Magnetization dynamics induced by in-plane currents in ultrathin magnetic nanostructures with Rashba spin-orbit coupling

Recent experiments on ultrathin magnetic layers with broken inversion symmetry reported anomalous current-driven magnetization dynamics. We show that the spin-transfer torque can be significantly modified by Rashba spin-orbit coupling and the modified spin-transfer torque can explain the anomalous magnetization dynamics. This work will be valuable for the development of next generation spintronic devices based on ultrathin magnetic systems.

Figure 1

Schematic structure. An ultrathin ($\lesssim$1 nm) magnetic layer is sandwiched between a heavy metallic layer and an insulating oxide layer.

Figure 2

Two possible structures of a Bloch-type transverse DW in a PMA system when a current flows to the right and $\alpha >\beta$ (Ref. 26). Thick and thin arrows represent the directions of $\mathrm{m}$ and STTs, respectively. Note that the direction of $\mathrm{m}$ deviates from $\pm \widehat{\mathrm{y}}$, which is a generic feature of a moving DW (Refs. 9 and 10) with $\alpha \ne \beta$.

Figure 3

Micromagnetic simulation results of the current-driven DW motion. In (a) and (b), RSOC effects are examined by using Eq. (4). (a) $v_{\mathrm{DW}}$ as a function of ${\tilde{\alpha }}_{\mathrm{R}}$ for $j_e=3.0\times {10}^{11}$ A/m${}^2$ (inset) and as a function of $j_e$ for ${\tilde{\alpha }}_{\mathrm{R}}=0$ (black squares) and ${\tilde{\alpha }}_{\mathrm{R}}=10$ (red circles). (b) DW tilting angle $\phi$ (measured clockwise from the $+\widehat{\mathrm{y}}$ direction in Fig. 2) indicates that the Walker breakdown is suppressed by FL-STT if ${\tilde{\alpha }}_{\mathrm{R}}=10$ and occurs for $j_e>1.0\times {10}^{12}$ A/m${}^2$ if ${\tilde{\alpha }}_{\mathrm{R}}=0$. In (c) and (d), SHE effects are examined by setting ${\mathrm{H}}_{\mathrm{R}}=0$ and instead adding to Eq. (4) the SHE-induced Slonczewski STT $\gamma \mathrm{M}\times [({\theta }_{\mathrm{SH}}\mathrm{M}/M_{\mathrm{s}})\times \left(H_{\mathrm{S}}\widehat{\mathrm{y}}\right)]$ (Ref. 27), where ${\theta }_{\mathrm{SH}}$ is the spin Hall angle, $H_{\mathrm{S}}=\hslash j_{e,\mathrm{N}}/\left(2e{M}_{\mathrm{s}}{t}_{\mathrm{F}}\right)$, $t_{\mathrm{F}}$ is the thickness of the ultrathin magnetic layer, and $j_{e,\mathrm{N}}$ is the charge current density in the heavy metal layer. $j_{e,\mathrm{N}}=j_e$ is assumed. $v_{\mathrm{DW}}$ (c) and $\phi$ (d) as a function of $j_e$ for ${\theta }_{\mathrm{SH}}=0$ (black squares) and 0.048 [red circles and green diamonds for the DW structures in Figs. 2a and 2b]. Red circles are not visible for $j_e>5\times {10}^{11}$ A/m${}^2$ since the corresponding DW structure in Fig. 2a becomes unstable. The inset in (c) shows $v_{\mathrm{DW}}$ as a function of ${\theta }_{\mathrm{SH}}$ at $j_e=3.0\times {10}^{11}$ A/m${}^2$ for the stable DW structure in Fig. 2b. The parameters for the simulation are as follows: $\alpha =0.5$, $\beta =0.25$ (Ref. 26), $M_{\mathrm{s}}=5.0\times {10}^5$ A/m, the PMA constant $K_{\mathrm{u}}=1.0\times {10}^6$ J/m${}^3$, the exchange stiffness constant $A_{\mathrm{ex}}=1.0\times {10}^{-11}$ J/m, $P=0.7$, $\gamma /2\pi =28.0113$ GHz T${}^{-1}$, and $t_{\mathrm{F}}=0.6$ nm.