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

Abstract

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 kinkantikinks 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.