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Description
Magnetic skyrmions are topologically nontrivial whirls of local magnetization, that can arrange into regular lattices, co-called skyrmion crystals (SkX). Dzyaloshinskii-Moriya interaction (DMI) is one of SkX stabilization mechanisms. There is a wide region on a phase diagram of a thin ferromagnetic film with DMI in a presence of an external magnetic field where SkX is a ground state of the system [1]. Whirling character of the ground state leads to a complicated band structure of SkX excitations. Besides the topologically trivial Goldstone mode, other low-energy bands may also possess non-zero Chern numbers. Recently it was theoretically shown that there is a topological transition in the spectrum of SkX excitations: gap between two low-lying bands closes with increasing of magnetic field, and after that gap reopens and Chern numbers are changed [2,3].
We investigate appearance of edge modes in a system with a nonuniform external magnetic field. We consider two half-planes with different values of external magnetic field: below topological transition and above it. We show that there is a chiral magnon edge mode in this system, localized on a border of these two areas. We compare two different approaches: numerical analysis of the full spectrum of excitations [4] and analysis of the reduced effective model developed earlier [3]. Character of wave functions is discussed; localization length dependence of model parameters is obtained.
[1] N. Nagaosa and Y. Tokura, Nature Nanotechnology 8, 899 (2013).
[2] S. A. Diaz, T. Hirosawa, J. Klinovaja, and D. Loss, Physical Review Research 2, 013231 (2020).
[3] V. E. Timofeev, Yu. V. Baramygina, D. N. Aristov, JETP Letters, 118, 12, 911-916, (2023).
[4] V. E. Timofeev and D. N. Aristov, Phys. Rev. B 105, 024422 (2022).
