Ferrimagnetic materials exhibit ultrafast dynamic behaviors similar to those of antiferromagnetic materials near the angular momentum compensation point, where a non-zero net spin density is maintained. This unique feature makes their magnetic structures detectable and manipulable by using traditional magnetic techniques, thus positioning ferrimagnetic materials as promising candidates for next-generation high-performance spintronic devices. However, effectively controlling the dynamics of ferrimagnetic domain walls remains a significant challenge in current spintronics research.

In this work, based on the classic Heisenberg spin model, Landau-Lifshitz-Gilbert (LLG) simulation is used to investigate the dynamic behaviors of ferrimagnetic domain walls driven by sinusoidal wave periodic magnetic field and square wave periodic magnetic field, respectively. The results show that these two types of oscillating magnetic fields induce distinct domain wall motion modes. Specifically, the domain wall surface, which has non-zero net spin angular momentum, oscillates in response to the external magnetic field. It is found that the domain wall velocity decreases as the net spin angular momentum increases. Moreover, the displacement of the ferrimagnetic domain wall driven by a sinusoidal magnetic field increases monotonically with time, while the displacement driven by a square wave magnetic field follows a more tortuous trajectory over time. Under high-frequency field conditions, the domain wall displacement shows more pronounced linear growth, and the domain wall surface rotates linearly with time. In this work, how material parameters, such as net spin angular momentum, anisotropy, and the damping coefficient, influence domain wall dynamics is also explored. Specifically, increasing the anisotropy parameter (d_z) or the damping coefficient (α) results in a reduction of domain wall velocity. Furthermore, the study demonstrates that, compared with the square wave magnetic fields, the sinusoidal magnetic fields drive the domain wall more efficiently, leading domain wall to move faster. By adjusting the frequency and waveform of the periodic magnetic field, the movement of ferrimagnetic domain walls can be precisely controlled, enabling fine-tuned regulation of both domain wall velocity and position.

Our findings show that sinusoidal magnetic fields, even at the same intensity, offer higher driving efficiency. The underlying physical mechanisms are discussed in detail, providing valuable insights for guiding the design and experimental development of domain wall-based spintronic devices.