Quantum effects for the two-dimensional soliton in isotropic ferromagnets

We evaluate a zero-point quantum correction to a Belavin-Polyakov soliton in an isotropic two-dimensional ferromagnet. By revising the scattering problem of quasiparticles by a soliton we show that it leads to the Aharonov-Bohm type of scattering; hence the scattering data cannot be obtained by the Born approximation. We prove 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 σ model.