Magnetic Moment vs Angular Momentum: Spin Hall Response in Bismuth

TL;DR

This paper investigates the difference between spin angular momentum and magnetic moment in spin currents within multiband systems, revealing that magnetic moments can dominate and significantly affect spin Hall responses in bismuth.

Contribution

The study introduces a multiband $k \, p$ model to compute intrinsic spin Hall conductivity tensors, highlighting the dominance of magnetic moments over angular momentum in bismuth.

Findings

Magnetic-moment tensor is about two orders of magnitude larger than angular-momentum tensor.

Magnetic-moment spin Hall angle exceeds unity.

Quasiparticle damping activates longitudinal components of the spin current.

Abstract

Spin currents can carry either spin angular momentum or its associated magnetic moment, which are no longer strictly proportional in multiband systems. Using a multiband $k \cdot p$ model, we compute the intrinsic spin Hall conductivity tensors of elemental Bi. The magnetic-moment tensor emerges about two orders of magnitude larger and far less anisotropic than the angular-momentum tensor, while quasiparticle damping activates otherwise longitudinal components. The magnetic-moment spin Hall angle exceeds unity, demonstrating that a clear distinction between the two currents is indispensable for multiband systems.