Soliton-magnon scattering in a two-dimensional isotropic magnetic material

We use the generalized sigma-model to analytically study the solution of th e problem of magnon scattering in two-dimensional isotropic ferromagnets an d antiferromagnets in the presence of a Belavin-Polyakov soliton. We obtain the exact analytical solution to this problem for the partial mode with th e azimuthal quantum number m=1. The scattering amplitude for other values o f m (i.e., values not equal to unity) are studied analytically in the long- and short-wavelength approximations and also numerically for an arbitrary value of the wave number. We establish the general laws governing the solit on-magnon interaction. For a magnetic material of finite dimensions we calc ulate the frequencies of the magnon modes. We also use the data on local mo des to derive the equations of motion of the soliton. Finally, we calculate the low-temperature (long-wavelength) asymptotic behavior of the magnon de nsity of states due to the soliton-magnon interaction. (C) 1999 American In stitute of Physics. [S1063-7761(99)02309-4].