Three-dimensional micromagnetic modelling of ferromagnetic domain structure

Abstract

The fidelity of magnetic recording materials (whether they be synthetic crystals on a recording tape, or natural crystals in rocks recording changes in the Earth's magnetic field) depends on the uniformity of their magnetic structure. Such structure is determined by minimizing the energies arising from atomic magnetic dipole interactions. Previous micromagnetic models of coupled spin structures have contained well defined constraints to make the calculations tractable. By using a supercomputer, we have been able to perform unconstrained calculations of minimum energy structures for cubic assemblies of up to 22×22×22 exchange-coupled spins. The critical size for transformation from a uniform single-domain structure to a non-uniform three-dimensional structure is about 0.1 µm for magnetite, as found previously from one-dimensional modelling. However, a variety of different non-uniform structures are possible, with energies and magnetic moments much less than those of conventional lamellar domains. The predicted moments of unweighted combinations of these states agree well with experimental measurements on magnetite in the size range 0.08-0.5 μm. Surface spin structures are such as to minimize flux leakage out of the particle and might be misleadingly imaged by the Bitter colloid technique as indicating a single-domain state.