Symmetry requirements for current-induced spin magnetization specific to chiral crystals: Multipole analysis and the hidden spin glide symmetry

TL;DR

This paper investigates the microscopic origins of current-induced spin magnetization in chiral crystals, revealing the importance of specific hopping and spin-orbit couplings, and introduces a multipole framework to understand these effects.

Contribution

It identifies the role of multipole degrees of freedom and spin glide symmetry in CISM, highlighting the significance of hopping along the z-axis in chiral crystals.

Findings

Chiral SOC has a unique multipole degree of freedom.

Hopping along the z-axis is crucial for CISM.

Spin glide symmetry breaking enables CISM in chiral crystals.

Abstract

Current-induced spin magnetization (CISM) specific to chiral crystals is microscopically analyzed using multipole theory to identify the necessary hopping and spin-orbit couplings (SOCs). Tight-binding models capturing the essence of chiral crystals are introduced to investigate the multipole degrees of freedom possessed by the Hamiltonian. The results reveal that chiral SOC has a multipole degree of freedom specific to chiral crystals. Subsequently, the CISM is evaluated numerically and analytically. The results show that in addition to the chiral SOC, hopping along the $z$-axis, which is irrelevant from a multipole perspective, is crucial for CISM. This hopping is required to break the combined symmetry of wavevector translation and spin flipping, which we refer to as spin glide symmetry. This confirms that hopping irrelevant to chirality can play a crucial role in physical properties arising from chirality without contradicting the framework of multipole theory.