Fluctuations of the Magnetization in Thin Films due to Conduction Electrons

TL;DR

This paper analyzes how conduction electrons influence magnetization fluctuations in thin ferromagnetic films, revealing non-local dynamics, oscillatory damping effects, and the colored nature of sd-exchange noise beyond the Gilbert approximation.

Contribution

It extends the understanding of magnetization dynamics by deriving a non-local equation of motion that accounts for non-adiabatic effects and provides a comprehensive noise analysis for thin films.

Findings

Damping is enhanced and oscillates with film thickness due to interfacial effects.

sd-exchange noise is inherently colored and depends on the Hamiltonian symmetry.

The Gilbert equation is only valid in the adiabatic limit; otherwise, new dynamics emerge.

Abstract

A detailed analysis of damping and noise due to a {\it sd}-interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey in general a non-local equation of motion which differs from the the Gilbert equation and is extended to the non-adiabatic regime. To lowest order in the exchange interaction and in the limit where the Gilbert equation applies, we show that the damping term is enhanced due to interfacial effects but it also shows oscillations as a function of the film thickness. The noise calculation is however carried out to all orders in the exchange coupling constant. The ellipticity of the precession of the magnetization is taken into account. The damping is shown to have a Gilbert form only in the adiabatic limit while the relaxation time becomes strongly dependent on the geometry of the thin film. It is also shown that the induced noise characteristic of sd-exchange is inherently colored in character and depends on the symmetry of the Hamiltonian of the magnetization in the film. We show that the sd-noise can be represented in terms of an external stochastic field which is white only in the adiabatic regime. The temperature is also renormalized by the spin accumulation in the system. For large intra-atomic exchange interactions, the Gilbert-Brown equation is no longer valid.