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Magnetic skyrmions at the scale of tens of nanometers are actively discussed in the last decade. These topological objects are experimentally observed as skyrmion crystals (SkX) in a tightly packed triangular configuration. The main focus of experimental investigations and numerical modeling nowadays shifts to the preparation and manipulation of individual skyrmions, aiming to use them in future electronic devices. The dynamics or heat transport properties of regularly arranged SkX, attract less attention.
Using the method of stereographic projection, we map the vector field of local magnetization to the complex-valued field. The static configuration of SkX is described by a simple trial function, with optimal parameters found numerically. The dynamics is then determined by considering the second variation of the action and eventual semi-classical quantization. The calculation of the spectra shows that several magnon branches have non-trivial topology and non-zero Chern numbers. [1] The topological character of low-energy magnon branches may change upon variation of external magnetic field. [2] We argue that the latter topological transition in magnon spectra should be visible in thermal Hall effect at low temperatures.
[1] V. E. Timofeev and D. N. Aristov, Phys. Rev. B 105, 024422 (2022).
[2] V. E. Timofeev and D. N. Aristov, JETP Lett. 117, 9 (2023); ibid. 118, 448 (2023); V. E. Timofeev, Yu. V. Baramygina, and D. N. Aristov, JETP Lett. 118, 911 (2023).
