Overcoming the speed limit in skyrmion racetrack devices by suppressing the skyrmion Hall effect

Magnetic skyrmions are envisioned as carriers of information in racetrack storage devices. Unfavorably, the skyrmion Hall effect hinders the fast propagation of skyrmions along an applied electric current and limits the device's maximum operation speed. In this Rapid Communication, we show that the maximum skyrmion velocity increases by a factor of 10 when the skyrmion Hall effect is suppressed, since the straight-line motion of the skyrmion allows for the application of larger driving currents. We consider a ferromagnet on a heavy-metal layer, which converts the applied charge current into a spin current by the spin Hall effect. The spin current drives the skyrmions in the ferromagnet via spin-orbit torque. We show by analytical considerations and simulations that the deflection angle decreases, when the spin current is polarized partially along the applied current direction, and derive the condition for complete suppression of the skyrmion Hall effect.

Figure 1

Proposed mechanism to suppress the skyrmion Hall effect. A ferromagnetic layer (FM) is attached to a heavy-metal layer (HM); the interfacial DMI stabilizes Néel skyrmions (red-white circular object) in the FM. When a charge current (density $\mathit{j}$) is applied in the HM the spin Hall effect (SHE) generates spins that are injected into the FM where they cause a SOT onto the magnetic moments. In highly symmetric materials the injected spins point into the $\pm y$ direction (white line) and the skyrmion moves at a certain skyrmion Hall angle angle ${\theta }_{\mathrm{Sk}}$ (white line). In HMs with a reduced symmetry the spin polarization has an angle $\delta$ in the $xy$ plane and the propagation direction of the skyrmion is altered by $\delta$ (orange). The skyrmion Hall effect is absent for $\delta ={\theta }_{\mathrm{Sk}}$ (see text).

Figure 2

Micromagnetic simulations comparing conventional and optimized setup. (a),(b) Conventional CoPt racetrack with $\delta =0^{\circ }$. (c)–(e) Optimized racetrack with $\delta =70.7^{\circ }$. Results of the simulations are shown after 1 ns propagation duration at different current densities ${\mathrm{\Theta }}_{\mathrm{SH}}j$ (indicated on the right). The optimal geometry yields a stable motion for much larger current densities, allowing for faster propagation of the skyrmion. The skyrmion's velocity in (e) is ten times as large as in the conventional scenario in (a); $v=481.2\mathrm{m}/\mathrm{s}$ compared to $v=48.1\mathrm{m}/\mathrm{s}$. Red: $-z$; blue: $+z$ magnetization; white shows the actual trajectory and dashed orange shows the predicted trajectory from the Thiele equation without confining potential. An animated version of this figure is presented in the Supplemental Material [57].

Figure 3

Skyrmion velocity and stability for different HM materials. (a) The range of allowed $\delta$ directions over $j$ (colored area). (b) The $j$ dependence of the velocity for selected $\delta$. The color in both panels corresponds to the velocity along the racetrack (blue positive, red negative; indicated with numbers). The colored lines correspond to constant $\delta$ values (indicated). Lines and velocities have been calculated from the Thiele equation, without considering pinning effects which become negligible at large current densities. Explicit results from the micromagnetic simulations are indicated by points (green: stable motion; red: skyrmion annihilation). The black line (STT) is taken from Ref. [11] for comparison.