Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain

TL;DR

This paper theoretically demonstrates a magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain by deriving a Dirac-like equation and analyzing wave packet dynamics.

Contribution

It introduces a Dirac-like equation for antiferromagnetic spin chains and shows the presence of Zitterbewegung, a relativistic quantum effect, in this classical magnetic system.

Findings

Derivation of a Dirac-like equation for antiferromagnetic magnons

Identification of pseudo-Hermitian Hamiltonian in the system

Observation of Zitterbewegung in spin wave dynamics

Abstract

We theoretically investigate the spin wave (magnon) excitations in a classical antiferromagnetic spin chain with easy-axis anisotropy. We obtain a Dirac-like equation by linearizing the Landau- Lifshitz-Gilbert equation in this antiferromagnetic system, in contrast to the ferromagnetic system in which a Schr\"{o}dinger equation is derived. The Hamiltonian operator in the Dirac-like equation is a pseudo-Hermitian. We compute and demonstrate the relativistic Zitterbewegung (trembling motion) in the antiferromagnetic spin chain by measuring the expectation values of the wave packet position.