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arXiv · 2501.03798

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

Kristjan O. Klausen·Snorri Ingvarsson
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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.

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Kristjan O. Klausen, Snorri Ingvarsson. 2025-01-07. Spinor formulation of the Landau-Lifshitz-Gilbert equation with geometric algebra. https://doi.org/10.1109/tmag.2024.3509214

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