Chern Numbers for Spin Models of Transition Metal Nanomagnets

TL;DR

This paper links the topological properties of nanomagnet wavefunctions, specifically Chern numbers, to their magnetic behavior, providing a new way to understand spin dynamics in transition metal nanoparticles.

Contribution

It introduces a topological framework using Chern numbers to describe the effective spin Hamiltonian of small ferromagnetic nanoparticles.

Findings

Chern numbers depend on spin-orbit coupling strength.

Topological properties influence magnetization dynamics.

Effective Hamiltonian captures nanoparticle spin behavior.

Abstract

We argue that ferromagnetic transition metal nanoparticles with fewer than approximately 100 atoms can be described by an effective Hamiltonian with a single giant spin degree of freedom. The total spin $S$ of the effective Hamiltonian is specified by a Berry curvature Chern number that characterizes the topologically non-trivial dependence of a nanoparticle's many-electron wavefunction on magnetization orientation. The Berry curvatures and associated Chern numbers have a complex dependence on spin-orbit coupling in the nanoparticle and influence the semiclassical Landau-Liftshitz equations that describe magnetization orientation dynamics.