Can the Landau-Lifshitz equation explain the spin-wave instability in ferromagnetic thin films for parallel pumping?

TL;DR

This paper investigates whether the Landau-Lifshitz equation alone can explain spin-wave instability thresholds in ferromagnetic thin films under parallel pumping, revealing limitations and differences compared to perpendicular pumping cases.

Contribution

It provides an analytical comparison of the Landau-Lifshitz equation's ability to explain spin-wave instabilities in different pumping geometries, highlighting the need to relate nonlinear terms to spin-wave line width.

Findings

The Landau-Lifshitz equation cannot fully explain the butterfly curve in parallel pumping.

The equation successfully explains Suhl instability in perpendicular pumping.

Nonlinear relaxation terms are key to understanding the instability thresholds.

Abstract

Spin-wave instability is studied analytically in the case of parallel pumping for thin films under external field perpendicular to the film plane. It is examined whether the instability threshold derived from only the Landau-Lifshitz (LL) equation can explain experimental instability threshold without using the microscopically-derived spin-wave line width, which is conventionally used. It is revealed that the butterfly curve cannot be explained from only the LL equation at least in an analytical way. By contrast, for the case of perpendicular pumping, the Suhl instability was well explained from the LL equation. The difference between the two cases comes from the nonlinear terms describing the relaxation of spin waves. It is suggested how the nonlinear terms in the LL equation should be related to the spin-wave line width for parallel pumping.