A ferromagnetic monolayer with model spin-orbit and dipole-dipole interactions

The authors have considered a classical spin model of a ferromagnetic monolayer with model spin-orbit and dipole-dipole interactions, which provide competing perpendicular and in-plane anisotropies respectively. In particular they plot the zero temperature phase diagram, which features, as well as the expected perpendicular and in-plane ferromagnetic phases, a series of unexpected perpendicular antiferromagnetic phases, although these are most important for anisotropy parameter values higher than the authors would expect to see in real monolayers. A mean field theory at finite temperatures predicts the existence of a first-order perpendicular to in-plane reorientation transition of the magnetization for certain values of the parameters. Computer simulations of this system were attempted, but were unsuccessful because of the large correlation lengths arising. The authors draw the tentative conclusion that straightforward Monte Carlo and molecular dynamics simulation is not a practicable way to investigate this system, and note the important technical point that data parallelization of conventional Monte Carlo methods with infinitely long-range interactions is not possible.