Macroscopic ferromagnetic dynamics

Chen Sun

doi:10.1063/5.0291439

Macroscopic ferromagnetic dynamics

2025-09-21

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DOI：10.1063/5.0291439

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In metals with finite magnetization (M) over right arrow, experiment shows that transverse polarized dc spin currents (J) over right arrow (i) both decay and precess on crossing a finite sample thickness. The present work uses Onsager's irreversible thermodynamics, with (M) over right arrow and (J) over right arrow (i) as fundamental variables, to develop a theory with aspects of the Landau-Lifshitz theory solely for the (M) over right arrow of (charged) electronic ferromagnets, and of the Leggett theory for the (M) over right arrow and (J) over right arrow (i) of (uncharged) nuclear paramagnets. As for the ferromagnet of Landau-Lifshitz, partial derivative(t)(M) over right arrow includes a characteristic decay time tau(M). As for the nuclear paramagnet, partial derivative(t)(J) over right arrow (i) includes a characteristic decay time tau(J), is driven by the gradient of a (vector) spin pressure, and precesses about a mean-field proportional to (M) over right arrow. The spin pressure has a coefficient G proportional to a velocity squared, and D-0 equivalent to 1/2G tau(J) serves as an effective diffusion coefficient. These equations apply when spin currents are generated. Using the derived dynamical equations for the magnetization and for the spin current, we obtain the steady-state (dc limit) solution whose transverse wavevector squared is complex, with real part from diffusion and imaginary part from precession. The ac case is also considered. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Keywords:

LIQUID-THEORY PARAMETERS

SPIN-WAVES

FERMI-LIQUID

IRREVERSIBLE-PROCESSES

RECIPROCAL RELATIONS

DIFFUSION

MAGNETIZATION

OSCILLATIONS

LEGGETT

Macroscopic ferromagnetic dynamics

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