Ultrafast domain wall motion in ferrimagnets induced by magnetic anisotropy gradient

The ultrafast magnetic dynamics in compensated ferrimagnets not only is similar to antiferromagnetic dynamics but, more importantly, opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling the domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is also confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradients and can be slightly accelerated under large gradients due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly enhanced by the second anisotropy and interfacial Dzyaloshinskii-Moriya interaction, which is highly appreciated for further experiments, including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming and highly efficient method of controlling the domain wall in ferrimagnets, benefiting future spintronic applications.

Figure 1

(a) Illustration of a domain wall in ferrimagnetic nanowire under an anisotropy gradient. Here the asymmetry of the domain wall center is exaggerated. (b) A schematic depiction of torques acting on the central spins of the domain wall.

Figure 2

The simulated (empty points) and calculated (solid lines) velocities as functions of (a) $\mathrm{\Delta }K$ for various ${\delta }_s$, and (b) ${\delta }_s$ for various $\mathrm{\Delta }K$ for $K_0=0.01$. (c) The simulated (empty points) and calculated (solid lines) angular velocities of the wall plane as functions of $\mathrm{\Delta }K$ for various ${\delta }_s$, and (d) the evolutions of the local $n_x$ and $n_y$ for ${\delta }_s>0$ (top half) and ${\delta }_s<0$ (bottom half). The rotations of the wall plane are shown in the insert of (d).

Figure 3

The simulated (empty points) and calculated (solid lines) velocities at the momentum compensation point as functions of (a) $K_0$ for various value of $\mathrm{\Delta }K$ for $\alpha =0.01$ and (b) $1/\alpha$ for $K_0=0.01J$ and $\mathrm{\Delta }K=0.5\times {10}^{-5}J/a$.

Figure 4

The simulated (dashed lines) and calculated (solid lines) (a) evolutions of the wall positions for various $\mathrm{\Delta }K$ and (b) instantaneous speed for various $\mathrm{\Delta }K$.

Figure 5

For $\mathrm{\Delta }K=0.5\times {10}^{-5}J/a$, the simulated (a) evolutions of the wall position for various $K_x$ for ${\delta }_s=0$ (dash line) and ${\delta }_s=0.022$ (solid line), and mean velocities as functions of (b) $K_x$ and (c) $D_y$ for ${\delta }_s=0$ (black line) and ${\delta }_s=0.022$ (blue line). The Walker breakdown regions are shown with green color. (d) The simulated (empty points) and calculated (solid lines) $|D_{\mathrm{WB}}|$ as a function of ${\delta }_s$ for various $\mathrm{\Delta }K$.