Rotationally invariant formulation of spin-lattice coupling in multi-scale modeling

TL;DR

This paper introduces a rotationally invariant theoretical framework for spin-lattice coupling in multi-scale modeling, connecting ab initio parameters with continuum theory, and validates it through simulations of ferromagnetic nanoparticles.

Contribution

It develops a new Hamiltonian formulation that conserves fundamental quantities and implements a corrected numerical method for simulating coupled spin and lattice dynamics.

Findings

Identification of a low-frequency mechanical response in ferromagnetic nanoparticles

Observation of the Einstein-de-Haas effect through particle rotation

Validation of the framework with simulations of magneto-mechanical phenomena

Abstract

In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic continuum theory. The derived Hamiltonian describes a closed system of spin and lattice degrees of freedom and explicitly conserves the total momentum, angular momentum and energy. Using a new numerical implementation that corrects earlier Suzuki-Trotter decompositions we perform simulations on the basis of the resulting equations of motion to investigate the combined magnetic and mechanical motion of a ferromagnetic nanoparticle, thereby validating our developed method. In addition to the ferromagnetic resonance mode of the spin system we find another low-frequency mechanical response and a rotation of the particle according to the Einstein-de-Haas effect. The framework developed herein will enable the use of multi-scale modeling for investigating and understanding a broad range of magneto-mechanical phenomena from slow to ultrafast time scales.