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.