Spin vortices, skyrmions and the Kosterlitz-Thouless transition in the two-dimensional antiferromagnet

Abstract

We investigate spin-vortex excitations in the two-dimensional antiferromagnet on the basis of the nonlinear sigma model. The model of two-dimensional Heisenberg quantum antiferromagnet is mapped onto the (2+1)D nonlinear sigma model. The 2D nonlinear sigma model has an instanton (or skyrmion) solution which describes an excitation of spin-vortex type. Quantum fluctuations of instantons are reduced to the study of the Coulomb gas, and the gas of instantons of the 2D nonlinear sigma model is in the plasma phase. We generalize this picture of instanton gas to the (2+1)D nonlinear sigma model. We show, using some approximation, that there is a Kosterlitz-Thouless transition from the plasma phase to the molecular phase as the temperature is lowered.

Polarizability of electrically induced magnetic vortex plasma

“…Since we are modeling thin-film material, we assume that the film thickness h is much less than the exchange length and neglect the variations of M in the transverse to the film direction. We also note that the same kind of analysis can be done also for an antiferromagnetic model, which also possesses the vortex excitations 45 . The most interesting energy part is the coupling energy 27 , which characterizes type-II multiferroics…”