THE EQUATIONS OF MOTION OF MICROMAGNETICS IN HAMILTONIAN FORM

The equations of motion describing the response of a ferromagnetic sys tem in the micromagnetic approximation are developed by applying Hamil ton'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 pro duce the characteristic Larmor precession associated with magnetic spi n systems under the influence of an external field. A suitable choice of the form of the generalised momenta and the standard form of the Ra yleigh dissipation energy density functional, leads to equations of mo tion which exhibit similar behaviour to the Landau-Lifshitz-Gilbert fo rm. It is shown that with our Hamiltonian formulation, micromagnetic s imulations of systems with very many degrees of freedom can be perform ed with a substantial increase in the upper limit on the timestep size .