Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra

Abstract

The Landau-Lifshitz-Gilbert 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 component-wise 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.

6 pages, 4 figures

References in corpus (6)

• Spin Transfer Torques
• Van der Waals heterostructures for spintronics and opto-spintronics
• The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
• Spin-transfer and spin-orbit torques in the Landau-Lifshitz-Gilbert equation
• Bath-induced spin inertia
• The fractional Landau-Lifshitz-Gilbert equation