Constrained Monte Carlo Method and Calculation of the Temperature Dependence of Magnetic Anisotropy

We introduce a constrained Monte Carlo method which allows us to traverse the phase space of a classical spin system while fixing the magnetization direction. Subsequently we show the method's capability to model the temperature dependence of magnetic anisotropy, and for bulk uniaxial and cubic anisotropies we recover the low-temperature Callen-Callen power laws in M. We also calculate the temperature scaling of the 2-ion anisotropy in L10 FePt, and recover the experimentally observed M^2.1 scaling. The method is newly applied to evaluate the temperature dependent effective anisotropy in the presence of the N'eel surface anisotropy in thin films with different easy axis configurations. In systems having different surface and bulk easy axes, we show the capability to model the temperature-induced reorientation transition. The intrinsic surface anisotropy is found to follow a linear temperature behavior in a large range of temperatures.