Out-of-plane vortex in a two-dimensional easy-plane ferromagnet with a magnetic field along the hard axis

In a two-dimensional easy-plane Heisenberg model with a magnetic field along the hard axis, switching between different vortex states (parallel and antiparallel to the field) was studied by means of a Monte Carlo simulation. The vortex-core magnetization appears to be conserved, whether a magnetic field is present or not. From conservation of the core magnetization, the switching field between the two vortex states were calculated, in good agreement with the Monte Carlo simulation.