Enhancing spin transfer torques in magnetic tunnel junctions by ac modulation*

Phenomena of spin transfer torques (STTs) have been attracting persistent interests due to promising prospects of STTs in designing nano devices. By using nonequilibrium Green's function method, we derive time-averaged formulism for spin transfer torques in a noncollinear magnetic tunneling system under ac modulation. Using these formulas, we further investigate ac spin transfer torques in a carbon-nanotube-based magnetic tunneling system. It shows that under ac modulation, the low-bias linear (quadratic) dependence of the in-plane (out-of-plane) torque on bias still holds, and the $\sin\theta$ dependence on noncollinear angle is maintained. By introducing photon-assisted tunneling, the bias-induced components of the in-plane and out-of-plane torques can be enhanced by about 12 and 75 times, respectively. Further analysis shows that optimized enhancement can be achieved by using ac driving frequency $\omega=\epsilon_0/k, k=1,2,...$, where $\epsilon_0$ marks a remote dc transmission peak, and ac amplitude $\Delta$ such that $\Delta/\omega$ maximizes a $k^{th}$-order Bessel function. Our findings suggest that ac modulation is an effective way for electrical manipulation of STTs, paving the road towards emerging STTs-based nanoelectronics and spintronics.