Dependence of nonlocal Gilbert damping on the ferromagnetic layer type in FM/Cu/Pt heterostructures

TL;DR

This study investigates how the nonlocal Gilbert damping in FM/Cu/Pt heterostructures depends on the ferromagnetic layer type, revealing a consistent inverse power law behavior linked to spin diffusion effects.

Contribution

It demonstrates that nonlocal Gilbert damping follows a universal inverse power law across different ferromagnetic materials, supporting spin diffusion as the primary mechanism.

Findings

Damping obeys a power law with exponent -1.04

Magnitude of damping is approximately 224 MHz·nm

Results support spin diffusion over resistivity as the damping origin

Abstract

We have measured the size effect in nonlocal Gilbert relaxation rate in FM(t$_{FM}$) / Cu (5nm) [/ Pt (2nm)] / Al(2nm) heterostructures, FM = \{ Ni$_{81}$Fe$_{19}$, Co$_{60}$Fe$_{20}$B$_{20}$, pure Co\}. Common behavior is observed for three FM layers, where the additional relaxation obeys both a strict inverse power law dependence $\Delta G =K \:t^{n}$, $n=-\textrm{1.04}\pm\textrm{0.06}$ and a similar magnitude $K=\textrm{224}\pm\textrm{40 Mhz}\cdot\textrm{nm}$. As the tested FM layers span an order of magnitude in spin diffusion length $\lambda_{SDL}$, the results are in support of spin diffusion, rather than nonlocal resistivity, as the origin of the effect.