# Enhancing the spin transfer torque in magnetic tunnel junctions by ac modulation

## TL;DR

This paper presents a theoretical study showing that ac modulation can significantly enhance spin transfer torque in magnetic tunnel junctions, offering a promising method for electrical control in spintronic devices.

## Contribution

It introduces a new theoretical framework for predicting time-averaged STT under ac modulation and demonstrates substantial torque enhancement via photon-assisted tunneling.

## Key findings

- Bias-induced torque components are greatly enhanced under ac modulation.
- The in-plane and out-of-plane torques are significantly increased by photon-assisted tunneling.
- The study provides conditions for optimal STT enhancement using ac modulation.

## Abstract

The phenomenon of spin transfer torque (STT) has attracted a great deal of interests due to its promising prospects in practical spintronic devices. In this paper, we report a theoretical investigation of STT in a noncollinear magnetic tunnel junction under ac modulation based on the nonequilibrium Green's function formalism, and derive a closed-formulation for predicting the time-averaged STT. Using this formulation, the ac STT of a carbon-nanotube-based magnetic tunnel junction is analyzed. 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 the noncollinear angle is maintained. By photon-assisted tunneling, the bias-induced components of the in-plane and out-of-plane torques can be enhanced significantly, about 12 and 75 times, respectively. Our analysis reveals the condition for achieving optimized STT enhancement and suggests that ac modulation is a very effective way for electrical manipulation of STT.