Mode- and size-dependent Landau-Lifshitz damping in magnetic nanostructures: Evidence for non-local damping

TL;DR

This study reveals that the effective damping in magnetic nanostructures varies significantly with size and mode, influenced by non-local effects like intralayer transverse-spin-pumping, impacting nanoscale spintronic device performance.

Contribution

It provides experimental evidence for non-local damping effects in nanomagnets, demonstrating size and mode dependence aligned with intralayer transverse-spin-pumping theory.

Findings

Damping varies with nanomagnet size and mode

Damping can increase by up to 40% compared to extended films

End-mode damping decreases as nanomagnet size reduces

Abstract

We demonstrate a strong dependence of the effective damping on the nanomagnet size and the particular spin-wave mode that can be explained by the theory of intralayer transverse-spin-pumping. The effective Landau-Lifshitz damping is measured optically in individual, isolated nanomagnets as small as 100 nm. The measurements are accomplished by use of a novel heterodyne magneto-optical microwave microscope with unprecedented sensitivity. Experimental data reveal multiple standing spin-wave modes that we identify by use of micromagnetic modeling as having either localized or delocalized character, described generically as end- and center-modes. The damping parameter of the two modes depends on both the size of the nanomagnet as well as the particular spin-wave mode that is excited, with values that are enhanced by as much as 40% relative to that measured for an extended film. Contrary to expectations based on the ad hoc consideration of lithography-induced edge damage, the damping for the end-mode decreases as the size of the nanomagnet decreases. The data agree with the theory for damping caused by the flow of intralayer transverse spin-currents driven by the magnetization curvature. These results have serious implications for the performance of nanoscale spintronic devices such as spin-torque-transfer magnetic random access memory.