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

Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic spin chain