# Estimating spin diffusion length and spin Hall angle from spin pumping-induced inverse spin Hall voltages

## TL;DR

This paper clarifies the accurate estimation of spin diffusion length in high spin-orbit materials like platinum, emphasizing the importance of thickness-dependent conductivity and spin diffusion length for reliable parameter extraction from spin pumping experiments.

## Contribution

It demonstrates that a thickness-dependent spin diffusion length, consistent with Elliott-Yafet relaxation, is essential for matching experimental results and improving parameter accuracy.

## Key findings

- Thickness-dependent conductivity and spin diffusion length are necessary.
- A thickness-dependent spin diffusion length aligns with Elliott-Yafet relaxation.
- Variations in estimated parameters impact technological applications.

## Abstract

There exists considerable confusion in estimating the spin diffusion length of materials with high spin-orbit coupling from spin pumping experiments. For designing functional devices, it is important to determine the spin diffusion length with sufficient accuracy from experimental results. An inaccurate estimation of spin diffusion length also affects the estimation of other parameters (e.g., spin mixing conductance, spin Hall angle) concomitantly. The spin diffusion length for platinum (Pt) has been reported in literature in a wide range of 0.5 - 14 nm, and particularly it is a constant value independent of Pt's thickness. Here, the key reasonings behind such wide range of reported values of spin diffusion length have been identified comprehensively. Particularly, it is shown here that a thickness-dependent conductivity and spin diffusion length is necessary to simultaneously match the experimental results of effective spin mixing conductance and inverse spin Hall voltage due to spin pumping. Such thickness-dependent spin diffusion length is tantamount to Elliott-Yafet spin relaxation mechanism, which bodes well for transitional metals. This conclusion is not altered even when there is significant interfacial spin memory loss. Furthermore, the variations in the estimated parameters are also studied, which is important for technological applications.