Magnetization Reversal of the Two-Dimensional Heisenberg Ferromagnet with Weak Ising Anisotropy

Fluctuations related to the Belavin-Polyakov pseudoparticle play an important role in the decay of the metastable state, where external field reverse to the spontaneous magnetization is applied. The energy at the saddle point is of the order of the exchange constant unless the external field is much weaker than the anisotropy. It is well known the isotropic Heisenberg ferromagnet in two-dimensional space does not show any phase transition. Belavin and Polyakov1l demonstrated that the phys ical origin of the finite correlation length is the existence of pseudoparticles with finite energy independent of their scale. But m real two-dimensional magnets, which have not been realized experi mentally yet, small uniaxial anisotropy always exists. With Ising anisotropy, no matter how small it is, the pseudoparticles collapse to disappear, and spontaneous magnetization occurs. The transition tem perature depends on the strength of the anisotropy logarithmically, 2l and we can observe the magnetization at relatively high temperatures. In this paper we show the pseudoparticle mode, though it may not exist stably, plays the principal role in the decay of a metastable state. We deal with a classical Heisenberg ferromagnet in the continuous limit with weak Ising anisotropy and applied magne tic field. The energy as a function of the spin configuration has the form,