Micromagnetics at Finite Temperature

Based on the micromagnetic method using Landau-Lifshitz (LL) or the equivalent LL-Gilbert equations, the motion of magnetic moments can be solved for typical ferromagnetic materials and devices; however, these calculations, in which the magnitude of magnetization moment ⃗M in a micromagnetic cell is set to a constant, cannot account for thermal fluctuation effects at finite temperatures. In this paper, a new micromagnetic method is brought up for ferromagnets based on the hybrid Monte Carlo algorithm, such that the magnetic properties-including M-H loops and domain structures-can be obtained at arbitrary temperature below Curie point T
_c
. At low temperatures below T
_c
, we test the standard problem 3 of micromagnetics, the results of the new model basically agree with the conventional micromagnetic model using LL equations, but the singularity due to the ⃗M × ⃗H term in the LL equations can be avoided, thus the simulated loops are more dependable especially for the soft magnetic materials; in the test for hard magnetic particles, the new model reduces back to the Stoner-Wohlfarth model. At higher temperatures, the new method is checked using a mean-field inspired free-energy model, the M-H loops can also be obtained and the decrease of coercivity versus T can be illustrated.