HAMILTONIAN DESCRIPTIONS OF THE MICROMAGNETICS OF FINITE CONTINUOUS MEDIA IN THE EFFECTIVE-FIELD FORMALISM

The equations of motion describing the response of a ferromagnetic sys tem in the micromagnetic approximation can be developed by applying Ha milton's principle to an action functional constructed from a Lagrangi an 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 Hamiltoni an density functional is introduced through the usual Legendre transfo rmation, 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 f ormally equivalent to the Landau-Lifshitz-Gilbert form. However, the f orm of the equations of motion permits a substantial increase in the t ime 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 re ctangular polycrystalline cobalt samples with in-plane randomly orient ed uniaxial anisotropy directions.