Magnetization reversal in a "quasi" single domain magnetic grain: a new   numerical micromagnetic technique
  Magnetization reversal in a fine ferromagnetic grain is simulated for the case of an instantaneously applied reversal magnetic field. The Hamiltonian of the system contains the exchange interaction, the uniaxial anisotropy, the Zeeman energy and the dipole-dipole interactions. A cubic grain is discretized into 64 cubic subgrains and the coupled gyromagnetic equations of motion are solved without phenomenological damping. A new scheme to solve these equations is developed that utilizes only two variables per sub-cube magnetization and strictly conserves the absolute magnitude. The initial stage of reversal is uniform rotation followed by a nonlinear excitation of nonuniform magnetic oscillations driven by this uniform mode. An excess of the initial Zeeman energy is transformed into nonlinear spin waves, allowing the average magnetization to substantially reverse. The process of magnetization reversal in fine quasi-single-domain grain exhibits general features of Hamiltonian wave systems with nonlinear diffusion. This nonlinear diffusion is forbidden for either a strong reversal field and/or a small grain size. 
Vladimir L. Safonov and H. Neal Bertram