Interfacial spin-orbit splitting and current-driven spin torque in anisotropic tunnel junctions

Spin transport in magnetic tunnel junctions comprising a single magnetic layer in the presence of interfacial spin-orbit interaction (SOI) is investigated theoretically. Due to the presence of interfacial SOI, a current-driven spin torque can be generated at the second order in SOI, even in the absence of an external spin polarizer. This torque possesses two components, one in plane and one perpendicular to the plane of rotation, that can induce either current-driven magnetization switching from an in-plane to out-of-plane configuration or magnetization precessions, similar to spin transfer torque in spin valves. Consequently, it appears that it is possible to control the magnetization steady state and dynamics by either varying the bias voltage or electrically modifying the SOI at the interface.

Figure 1

(a) Schematics of a semimagnetic tunnel junction. (b) Influence of the spin torque on the magnetization. Angular dependence of (c) TAMR and (d) perpendicular torque $T_{\perp }$ at zero bias for a rotation in the (010) planes and ${\alpha }_R\in$[1,5] eV Å${}^2$. The parameters are adapted for an Fe-MgO interface: $U_0=$1 eV, $d=0.6$ nm, $k_F^{\uparrow }=1.09$ nm${}^{-1}$, $k_F^{\downarrow }=0.4$ nm${}^{-1}$. Inset in (d) shows $\varphi$ dependence of the perpendicular torque.

Figure 2

Nonequilibrium in-plane torque $T_{\left|\right|}(V_b)$ as a function of (a) the Rashba parameter and (b) bias voltage. The dashed line shows the nonequilibrium perpendicular torque for $V_b=0.8$ V in (a) and $a_R=4$ eV Å${}^2$ in (b). The parameters are the same as in Fig. 1.

Figure 3

Stability diagram of the magnetization in the presence of perpendicular and in-plane anisotropy as well as in-plane torque. The parameters are magnetic damping $\eta =0.01$, perpendicular anisotropy $Q_{\perp }=0.75$, and saturation magnetization $M_s=1.6$T[20]. The dashed lines are guides for the eye.

Figure 4

Magnetization trajectory for a magnetization initially perpendicular to the plane and submitted to an in-plane anisotropy $Q_{\left|\right|}=0.2$ and (a) ${\tau }_{\left|\right|}=-0.0125$, (b) ${\tau }_{\left|\right|}=-0.02$, and (c) ${\tau }_{\left|\right|}=-0.0375$. (d) Dependence of the oscillation frequency as a function of the in-plane torque.