# The microscopic Einstein-de Haas effect

## TL;DR

This paper models the microscopic Einstein-de Haas effect using a non-collinear tight-binding approach, revealing the roles of spin-orbit coupling, magnetic fields, and electronic orbital contributions in transferring spin to mechanical angular momentum.

## Contribution

It introduces a detailed microscopic model of the Einstein-de Haas effect incorporating spin-orbit coupling and external magnetic fields, advancing understanding beyond semi-classical explanations.

## Key findings

- Validation of the EdH effect through generated torque on the dimer.
- Identification of additional torque contributions from orbital angular momentum and Faraday electric fields.
- Analysis of energy level crossings and magnetic field variation effects.

## Abstract

The Einstein-de Haas (EdH) effect, where the spin angular momentum of electrons is transferred to the mechanical angular momentum of atoms, was established experimentally in 1915. While a semi-classical explanation of the effect exists, modern electronic structure methods have not yet been applied to modelling the phenomenon. In this paper we investigate its microscopic origins by means of a non-collinear tight-binding model of an $\textrm{O}_2$ dimer, which includes the effects of spin-orbit coupling, coupling to an external magnetic field, and vector Stoner exchange. By varying an external magnetic field in the presence of spin-orbit coupling, a torque can be generated on the dimer, validating the presence of the EdH effect. Avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We find also that the torque exerted on the nuclei by the electrons in a time-varying $B$ field is not only due to the EdH effect. Other contributions arise from field-induced changes in the electronic orbital angular momentum and from the direct action of the Faraday electric field associated with the time-varying magnetic field.