Hamiltonian descriptions of the micromagnetics of finite continuous media in the effective field formalism

Abstract

The equations of motion describing the response of a ferromagnetic system in the micromagnetic approximation can be developed by applying Hamilton's principle to an action functional constructed from a Lagrangian density composed of the usual free energy expression, together with a suitably chosen expression for the kinetic energy density so as to produce the characteristic Larmour precession associated with magnetic spin systems under the influence of an external field. If a Hamiltonian density functional is introduced through the usual Legendre transformation, it can be shown that by a suitable choice of the form of the generalised momenta and the standard form of the Rayleigh dissipation energy density functional, equations of motion are derived which are formally equivalent to the Landau-Lifshitz-Gilbert form. However, the form of the equations of motion permits a substantial increase in the time step. An alternative description which avoids the introduction of a kinetic energy term, but which retains all the essential attributes of the former approach, is described. The model is applied to small rectangular polycrystalline cobalt samples with in-plane randomly oriented uniaxial anisotropy directions.