Topological pumping of bimerons in spiral magnets

Abstract

Precise positioning of topological defects is essential for racetrack memories, where their positions along a magnetic nanotrack encode information. Traditional methods achieve nanometric precision by engineering pinning landscapes that enforce discrete steps in defect motion. However, accessing each bit requires overcoming a depinning threshold, which increases power consumption. Here, we demonstrate that spiral magnets provide a natural ruler, enabling precise positioning of bimerons (topological spin textures analogous to skyrmions) without relying on engineered pinning sites. A rotating magnetic field couples directly to the bimeron position, displacing it by exactly one spiral period per full rotation of the field. Such quantized transport of skyrmionic textures, reminiscent of Thouless pumping, is topologically protected and remains robust against perturbations, positioning spiral magnets as a natural skyrmion racetrack. The findings establish a paradigm for topologically protected transport of spin textures.

Figures (4)

• Figure 1: (a) The spiral background breaks translational and rotational symmetries. Black and red boxes indicate the two stripes of width $\Delta x = \pi/Q$ at different positions relative to the spiral where the bimeron is inserted in panels (b) and (c). The colors encode the magnetization component $m_z$. The spiral plane rotates by $2\pi$ about $\hat{x}$, within the black box (b), and about $\hat{y}$, within the red box (c), upon moving along $-y$. These twists of the spiral plane, shown in the right insets of panels (b) and (c), correspond to bimerons with vortex helicities $\varphi = 0$ and $\varphi = \pi/2$, respectively. For either case, the spin texture consists of a vortex with positive $m_z$ (red) and an antivortex with negative $m_z$ (blue), each with topological charge $1/2$. Therefore, the total topological charge of the bimeron is $1$, equal to that of a skyrmion.
• Figure 2: Effective potential induced by the rotating magnetic field $U_{\Delta\bar{x}}$ as a function of the bimeron position relative to the spiral background $\Delta\bar{x}$, plotted at different times $t$. (a) For a slowly rotating field, the bimeron (red dot) follows the sliding potential $U_{\Delta\bar{x}}$, residing near a minimum. (b) Above a critical rotation frequency, the bimeron is no longer confined within a well of $U_{\Delta\bar{x}}$ because of the gyrotropic and damping forces.
• Figure 3: (a) Time-averaged velocity $\bar{v}_x$ of a bimeron moving under the action of a rotating magnetic field with angular frequency $\omega$. Blue dots indicate the numerical result of the LLG equation Landau35Gilbert04Skubic08 for $Q = 8.38\cdot10^8\,\mathrm{m}^{-1}$, $\lvert{\bf H}\rvert = 0.1\;\mathrm{T}$, $\alpha = 0.1$ and $\mu = \mu_\mathrm{B}$, where $\mu_\mathrm{B}$ is the Bohr magneton. The red line shows the analytical solution Eq. (\ref{['eq:2Reg']}) with fitted critical angular frequency $\omega^* = 1.29\cdot10^9\,\mathrm{s}^{-1}$. Using Eq. (\ref{['eq:EqSteady']}), we estimate $\omega^*$ analytically: $\omega^* = 1.12\cdot10^9\,\mathrm{s}^{-1}$. Panels (b) and (c) show the bimeron velocity $v_x = \Delta\dot{\bar{x}}$ as a function of time in the two dynamical regimes. (b) For $\omega = 5\cdot10^8\,\mathrm{s}^{-1} < \omega^*$, $v_x$ reaches the steady-state velocity after a transient in which the bimeron adjusts to its equilibrium position on the sliding potential shown in Fig. \ref{['fig:Potential']}(a). (c) For $\omega = 2\cdot10^9\,\mathrm{s}^{-1} > \omega^*$, $v_x$ oscillates with a nonzero average $\bar{v}_x$, as the bimeron no longer follows a minimum of the potential (see Fig. \ref{['fig:Potential']}(b)).
• Figure 4: Dynamical phase diagram for bimeron pumping, defined in terms of $n$, the average bimeron displacement along $x$ per field rotation, in units of the spiral period. The values of $n$ are obtained by numerically solving the collective-coordinate equations of motion, using the parameters in Appendix B and in-plane anisotropy $K_y = 0.01\;\mathrm{meV}$. (a) Ferromagnetic $J_\perp$ case: $\lvert{\bf H}\rvert$ is the amplitude of the rotating field and $\omega$ its angular frequency. The topological region ($n = w = 1$) corresponds to bimeron pumping by one spiral period for each field rotation, whereas in the trivial region ($n = 0$) the bimeron does not move. Between these two regimes, $n$ takes non-integer values, indicating the onset of non-adiabatic dynamics. (b) Antiferromagnetic $J_\perp$ case (spin $S = 1$), where the magnetic field has a rotating component with fixed amplitude $\lvert{\bf H}_\mathrm{rot}\rvert = 0.15 \;\mathrm{T}$ and a static component ${\bf H}_\mathrm{static}$ along $x$. The bell-shaped topological region is centered at the static field ${\bf H}_\mathrm{static}^*$ that compensates the in-plane anisotropy. Here, the bimeron is pumped by half a spiral period for each field rotation, corresponding to $n = w_\mathrm{AF}/2 = 1/2$.