The equations of motion of micromagnetics in Hamiltonian form

The equations of motion describing the response of a ferromagnetic system in the micromagnetic approximation are 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 Larmor precession associated with magnetic spin systems under the influence of an external field. A suitable choice of the form of the generalised momenta and the standard form of the Rayleigh dissipation energy density functional, leads to equations of motion which exhibit similar behaviour to the Landau-Lifshitz-Gilbert form. It is shown that with our Hamiltonian formulation, micromagnetic simulations of systems with very many degrees of freedom can be performed with a substantial increase in the upper limit on the timestep size.