Traveling Skyrmions in Chiral Antiferromagnets

Abstract

Skyrmions in antiferromagnetic (AFM) materials with the Dzyaloshinskii-Moriya (DM) interaction are expected to exist for essentially the same reasons as in DM ferromagnets (FM). On the other hand, the dynamics of solitons in AFM is substantially different [1,2]. We give the fundamental formula and a corresponding argument to show that traveling solitary waves (such as skyrmions) are possible in an AFM in contrast to the dynamics observed in FM. The formula shows that the skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the dynamical behavior. We calculate numerically the configuration of skyrmions in chiral antiferromagnets that are traveling as solitary waves. They are found to be elongated and they expand in size with the velocity (Fig. 1). The velocity takes values from zero up to a maximum value, which depends on a scaled DM parameter λ. The maximum skyrmion velocity is found analytically as a function of λ. The formula is based on a strong theoretical argument that links the breakdown of a traveling skyrmion with the DM parameter value λ=2/π for the transition from the uniform to the spiral state. The energy and the linear momentum of an AFM skyrmion lead to a proper definition of its mass. We give the details of the energy-momentum dispersion of traveling skyrmions and explore their particle-like character based on exact relations. The traveling skyrmion behaves as a Newtonian particle for small velocities, while it presents relativistic behavior for velocities close to the critical. It is notable that the energy-momentum formula differs from the standard relativistic one by a constant shift of the energy. The solitonic and particle-like behavior of skyrmions in AFM is in stark contrast to the dynamical behavior of their FM counterparts [3]. We acknowledge support by the project ThunderSKY, funded by HFRI and GSRT, under Grant No. 871.