Spin Orbit Coupling and Spin Waves in Ultrathin Ferromagnets: The Spin Wave Rashba Effect

TL;DR

This paper theoretically investigates how spin orbit coupling affects spin wave excitations in ultrathin Fe ferromagnetic layers on W(110), revealing modifications in dispersion relations and increased linewidths due to the Rashba effect.

Contribution

It introduces a formalism to analyze spin wave behavior influenced by spin orbit coupling, highlighting the Rashba effect's impact on dispersion and linewidth in ultrathin ferromagnets.

Findings

Linear dispersion relation due to Dzyaloshinskii-Moriya interaction

Enhanced linewidths of spin wave modes from spin orbit coupling

Rashba-like energy band structure in spin wave dispersion

Abstract

We present theoretical studies of the influence of spin orbit coupling on the spin wave excitations of the Fe monolayer and bilayer on the W(110) surface. The Dzyaloshinskii-Moriya interaction is active in such films, by virtue of the absence of reflection symmetry in the plane of the film. When the magnetization is in plane, this leads to a linear term in the spin wave dispersion relation for propagation across the magnetization. The dispersion relation thus assumes a form similar to that of an energy band of an electron trapped on a semiconductor surfaces with Rashba coupling active. We also show SPEELS response functions that illustrate the role of spin orbit coupling in such measurements. In addition to the modifications of the dispersion relations for spin waves, the presence of spin orbit coupling in the W substrate leads to a substantial increase in the linewidth of the spin wave modes. The formalism we have developed applies to a wide range of systems, and the particular system explored in the numerical calculations provides us with an illustration of phenomena which will be present in other ultrathin ferromagnet/substrate combinations.