Anisotropic Gyromagnetic Ratio and Orthogonal Einstein-de Haas Effect

TL;DR

This paper predicts an orthogonal Einstein-de Haas effect caused by anisotropic gyromagnetic ratios, linking phonon angular momentum with spin-order configurations through a microscopic theoretical framework.

Contribution

It introduces the concept of an orthogonal Einstein-de Haas effect and explains its microscopic origin via spin-orbit coupling and phonon angular momentum analysis in ferromagnets.

Findings

Demonstrates the orthogonal Einstein-de Haas effect theoretically.

Shows phonon angular momentum has a dipolar structure in spin space.

Reveals different contributions of spin-orbit coupling components.

Abstract

We theoretically demonstrate an orthogonal Einstein-de Haas effect, where the rotation of ferromagnetic materials is caused by the change of magnetization in the direction orthogonal to the rotation axis. This amounts to an anisotropic gyromagnetic ratio. To reveal its microscopic origin, we treat the spin-orbit coupling as a perturbation, integrate out the electronic degree of freedom, and show that in collinear ferromagnets the phonon angular momentum admits a dipolar structure in the spin-order space due to the constraint of the spin group symmetry. The spin-flipping and spin-conserving parts of the spin-orbit coupling contribute differently to such a dipolar structure. All these features are exemplified in a lattice electron-phonon model with ferromagnetic order and $C_{1h}$ point group symmetry. Our work lays the ground for revealing the connection between phonon angular momentum and general spin-order configurations.