Driving chiral domain walls in antiferromagnets using rotating magnetic fields

We show theoretically and numerically that an antiferromagnetic domain wall can be moved by a rotating magnetic field in the presence of Dzyaloshinskii-Moriya interaction (DMI). Two motion modes are found: rigid domain wall motion at low frequency (corresponding to the perfect frequency synchronization) and the oscillating motion at high frequency. In the full synchronized region, the steady velocity of the domain wall is universal, in the sense that it depends only on the frequency of the rotating field and the ratio between DMI strength and exchange constant. The domain wall velocity is independent of the Gilbert damping and the rotating field strength. Moreover, a rotating field in megahertz is sufficient to move the antiferromagnetic domain wall.

Figure 1

Illustration of an antiferromagnetic domain wall in an AFM nanowire along the $z$ axis and the nearest-neighbor spacing is $a$. The rotating magnetic field is applied in the $xy$ plane.

Figure 2

The domain wall profile obtained by solving the LLG equation. The used simulation parameters are $K_0/J=0.002$, $D_0/J=0.02$, and $H/H_0=0.004$ with $H_0=JS/\hslash \gamma$.

Figure 3

(a) The DW position as a function of time for $\omega /{\omega }_0={10}^{-5}$ and $\omega /{\omega }_0=2\times {10}^{-4}$. (b) The DW tilt angle as a function of time for $\omega /{\omega }_0={10}^{-5}$ and $\omega /{\omega }_0=2\times {10}^{-4}$. The dimensionless time 10 corresponds to approximately 40 ns for ${\mathrm{KMnF}}_3$. The data is obtained by solving the LLG equation numerically. The used simulation parameters are $H/H_0=5\times {10}^{-4}$, $\alpha =5\times {10}^{-4}$, $D_0/J=0.02$, and $K_0/J=0.002$.

Figure 4

The critical frequency ${\omega }_c$ as a function of the rotating field strength. The dots are obtained using numerical simulation. The lines are plotted using Eq. (13). The dimensionless field strength 5.0 corresponds to 7.07 mT while the dimensionless frequency 4.0 corresponds to 0.99 GHz for ${\mathrm{KMnF}}_3$.

Figure 5

The (average) DW velocity as a function of the rotating field frequency obtained by numerical simulations with parameters (i) $\alpha =0.0003$ and $H/H_0=0.0005$, and (ii) $\alpha =0.0001$ and $H/H_0=0.0003$. Gray lines are plotted using analytical equations (12) and (17). The dimensionless frequency 1.0 corresponds to 0.25 GHz while the dimensionless velocity 1.0 corresponds to 0.1 m/s for ${\mathrm{KMnF}}_3$.

Figure 6

The DW velocity as a function of the rotating field frequency for the 2D/3D system. The parameters used in simulations are $\alpha =0.0003$ and $H/H_0=0.0005$.