Optically Controlled Skyrmion Number Current

TL;DR

The paper addresses low-dissipation control of magnetic Skyrmions by introducing a Skyrmion-number current generated through a time-dependent Hamiltonian that couples spins to circularly polarized light via a Zeeman term. By perturbing the Landau-Lifshitz-Gilbert dynamics around the Belavin-Polyakov Skyrmion, it derives an anisotropic breathing boundary and explicit expressions for the Skyrmion-number current $\mathbf{J}_Q$ and driving term $\mathbf{D}$, showing that a nonzero current arises only for $Q=\pm1$ when axial symmetry is broken. The resulting Skyrmion dynamics exhibit a limit cycle in momentum space, with the orbit characteristics tunable by the light amplitude $B_0$, exchange coupling $J$, and damping $\alpha$, and modulated by the Skyrmion helicity $\varphi_0$. The work further analyzes anisotropy and DMI effects, deriving bounds on $B_0$ and discussing experimental platforms (e.g., ferrimagnetic multilayers and CrI$_3$) to realize optically driven Skyrmion motion, linking topological currents to practical Skyrmion control. Overall, it provides a topological, low-dissipation route to steer Skyrmions via optical means with potential impact on spintronic devices.

Abstract

We propose a mechanism to control the motion of magnetic Skyrmions through the generation of a Skyrmion number current. This current is induced and tuned by an explicitly time-dependent Hamiltonian that includes a Zeeman term arising from the interaction between the spin system and circularly polarized light. To capture the effect, we apply a first-order perturbation method to the Landau-Lifshitz-Gilbert equation, using a breathing Skyrmion ansatz based on the Belavin-Polyakov profile. This approach reveals that the time-dependent deformation of the Skyrmion boundary produces an anisotropic breathing mode, which in turn generates a nonzero Skyrmion number current. The resulting dynamics in momentum space form a limit cycle, whose characteristics depend on the external magnetic field amplitude, the Heisenberg exchange coupling, and the Gilbert damping constant. Our formulation not only clarifies the topological origin of optically driven Skyrmion motion but also points to Skyrmion number currents as a low-dissipation alternative to electric currents for efficient Skyrmion control.

Figures (4)

• Figure 1: The ratio between the distance from center to boundary, $r_{\text{bound}}$, and the unperturbed Skyrmion radius, plotted against $\omega t$ for a single period, from $t=0$ up to $t=2\pi/\omega$. This plot shows the anisotropic breathing of the $Q=1$ Skyrmion with different phases in each direction.
• Figure 2: (a) Skyrmion's trajectory on the plane, $\textbf{R}(t)$, with initial position $\textbf{R}(0)=(0,0)$. (b) Limit cycle of $\dot{\textbf{R}}(t)$ with initial condition $\dot{\textbf{R}}(0)=(0,0)$. (c) Skyrmion phase space, $\dot{R}_i(t)$ against $R_i(t)$, of the horizontal position $X(t)$ ($i=x$, blue curve) and vertical position $Y(t)$ ($i=y$, red curve). (d) The Skyrmion velocity components $\dot{R}_i(t)$, with $i\in\{x,y\}$, plotted against phase, $\omega t$, for several period of oscillation. This figure shows the transition from the transient state to the steady state, which forms a limit cycle. All of these plots represent Skyrmion dynamics of Neel-type under constant light with $\eta_1=\eta_2=\alpha\gamma=1$ and $M_S\omega=40$.
• Figure 3: (a) The plot of average magnitude of velocity (blue) and stationary displacement (red) with variation of ratio $\eta_1/\eta_2$. Both of these quantities are proportionally increasing with respect to the ratio. (b) the direction of displacement represented by the horizontal (blue) and vertical (red) component of $\tilde{\textbf{d}}$ against various $\varphi_0$. Each of the data point above are numerically obtained with $(\varphi_0=0,M_S\omega=40,\alpha\gamma=1)$ for figure (a) and $(M_S\omega=40,\eta_1/\eta_2=\alpha\gamma=1)$ for figure (b).
• Figure 4: (blue curve) Trajectory of Neel ($\varphi_0=0$) and anti-Neel ($\varphi_0=\pi$) Skyrmion, and (red curve) Trajectory of Bloch ($\varphi_0=\pi/2$) and anti-Bloch ($\varphi_0=-\pi/2$) Skyrmion. We use $\eta_1/\eta_2=\alpha\gamma=1$ and $M_S\omega=40$ for the numerical calculation. The displacement magnitude is effectively the distance to the center of the confined orbit $\textbf{R}$ in real-space.