Conversion between electron spin and microscopic atomic rotation

TL;DR

This paper explores the microscopic mechanism linking electron spin and atomic rotation in crystals, demonstrating how local atomic rotations influence spin magnetization via spin-orbit interaction, with results depending on band gap size.

Contribution

It provides a theoretical model showing how atomic rotations induce spin magnetization through spin-orbit coupling, highlighting the dependence on electronic band structure.

Findings

Time-averaged spin magnetization is generated by atomic rotations.

Spin magnetization vanishes in systems with time-reversal symmetry.

Magnitudes decrease with larger band gaps.

Abstract

We theoretically investigate the microscopic mechanism of conversion between the electron spin and the microscopic local rotation of atoms in crystals. In phonon modes with angular momenta, the atoms microscopically rotate around their equilibrium positions in crystals. In a simple toy model with phonons, we calculate the spin expectation value by using the adiabatic series expansion. We show that the time-averaged spin magnetization is generated by the microscopic local rotation of atoms via the spin-orbit interaction. On the other hand, in the system with a simple vibration of atoms, time-averaged spin magnetization becomes zero due to the time-reversal symmetry. Moreover, the magnitude of the time-averaged spin magnetization depends on the inverse of the difference of instantaneous eigenenergy, and we show that it becomes smaller in band insulators with a larger gap.