Spinor Formulation of the Landau–Lifshitz–Gilbert Equation With Geometric Algebra

The Landau–Lifshitz–Gilbert (LLG) equation for magnetization dynamics is recast into spinor form using the real-valued Clifford algebra (geometric algebra) of three-space. We show how the undamped case can be explicitly solved to obtain componentwise solutions, with clear geometrical meaning. Generalizations of the approach to include damping are formulated. The implications of the axial property of the magnetization vector are briefly discussed.