A spin-rotation mechanism of Einstein-de Haas effect based on a ferromagnetic disk

TL;DR

This paper presents a microscopic spin-rotation mechanism for the Einstein-de Haas effect, using spin-lattice equations to explain angular momentum transfer in ferromagnetic disks, with implications for magneto-mechanical applications.

Contribution

It introduces a detailed spin-rotation coupling model based on elasticity theory, elucidating the microscopic mechanism behind the Einstein-de Haas effect and its inverse.

Findings

Angular momentum transfer timescale ~0.01 ns for 100 nm disks

Linear relationship between magnetic field strength and rotation frequency

Spin-lattice relaxation time inversely proportional to magnetic field in damping conditions

Abstract

Spin-rotation coupling (SRC) is a fundamental phenomenon that connects electronic spins with the rotational motion of a medium. We elucidate the Einstein-de Haas (EdH) effect and its inverse with SRC as the microscopic mechanism using the dynamic spin-lattice equations derived by elasticity theory and Lagrangian formalism. By applying the coupling equations to an iron disk in a magnetic field, we exhibit the transfer of angular momentum and energy between spins and lattice, with or without damping. The timescale of the angular momentum transfer from spins to the entire lattice is estimated by our theory to be on the order of 0.01 ns, for the disk with a radius of 100 nm. Moreover, we discover a linear relationship between the magnetic field strength and the rotation frequency, which is also enhanced by a higher ratio of Young's modulus to Poisson's coefficient. In the presence of damping, we notice that the spin-lattice relaxation time is nearly inversely proportional to the magnetic field. Our explorations will contribute to a better understanding of the EdH effect and provide valuable insights for magneto-mechanical manufacturing.