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A Guide to Phenomenological Damping Formulations

Published

Author(s)

J O. Rantschler, C Alexander

Abstract

There are several phenomenological damping formulations currently in use in the literature. Beyond the Landau-Lifshitz equation (LL) and the Bloch-Bloembergen equations (BB), there is Safonov and Bertram s (SB) method designed to bridge between microscopic physics and macroscopic magnetic motions [1]. For small oscillations and for small damping, each is equivalent. However, each has different interpretations and effects when dealing with the dynamics of the magnetization, and each equation has at least one slightly different interpretation that can lead to different behavior, such as those predicted between LL and the Landau-Lifshitz-Gilbert (LLG) equation [2]. Callen wrote a general equation for the dynamics of the magnetization that reflects the fact that magnetic motions can move in either of three directions, along the magnetization, along the direction of the torque, and perpendicular to them both [3]. We here systematically examine LL, BB, SB and some variants in light of Callen s equation by constructing a damped harmonic oscillator and comparing terms. This allows us to show the differences between each formulation both in terms of the effects of the damping on the magnetization (i.e., in slowing or canting) and in light of various ferromagnetic resonance experiments.
Citation
Journal of Applied Physics

Keywords

Bloch-Bloembergen equations (BB), Landau-Lifshitz equation (LL), oscillations microscopic physics

Citation

Rantschler, J. and Alexander, C. (2008), A Guide to Phenomenological Damping Formulations, Journal of Applied Physics (Accessed February 27, 2024)
Created October 16, 2008