High Antiferromagnetic Domain Wall Velocity Induced by Néel Spin-Orbit Torques

We demonstrate the possibility to drive an antiferromagnetic domain wall at high velocities by fieldlike Néel spin-orbit torques. Such torques arise from current-induced local fields that alternate their orientation on each sublattice of the antiferromagnet and whose orientation depends primarily on the current direction, giving them their fieldlike character. The domain wall velocities that can be achieved by this mechanism are 2 orders of magnitude greater than the ones in ferromagnets. This arises from the efficiency of the staggered spin-orbit fields to couple to the order parameter and from the exchange-enhanced phenomena in antiferromagnetic texture dynamics, which leads to a low domain wall effective mass and the absence of a Walker breakdown limit. In addition, because of its nature, the staggered spin-orbit field can lift the degeneracy between two 180° rotated states in a collinear antiferromagnet, and it provides a force that can move such walls and control the switching of the states.

Figure 1

(a) Crystal structure of AF CuMnAs. The two spin sublattices of the Mn atoms are ${\mathbf{M}}_{1/2}$ (red and purple). The current-induced staggered NSOT field (${\mathbf{B}}_{\mathrm{N}1/\mathrm{N}2}$—green and blue) has an opposite sign at each Mn sublattice. The nonmagnetic As atoms (light grey) provide the locally broken inversion symmetry at the Mn inversion partner sites. ${\mathbf{J}}_{\mathrm{c}}$ represents the current. (b) AFDW between 180° rotated AF domains in the presence of the staggered NSOT field. The energy density has opposite sign in the left and right domains, producing a ponderomotive force. (c,d) AFDW between 90° rotated AF domains in (c) the staggered NSOT field and (d) the uniform Zeeman (${\mathbf{B}}_Z$) field.

Figure 2

(a) Schematic of Bloch domain wall velocity vs field for an AF (magenta line) and a FM (blue line). At low fields both FM and AF have the same velocity vs field, but beyond the Walker breakdown, the FM slows down as the domain wall character oscillates between Bloch and Néel. (b,c) Illustration of torques exerted on the AFDW and FMDW center. (b) The Néel field generates a torque (${\mathrm{\Gamma }}_{1N/2N}$) that cants ${\mathbf{M}}_{1/2}$ forward, and the much larger internal torque from the exchange interaction (${\mathrm{\Gamma }}_{\text{ex}}$) rotates the sublattice magnetizations towards their respective easy axis directions, which causes the AFDW motion. ${\mathrm{\Gamma }}_{\text{ex}}/{\mathrm{\Gamma }}_{1N/2N}\gg 1$ leads to a small deformation of the DW from its equilibrium (Bloch) configuration, i.e., to a very small AFDW mass. (c) In a FM the external driving field torque can reach a similar magnitude as the internal anisotropy torque (${\mathrm{\Gamma }}_{\text{an}}$), leading to larger deformation of the FMDW, i.e., to a much larger FMDW mass.

Figure 3

Velocity of a 180° (violet line) and a 90° (green-blue line) AFDW vs an effective Néel field and a 90° AFDW (magenta line) vs a Zeeman field calculated for ${\mathrm{Mn}}_2\mathrm{Au}$ (we set AF magnon velocity $c=30\mathrm{km}/\mathrm{s}$).

Figure 4

Shift of (a) an AFDW (magenta lines) and (b) a FMDW (blue lines) under the action of a field pulse (duration of pulse shown as grey region). Field values in both cases correspond to the steady velocity of $250\mathrm{m}/\mathrm{s}$ in the dc field. Relaxation times are ${\tau }_{\mathrm{AF}}=1\mathrm{ps}$ and ${\tau }_{\mathrm{FM}}=1\mathrm{ns}$ for AF and FM, respectively. In (a) the pulse duration $\tau =2\mathrm{ps}$ is much smaller than the relaxation time of FM (${\tau }_{\mathrm{FM}}$) but larger than ${\tau }_{\mathrm{AF}}$. The inset shows the time dependence at large time scales. In (b) the pulse duration $\tau =2\mathrm{ns}$ is larger than ${\tau }_{\mathrm{FM}}\gg {\tau }_{\mathrm{AF}}$.