Current-driven spiral domain wall in a ferrimagnet near the magnetization compensation point

A spiral domain wall emerges when the Dzyaloshinskii-Moriya vector is along the easy axis. While the ferromagnetic spiral wall has been well studied, its ferrimagnetic counterpart has nevertheless not been explored. Here, using the collective variable approach, we derive the spiral domain-wall solutions in a ferrimagnetic nanostrip with a longitudinal easy axis and a bulk Dzyaloshinskii-Moriya interaction. At the magnetization compensation point, the wall rotates and propagates steadily in a wide current range. The (angular) velocity of this wall increases almost linearly with the experimentally feasible currents. Also, the wall exhibits a relativistic-like contraction with increasing velocity. Near this point, the wall moves smoothly with its velocity linearly depending on the current below the Walker breakdown. Above this critical current, all the internal parameters of the wall, such as the azimuthal angle, width, and spiral pitch, as well as their rates of change, oscillate periodically. The wall moves forward with its velocity varying periodically. These different behaviors at or near the compensation point are ascribed to the tunable demagnetization effect. The adjustability of FiM parameters, combining with the twist induced by the Dzyaloshinskii-Moriya interaction, can effectively change the DW's propagation and rotation.