Quantum effects for the 2D soliton in isotropic ferromagnets

Abstract

We evaluate a zero-point quantum correction to a Belavin-Polyakov soliton in an isotropic 2D ferromagnet. By revising the scattering problem of quasi-particles by a soliton we show that it leads to the Aharonov-Bohm type of scattering, hence the scattering data can not be obtained by the Born approximation. We proof that the soliton energy with account of quantum corrections does not have a minimum as a function of its radius, which is usually interpreted as a soliton instability. On the other hand, we show that long lifetime solitons can exist in ferromagnets due to an additional integral of motion, which is absent for the sigma-model.