  We theoretically study a ferrimagnetic domain-wall motion driven by a
rotating magnetic field. We find that, depending on the magnitude and the
frequency of the rotating field, the dynamics of a ferrimagnetic domain wall
can be classified into two regimes. First, when the frequency is lower than a
certain critical frequency set by the field magnitude, there is a stationary
solution for the domain-wall dynamics, where a domain-wall in-plane
magnetization rotates in-phase with the external field. The field-induced
precession of the domain wall gives rise to the translational motion of the
domain wall via the gyrotropic coupling between the domain-wall angle and
position. In this so-called phase-locking regime, a domain-wall velocity
increases as the frequency increases. Second, when the frequency exceeds the
critical frequency, a domain-wall angle precession is not synchronous with the
applied field. In this phase-unlocking regime, a domain wall velocity decreases
as the frequency increases. Moreover, the direction of the domain-wall motion
is found to be reversed across the angular compensation point where the net
spin density of the ferrimagnet changes its sign. Our work suggests that the
dynamics of magnetic solitons under time-varying biases may serve as platform
to study critical phenomena.
