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.
@article{arxiv.2501.03798,
title = {Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra},
author = {Kristjan O. Klausen and Snorri Ingvarsson},
journal= {arXiv preprint arXiv:2501.03798},
year = {2025}
}