Cell size corrections for nonzero-temperature micromagnetics

Micromagnetic calculations at nonzero temperatures depend on the computational cell size. This paper shows that the spontaneous magnetization MS of exchange-coupled moments has to be scaled by a Bloch-like law, which is similar to the well-known temperature dependence of MS. Using this scaling law, nonatomistic Metropolis Monte Carlo and stochastic Landau–Lifshitz–Gilbert simulations are performed in an external field of 0.1T. The error of the equilibrium magnetization at a temperature of T∕TC=0.38 and a cell size of 1.5nm is then 0.9% as compared with atomistic calculations. In contrast, a cell size-independent MS leads to an overestimation of the temperature of 3.2%.