Current-driven nonlinear skyrmion dynamics in altermagnets

Abstract

The center of mass and helicity are two dynamic degrees of freedom of skyrmions. In this work, we study the current-driven skyrmion motion in frustrated altermagnets. Contrary to conventional wisdom, we find that the skyrmion helicity is not locked with the skyrmion Hall angle, but unidirectionally rotates with a global angular velocity proportional to the square of the current density. In addition, we find that the helicity rotation velocity is highly anisotropic, depending on the direction of current flows. We also observe helicity oscillation in the terahertz regimes, where the nonlinear mixing between the fast and slow modes generates a magnon frequency comb. Full atomistic spin dynamics simulations verify our theoretical predictions. Our results establish frustrated altermagnets as a promising platform for skyrmionics, THz technology, and frequency comb.

Figures (4)

• Figure 1: (a) Model of bilayer frustrated altermagnet with spin directions $\mathbf S^{n}$ ($n=1,2$). Anisotropic exchange interactions $J_{31}$ and $J_{32}$ act within each sublattice and obey twofold symmetry (green/orange bonds). One layer is shifted by $\sqrt{2}a/2$ along the diagonal line for clarity. (b) Schematic of altermagnetic skyrmion motion under electron flow. Adiabatic STT induces transverse Hall motion and nonlinear helicity ($\eta$) rotation assisted by the emergent magnetic quadrupole (dashed brown circle). $\Theta$ and $\Phi$ denote the angles of current and skyrmion velocity with respect to the $\hat{x}$-direction; red and blue arrows indicate alternating sublattice magnetizations.
• Figure 2: Trajectories of an altermagnetic skyrmion for current directions $\Theta = 0^\circ$ (a) and $45^\circ$ (b). The red stars indicates the initial position of the skyrmion center. Corresponding time-evolution of the skyrmion velocity and helicity rotation frequency for $\Theta = 0^\circ$ (c) and $45^\circ$ (d), respectively. Calculations are performed using parameters $u=1000~\mathrm{m/s}$, $\alpha=0.001$, and $\beta=0.0002$.
• Figure 3: Skyrmion propagation velocity (a) and helicity rotation frequency (c) as a function of the electron drift velocity $u$, with symbols from simulations and curves from Eqs. (\ref{['eq9']}). Skyrmion Hall angle (b) and helicity rotation frequency (d) vs. current direction (azimuthal: $\mathbf{j}$ angle) and electron drift velocity (radial: $u$ in units of m/s). In calculations, we set $I_{3}=2.4~\mathrm{meV}$, $\alpha=\beta=0.05$, and $J_{\mathrm{int}} = 4.2~\mathrm{meV}$.
• Figure 4: (a) Time-evolution of skyrmion helicity $\eta$ by varying $u$. (b) FFT spectra of the time-evolving skyrmion helicity for $u = 600~\mathrm{m/s}$. Fast (c) and slow (d) frequency component of skyrmion helicity oscillation as a function of $\beta$. In calculations, we consider current flowing along the $\hat{x}$-direction and adopt the following model parameters: $I_{3}=2.4~\mathrm{meV}$, $\alpha=0.05$, and $J_{\mathrm{int}}=4.2~\mathrm{meV}$.