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-mu m 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.