Current-controlled chirality dynamics in a mesoscopic magnetic domain wall

Chirality as internal degree of freedom of a mesoscopic domain wall inside a quasi-one-dimensional fixture can be controlled by spin-polarized current for ferro- as well as antiferromagnetic domain walls. We show that the current density required for the chirality manipulation can be significantly reduced in the low-temperature regime where the chirality dynamics exhibits quantum effects. In this quantum regime, weak currents can excite Bloch oscillations of the domain wall angular rotation velocity, with the oscillation frequency proportional to the current, modulated by a much higher magnon-range frequency. In addition to that, the Wannier-Stark localization effects enable controlled switching between different chiral states, suppressing inertial effects characteristic for the classical regime. We also show that for recently discovered novel class of magnetic materials — altermagnets — chirality switching can be driven by the usual charge current (not spin polarized).

Figure 1

Schematic picture of the mesoscopic domain wall in a quasi-one-dimensional fixture. Arrows show the direction of the magnetic order parameter (magnetization or the Néel vector).

Figure 2

Illustration of the toy model of altermagnet described by Eq. (20). Arrows denote localized spins, and the dashed line indicates the magnetic unit cell.

Figure 3

The average angular velocity $\langle d{\varphi }_w/d\tau \rangle$ vs the dimensionless time $\tau =\hslash t/2m$ for $\xi =5$, and bias (a) $b=0.1\mathrm{\Delta }$; (b) $b=0.6\mathrm{\Delta }$. The ground state for $b=0$ has been used as the initial state at $t=0$. The energies of the first four lowest-lying states at $\xi =5$ in units of ${\hslash }^2/2m$ are $E_0\approx 0.115$, $E_1\approx 0.159$, $E_2\approx 5.636$, and $E_3\approx 6.343$. Bloch oscillations with the frequency $\pi b\hslash$ are modulated with the secondary frequency $(E_3-E_0)/\hslash$ due to the excitation of the third excited state.

Figure 4

Chirality dynamics with the Wannier state localized in the right well used as the initial state at $t=0$. Shown are: (a), (c) the average angular velocity $\langle d{\varphi }_w/d\tau \rangle$, and (b), (d) the probability density ${\left|\psi \right|}^2$ as functions of the dimensionless time $\tau =\hslash t/2m$ for $\xi =5$. The bias is $b=0.1\mathrm{\Delta }$ in (a), (b), and $b=0.6\mathrm{\Delta }$ in (c), (d).

Figure 5

Chirality switching with the Wannier state localized in the right well used as the initial state at $t=0$, under the action of a pulse with the amplitude $b=0.5\mathrm{\Delta }$ and the duration of $\mathrm{\Delta }{t}_1=2\pi /{\omega }_B$, followed by another pulse of the same amplitude after the time interval of $\mathrm{\Delta }{t}_2=\pi \hslash /\mathrm{\Delta }$. Shown are: (a) the average angular velocity $\langle d{\varphi }_w/d\tau \rangle$ and (b) the probability density ${\left|\psi \right|}^2$ as functions of the dimensionless time $\tau =\hslash t/2m$ for $\xi =5$.

Figure 6

Zener breakdown for a strong bias: (a), (c) the average angular velocity $\langle d{\varphi }_w/d\tau \rangle$, and (b), (d) the probability density ${\left|\psi \right|}^2$ as functions of the dimensionless time $\tau =\hslash t/2m$ for $\xi =5$. The bias is $b=1.5\mathrm{\Delta }$ in (a), (b), and $b=5\mathrm{\Delta }$ in (c), (d). The ground state for $b=0$ has been used as the initial state at $t=0$.