Spin-Hall Torques Generated by Rare-Earth (Lanthanide) Thin Films

TL;DR

This study experimentally measures spin-Hall torques in rare-earth thin films and compares results with first-principles calculations, revealing the influence of $f$ orbitals on spin Hall conductivity and suggesting ways to enhance it.

Contribution

It provides the first experimental survey of spin-Hall torques in rare-earth metals and correlates these with first-principles calculations, highlighting the role of $f$ orbitals.

Findings

Gd, Dy, Ho, and Lu exhibit measurable spin-Hall torque ratios.

DFT calculations show $f$ orbitals enhance spin Hall conductivity in Dy and Ho.

The results suggest shifting the electron chemical potential could strengthen the spin Hall effect.

Abstract

We report an initial experimental survey of spin-Hall torques generated by the rare-earth metals Gd, Dy, Ho, and Lu, along with comparisons to first-principles calculations of their spin Hall conductivities. Using spin torque ferromagnetic resonance (ST-FMR) measurements and DC-biased ST-FMR, we estimate lower bounds for the spin-Hall torque ratio, $\xi_{SH}$, of $\approx$ 0.04 for Gd, $\approx$ 0.05 for Dy, $\approx$ 0.14 for Ho, and $\approx$ 0.014 for Lu. The variations among these elements are qualitatively consistent with results from first principles (density functional theory, DFT, in the local density approximation with a Hubbard-U correction). The DFT calculations indicate that the spin Hall conductivity is enhanced by the presence of the partially-filled $f$ orbitals in Dy and Ho, which suggests a strategy to further strengthen the contribution of the $f$ orbitals to the spin Hall effect by shifting the electron chemical potential.