Small-amplitude mobile solitons in the two-dimensional ferromagnet

Abstract

Two-parameter small-amplitude magnetic solitons moving with arbitrary velocity on a two-dimensional easy-axis ferromagnet are obtained from the approximate solution of the dynamics equations for this system. Both radially symmetric solitons and structures with a quasivortex core are considered. These solitons are characterized by precession of the magnetization about the easy axis, and the corresponding integrals of motion, namely, the energy E, the linear momentum P, and the number of bound magnons N are calculated. The radially symmetric solitons are shown to have the lower energy of the two and they are stable, whereas the lower energy solitons are unstable. For the stable solitons it was found that the dispersion relation $E=E(P,N)$ was found to have a minimum at the value of ${E}_{0}{=11.2\mathrm{JS}}^{2}$ on the ellipse of arbitrary size. It is remarkable that this energy is approximately independent of the parameters except for the exchange constant J and the value of the atomic spin S. Also, the value of ${E}_{0}$ is only slightly smaller than the energy of the well-known Belavin-Polyakov soliton, ${E}_{0}{=0.93E}_{\mathrm{BP}},$ where ${E}_{\mathrm{BP}}=4\ensuremath{\pi}{\mathrm{JS}}^{2}.$ Finally the soliton dispersion relation is used to calculate the soliton density, and a comparison of the soliton density with the magnon density shows that there is a wide range of temperatures where solitons will give the dominant contributions to thermodynamic quantities. It is expected that these solitons will give an essential contribution to observed dynamical quantities such as the spin-correlation functions.