Domain-wall motion driven by a rotating field in a ferrimagnet

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.

Figure 1

Schematic of the magnetization configuration of a ferrimagnetic domain wall, where blue and red arrows represent the magnetic moments of two sublattices of the ferrimagnet. The domain-wall position is denoted by $X\left(t\right)$ and the in-plane domain-wall magnetization angle is denoted by $\mathrm{\Phi }\left(t\right)$. The external field $\mathbf{H}\left(t\right)$ rotates within the $xy$ plane and the domain-wall in-plane magnetization lags behind the external field by $\mathrm{\Delta }\mathrm{\Phi }\left(t\right)$.

Figure 2

(a) Domain-wall velocity $\langle \dot{X}\rangle$ as a function of the rotating-field frequency $f=\omega /2\pi$ for various configurations with the parameters shown in Table 1. The lines are analytical solutions, Eq. (13) for $\omega <{\omega }_H$ (phase-locking regime where a domain-wall magnetization precesses at the same frequency as the external field) and Eq. (15) for $\omega >{\omega }_H$ (phase-unlocking regime where a domain-wall magnetization rotates slower than the external field). The dots represent simulation results. Note that the domain-wall velocity changes its sign as the temperature varies across the angular momentum compensation point $T_A$. (b) Domain-wall velocity as a function of the net spin density ${\delta }_s$ within the phase-locked regime for the frequency $f=90$ MHz. The data from all the temperatures $T_1,T_2,...,T_9$ except the magnetization compensation point $T_4\left(T_M\right)$, where the frequency $f=90$ MHz belongs to the phase-unlocking regime, is used. The squares and the triangles represent the analytical solutions [Eq. (13)] and the simulation results, respectively.

Figure 3

(a) Domain-wall velocity $\langle \dot{X}\rangle$ as a function of the rotating-field frequency $f=\omega /2\pi$ for the case of $T_5$ (defined in Table 1). The lines and the dots represent the analytical solutions and the simulation results, respectively. The critical frequency ${\omega }_H$ which separates the two distinct regimes of domain-wall dynamics is calculated from Eq. (8) and is shown as the vertical dashed line. When the frequency is below the critical frequency, the dynamics of the domain wall is in the phase-locking regime, where the domain wall precesses at the same frequency of the rotating field and thus the velocity increases linearly as a function of the frequency. When the frequency is above the critical frequency, the dynamics of the domain wall motion is in the phase-unlocking regime and the resultant velocity decreases as the frequency increases. (b) and (c) Time evolution of the $y$ component of the magnetization $m_y$ at the domain-wall center and the external field $H_y$ for the rotating-field frequency of (b) 70 MHz and (c) 260 MHz. The black solid line and the red dashed line are obtained from the simulations. The blue dotted lines are the analytical solutions obtained from (b) Eq. (12) and (c) Eq. (14).