Monte Carlo simulation of two‐dimensional domain structures in magnetite

A Monte Carlo method was applied for micromagnetic studies of two‐dimensional domain structures of a 1‐μm magnetite cube in zero field. By using this method we could incorporate the effect of thermal agitation into micromagnetic modeling. Starting from an initial single‐domain structure (a saturated state), we obtained a closure domain structure with three body and four closure domains. This structure is quite different from the checkerboard‐like structure obtained by a conjugate gradient method, and it gives a much lower energy and saturation remanence ratio. An initial lamellar two‐domain structure evolved into a vortex structure, which was also reached from an initial quasi‐vortex structure. Although such a vortex structure has a lower energy than the closure domain structure, it was not attainable from an initial single‐domain structure at room temperature. The Monte Carlo method is effective in finding a path to escape from unstable local energy minima and reach a stable local energy minimum, although not necessarily a global minimum, at a given temperature. The structure corresponding to such a stable local minimum should represent a realistic domain structure, comparable to what would be attained in nature with the aid of thermal fluctuations of spins.