Numerical simulation of magnetic discrete breathers in a Heisenberg spin chain with antisymmetric exchange

I.G. Bostrem, V.E. Sinitsyn, A.S. Ovchinnikov, M.I. Fakhretdinov, E.G. Ekomasov show affiliations and emails
Received 22 December 2020; Accepted 21 January 2021;
This paper is written in Russian
Citation: I.G. Bostrem, V.E. Sinitsyn, A.S. Ovchinnikov, M.I. Fakhretdinov, E.G. Ekomasov. Numerical simulation of magnetic discrete breathers in a Heisenberg spin chain with antisymmetric exchange. Lett. Mater., 2021, 11(1) 109-114
BibTex   https://doi.org/10.22226/2410-3535-2021-1-109-114

Abstract

Spatially localized breather excitations are investigated for the model of a discrete Heisenberg spin chain, which includes an antisymmetric exchange interaction and single-ion anisotropy of the easy-plane type. Taking into account the antisymmetric exchange leads to the excitation of only antisymmetric magnetic discrete breathers.By using numerical methods, we consider possibility of the spatially localized breather-type excitations for the model of the discrete Heisenberg spin chain, which includes the antisymmetric exchange interaction, the single-ion anisotropy of the easy plane type, and the Zeeman interaction with an external magnetic field, which exceeds a critical field of the transition to the state of forced ferromagnetism. To find solutions, we used equations of motion for spin operators. The case is considered when the frequency of discrete magnetic breathers lies above the upper edge of the spin wave spectrum. The chain length used in the calculations had been taken as 100 and 101 nodes, and the open boundary conditions were used. To carry out numerical calculations, an original program was written which simplifies maximally calculation of spin deviations inside the chain and enables us to use parallel computing technologies. A classification of symmetric and antisymmetric solutions was established, which made it possible to halve a number of calculations for spin deviations. An algorithm was elaborated to specify the amplitudes of spin deviations, that makes possible to construct a desired breather solution in a reasonable amount of time. The numerical calculations of the spin spatial distribution show that it has an antisymmetric ordering with respect to the center of the chain in the presence of the Dzyaloshinskii-Moriya interaction. The center of the solution can be located either between the lattice nodes (Page mode) in the case of an even number of lattice sites, or directly at the node in the case of the odd number (Takeno-Sievers mode). In the first case, the breather mode contains an odd number of pairs of magnetic kink-antikinks with a maximum of the envelope function at the center. Breather modes include an even number of these pairs for an odd number of lattice nodes.

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Funding

1. Russian Foundation for Basic Research - 20-02-00213