  We analyze the dynamics of a domain wall in an easy-axis antiferromagnet
driven by circularly polarized magnons. Magnons pass through a stationary
domain wall without reflection and thus exert no force on it. However, they
reverse their spin upon transmission, thereby transferring two quanta of
angular momentum to the domain wall and causing it to precess. A precessing
domain wall partially reflects magnons back to the source. The reflection of
spin waves creates a previously identified reactive force. We point out a
second mechanism of propulsion, which we term redshift: magnons passing through
a precessing domain wall lower their frequency by twice the angular velocity of
the domain wall; the concomitant reduction of magnons' linear momentum
indicates momentum transfer to the domain wall. We solve the equations of
motion for spin waves in the background of a uniformly precessing domain wall
with the aid of supersymmetric quantum mechanics and compute the net force and
torque applied by magnons to the domain wall. Redshift is the dominant
mechanism of propulsion at low spin-wave intensities; reflection dominates at
higher intensities. We derive a set of coupled algebraic equations to determine
the linear velocity and angular frequency of the domain wall in a steady state.
The theory agrees well with numerical micromagnetic simulations.
