Spin waves of a current-injected thin ferromagnetic stripe

Abstract

Within a micromagnetic model we present the theory of linearized spin waves of a current-carrying rectangular ferromagnetic stripe treated as a slab of infinite extent. After determining the nonuniform scissorlike magnetic ground state that results when a dc electric current is applied along an in-plane easy axis, we calculate both ferromagnetic resonances and spin-wave dispersion as a function of slab thickness. For Permalloy stripes less than $1\text{ }\ensuremath{\mu}\text{m}$ in thickness, increasing current stiffens the response of bulk spin waves, and their dispersion becomes increasingly asymmetric with respect to the easy axis---shifting to lower (higher) frequencies with (opposite) the direction of current. Also, the frequency and direction of propagation of the Damon-Eshbach surface mode are substantially modified by the current, with changed surface-mode behavior exhibited. Above $1\text{ }\ensuremath{\mu}\text{m}$ in thickness the lowest-lying resonance frequency of the Permalloy stripe softens to zero with increasing current and a gap opens up to finite wavelengths along the direction of current, indicative of a ground-state instability. We discuss the implication of our results to the characterization of the magnetic state of these rectangular structures.