jpn. J. Appl. Phys. 54, 053001 (2015). Crossref
4. T. H. R. Skyrme. Proc. R. Soc. A. 247, 260 (1958). Crossref
5. A. N. Bogdanov, U. K. Rößler. Phys. Rev. Lett. 87, 037203 (2001). Crossref
6. A. N. Bogdanov, A. Hubert. J. Magn. Magn. Mater. 138, 255 (1994). Crossref
7. A. Abanov, V. L. Pokrovsky. Phys. Rev. B. 58, R8889 (1998). Crossref
8. W. Jiang, P. Upadhyaya, W. Zhang, G. Yu, M. B. Jungfleisch, F. Y. Fradin, J. E. Pearson, Y. Tserkovnyak, K. L. Wang, O. Heinonen, S. G. E. Te Velthuis, A. Hoffmann. Science (Washington, DC, U. S.). 349, 283 (2015). Crossref
9. C. Moreau-Luchaire, C. Moutafis, N. Reyren, et al. Nat. Nanotechnol. 11, 444 (2016). Crossref
10. S. Woo, K. Litzius, B. Kruger, et al. Nat. Mater. 15, 501 (2016). Crossref
11. O. Boulle, J. Vogel, H. Yang, et al. Nat. Nanotechnol. 11, 449 (2016). Crossref
12. A. B. Butenko, A. A. Leonov, U. K. Rößler, A. N. Bogdanov. Phys. Rev. B. 82, 052403 (2010). Crossref
13. S. E. Hog, A. Bailly-Reyre, H. T. Diep. J. Magn. Magn. Mater. 455, 32 (2018). Crossref
14. T. Okubo, S. Chunghi, H. Kawamura. Phys. Rev. Lett. 108, 017206 (2012). Crossref
15. I. Levatić, P. Popčević, V. Šurija, A. Kruchkov, H. Berger, A. Magrez, J. S. White, H. M. Rønnow, I. Živković. Scientific Rep. 6, 21347 (2016). Crossref
16. S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P. Böni. Science. 123, 915 (2009). Crossref
17. X. Yu, A. Kikkawa, D. Morikawa, K. Shibata, Y. Tokunaga, Y. Taguchi, Y. Tokura. Phys. Rev. B. 91, 054411 (2015). Crossref
18. S. Buhrandt, L. Fritz. Phys. Rev. B. 88, 195137 (2013). Crossref
19. F. Buttner, C. Moutafis, M. Schneider, et al. Nat. Phys. 11, 225 (2015). Crossref
20. H. Pei, S. Guo, L. Ren, C. Chen, B. Luo, X. Dong, K. Jin, R. Ren, H. F. Zeeshan. Sci. Rep. 7, 1 (2017). Crossref
21. S. E. Hog, F. Kato, H. Koibuchi, H. T. Diep. J. Magn. Magn. Mater. 498, 166095 (2020). Crossref
22. A. P. Pyatakov. Phys. B (Amsterdam, Neth.). 542, 59 (2018). Crossref
23. X. Hao, F. Zhuo, A. Manchon, X. Wang, H. Li, Z. Cheng. Applied Physics Reviews. 8 (2), 021402 (2021).
24. I. F. Sharafullin, M. K. Kharrasov, H. T. Diep. Phys. Rev. B. 99, 214420 (2019). Crossref
25. A. G. Nugumanov, I. F. Sharafullin. Letters on Materials. 12 (2), 116 (2022). Crossref
26. S. Heinze, K. Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, S. Blugel. Nat. Phys. 7, 713 (2011). Crossref
27. A. S. Samardak, A. G. Kolesnikov, A. V. Davydenko, M. E. Steblii, A. V. Ognev. Phys. Metals Metallogr. 123 (3), 238 (2022). Crossref
28. H. T. Diep. Theory of magnetism. Singapore, World Scientific (2014) 440 p.


1. State assignment of Russian Federation for the implementation of scientific research by laboratories - 075-03-2021-193/5