How to move domain walls in an antiferromagnet*

Domain walls (DWs) in an easy-axis antiferromagnet can be driven by several stimuli: a charge current (in conducting antiferromagnets), a magnon current, and a temperature gradient. In this talk, we discuss the dynamics of a DW induced by two latter external perturbations, which are applicable in both metallic and insulating antiferromagnets. First of all, we study the Brownian dynamics of a DW subjected to a temperature gradient [1]. To this end, we derive the Langevin equation for the DW's center of mass with the aid of the fluctuation-dissipation theorem. A DW behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of DWs, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a DW. We briefly address other mechanisms of thermally driven DW motion. Secondly, we analyze the dynamics of a DW driven by circularly polarized magnons [2]. Magnons passing through a DW reverse their spin upon transmission, thereby transferring two quanta of angular momentum to the DW and causing it to precess. A precessing DW partially reflects magnons back to the source. The reflection of magnons creates a previously identified reactive force [3]. We point out a second mechanism of propulsion of the DW, which we term redshift: magnons passing through a precessing DW reduce their linear momentum and transfer the decrease to the DW. We solve the equations of motion for magnons in the background of a uniformly precessing DW with the aid of supersymmetric quantum mechanics and compute the net force and torque applied by magnons to the DW. The theory agrees well with micromagnetic simulations. \\ [4pt] [1] S. K. Kim, O. Tchernyshyov, and Y. Tserkovnyak, Phys. Rev. B \textbf{92}, 020402(R) (2015) \\ [0pt] [2] S. K. Kim, Y. Tserkovnyak, and O. Tchernyshyov, Phys. Rev. B \textbf{90}, 104406(E) (2014) \\ [0pt] [3] E. G. Tveten, A. Qaiumzadeh, and A. Brataas, Phys. Rev. Lett. \textbf{112}, 147204 (2014)