Spin-orbit torque driven chiral magnetization reversal in ultrathin nanostructures

We show that the spin-orbit torque induced magnetization switching in nanomagnets presenting Dzyaloshinskii-Moriya (DMI) interaction is governed by a chiral domain nucleation at the edges. The nucleation is induced by the DMI and the applied in-plane magnetic field followed by domain-wall propagation. Our micromagnetic simulations show that the dc switching current can be defined as the edge nucleation current, which decreases strongly with increasing amplitude of the DMI. This description allows us to build a simple analytical model to quantitatively predict the switching current. We find that domain nucleation occurs down to a lateral size of $25\mathrm{nm}$, defined by the length scale of the DMI, beyond which the reversal mechanism approaches a macrospin behavior. The switching is deterministic and bipolar.

Figure 1

(a) Time evolution of the average out-of-plane magnetization for different applied current densities (variations in steps of ${10}^{11}\mathrm{A}/{\mathrm{m}}^2$). The minimum current to trigger switching, i.e., the critical current, is highlighted in blue. The green curve indicates the threshold of turbulent behavior (see text). (b) Sketch of the magnetization configuration at different stages of the switching process. (c) Magnetization orientation in the center and at the left and right edges. The current-induced dampinglike torque (represented as effective field ${\vec{H}}_{\text{DL}}$) can only drive the left edge magnetization into instability, resulting in a nucleation at the left edge. (d) Snapshots of the magnetization configuration showing the reversal from down (black) to up (white) via domain-wall nucleation and propagation under an externally applied field of ${\mu }_{0}H=0.1\mathrm{T}$ and a current density of $2.6\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$.

Figure 2

(a) Critical current for destabilizing the system as a function of the DMI strength. (b) The relation between the critical current and the switching time $t_0$ for two different values of DMI. The inset shows the data for $D=2\text{mJ}/{\text{m}}^2$ but in a transformed coordinate system $J_{\text{app}}$ vs $t_0^{-1}$. (c) The switching time vs current for different dot diameters. (d) Critical current and current density for different dot sizes. The calculation of the current assumes a 3-nm-thick Pt line.

Figure 3

(a) Switching time as a function of the applied current density, varying intrinsic and extrinsic parameters. For the temperature case, the average $t_0$ is plotted. The single event switching time is defined as before, while the average $t_0$ is defined as the time when the probability of stochastic switching reaches $90\%$. (b) Several switching graphs $\langle m_z\rangle \left(t\right)$ for varying damping at $T=50\mathrm{K}$ and $J_{\text{app}}=2.6\times {10}^{12}\mathrm{A}/{\mathrm{m}}^2$. For fixed $\alpha$ variations are only due to temperature fluctuations.