Reversible Steady Domain-Wall Motion Driven by a Direct Current

Abstract

Understanding and manipulating nanoscale domain wall (DW) dynamics is a central topic in magnetism and spintronics for its promising applications in logic and memory devices. In most magnetic systems, inertia affects only transient DW dynamics, while the long-time DW motion is uniquely determined by the magnitude and direction of the applied current. Here we show that this paradigm breaks down in ferrimagnets near the angular momentum compensation point. We demonstrate that a DW can propagate steadily either forward or backward even under a direct current, with the direction controlled solely by the current strength. This anomalous phenomenon originates from the inertial dynamics of an internal DW collective coordinate, which behaves as a massive object evolving in a current-dependent double-well potential. Depending on the driving current, the system relaxes into distinct stable states associated with opposite directions of motion. Our findings reveal an unexpected role of inertia in nonlinear spin dynamics, and enable low-energy spintronic functionalities including sensitive magnetic-field detection and reconfigurable one-port devices.

Figures (4)

• Figure 1: (a) Schematic of a head-to-head ferrimagnetic DW. (b) Schematic of the steady DW velocity driven by a direct current. The blue, orange, and green regions indicate the three different regimes of DW motion. $j_{\mathrm{c1}},j_{\mathrm{c2}}$ are two critical current densities.
• Figure 2: Illustration of potential landscapes and torque analysis of a ferrimagnetic DW driven by spin torque for different current densities, (a,b) $j<j_{\mathrm{c2}}$, (c,d) $j_{\mathrm{c2}}<j<j_{\mathrm{c1}}$, (e,f) $j>j_{\mathrm{c1}}$. The orange circles in (a,c,e) indicate the position of stable DW tilting angles, the orange and green arrows indicate the directions of spin torques of $\boldsymbol{n}\times\hat{y}$ and $-\boldsymbol{n} \times(\boldsymbol{n}\times\hat{y})$.
• Figure 3: (a) DW velocity as a function of applied current density in the vicinity of AMCP. $\delta_s =0.275 \times10^{-7} \mathrm{J} \cdot \mathrm{s}/\mathrm{m}^3$ (light blue), $0$ (orange), $-0.272 \times10^{-7} \mathrm{J} \cdot \mathrm{s}/\mathrm{m}^3$ (light green). Symbols are micromagnetic simulations and the curves are theoretical predictions by Eq. \ref{['LLGz0']}. The dashed line indicates the position of $j_{\mathrm{c2}}$. (b) The time evolution of DW plane angle for $j/j_{\mathrm{c1}}=0.793$ (blue) and $0.907$ (red), respectively. (c-d) The relative window width for reversible DW motion $(j_{\mathrm{c1}}-j_{\mathrm{c2}}) /j_{\mathrm{c1}}$ as a function of net spin density $\delta_s$ and inter-sublattice coupling $J$, respectively. The dark red stars directly connected by solid lines are numerical solutions to Eqs. \ref{['collecteq']}, while the open blue circles are micromagnetic simulations.
• Figure 4: (a) Schematic of magnetic sensor based on DW motion. (b) Direction of DW motion as a map of current density and external field. (c) Two typical sets (boxed in (b)) of $z_0(t)$ and $\phi(t)$ for forward and backward motion. (d) The DW displacement $\delta z_0$ after applying a direct current pulse with a duration of 0.5 ns, the values of $j/j_{\mathrm{c1}}$ and $\mu_0 H_y$ are same as (b).