Spin-Dynamical Analysis of Supercell Spin Configurations

TL;DR

This paper introduces a model-independent method to extract spin-wave frequencies and dispersion relations from supercell spin configurations, applicable to harmonic spin wave systems, with a quantum derivation and case study on a 3D Heisenberg ferromagnet.

Contribution

A novel, model-independent approach for analyzing spin dynamics directly from supercell configurations, linking observed spin orientations to spin-wave properties.

Findings

Successfully extracted spin-wave dispersion curves from Monte Carlo configurations.

Established the relationship between the spin coordinate matrix eigenvalues and spin-wave frequencies.

Validated the method with a quantum-mechanical derivation and a case study on a 3D Heisenberg ferromagnet.

Abstract

A model-independent approach capable of extracting spin-wave frequencies and displacement vectors from ensembles of supercell spin configurations is presented. The method is appropriate for those systems whose spin-dynamical motion is well characterised by small-amplitude fluctuations that give harmonic spin waves. First, the the spin-dynamical matrix is described and its eigenvalues shown to correspond to the spin-wave mode frequencies. The generalised spin coordinate matrix - a quantity that may be calculated from the observed spin orientations in an ensemble of spin configurations - is then introduced and its relationship to the spin-dynamical matrix established. Its eigenvalues are subsequently shown to be related to the spin-wave mode frequencies, allowing the extraction of spin-wave dispersion curves from configurational ensembles. Finally, a quantum-mechanical derivation of the same results is given, and the method applied as a case study to spin Monte-Carlo configurations of a 3D Heisenberg ferromagnet.