Magnonic analog of relativistic Zitterbewegung in an antiferromagnetic   spin chain
  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. 
Weiwei Wang, Chenjie Gu, Yan Zhou, Hans Fangohr
cond-mat.str-el cond-mat.mtrl-sci