Abstract
This chapter deals with spatially uniform magnetization dynamics, which is mathematically described by the Landau–Lifshitz–Gilbert (LLG) or Landau–Lifshitz (LL) equation coupled through the effective field with the magnetostatic Maxwell equations. The particle magnetization is spatially uniform and the solution of the magnetostatic Maxwell equations is given in terms of the demagnetizing factors. As a result, the effective magnetic field is expressed as a vectorial algebraic function of the spatially uniform magnetization. The entire system of the LLG–Maxwell equations is exactly transformed into a single nonlinear LLG (or LL) equation. The structural aspects of the nonlinear magnetization dynamics described by the LL equation are also discussed. Basic qualitative features of the dynamics under applied magnetic field directly follow from the confinement of this dynamics to the unit sphere. The LLG and LL equations can be generalized to situations when the magnetization dynamics is driven not only by the applied magnetic field, but by some other forces such as spin-polarized current injection. Equilibrium states for the case when the component of the applied magnetic field along one of the principal anisotropy axes is equal to zero are also discussed.
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