Study of intrinsic spin and orbital Hall effects in Pt based on a (6s, 6p, 5d) tight-binding model

TL;DR

This study investigates the intrinsic spin and orbital Hall effects in platinum using a detailed multiorbital tight-binding model, revealing large conductivities driven by spin-orbit interactions and interorbital transitions.

Contribution

It introduces a multiorbital tight-binding model to explain the large intrinsic spin and orbital Hall effects in platinum, emphasizing the role of effective magnetic flux from interorbital transitions.

Findings

SHC reaches 1000 /eΩcm at low resistivity

OHC remains larger than SHC across conditions

Large effective magnetic flux causes significant SHE and OHE

Abstract

We study the origin of the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in Pt based on a multiorbital tight-binding model with spin-orbit interaction. We find that the SHC reaches 1000 \hbar/e\Omega cm when the resistivity \rho is smaller than ~10 \mu\Omega cm, whereas it decreases to 300 \hbar/e\Omega cm when \rho ~ 100 \mu\Omega cm. In addition, the OHC is still larger than the SHC. The origin of huge SHE and OHE in Pt is the large ``effective magnetic flux'' that is induced by the interorbital transition between d_{xy}- and d_{x2-y2}-orbitals with the aid of the strong spin-orbit interaction.