  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.
