Time-dependent spintronic transport and current-induced spin transfer torque in magnetic tunnel junctions

Zhen-Gang Zhu, Gang Su,* Qing-Rong Zheng, and Biao Jin

Department of Physics, The Graduate School of the Chinese Academy of Sciences, P.O. Box 3908, Beijing 100039, China

~Received 16 April 2003; revised manuscript received 20 August 2003; published 15 December 2003!

The responses of the electrical current and the current-induced spin transfer torque ~CISTT! to an ac bias in addition to a dc bias in a magnetic tunnel junction are investigated by means of the time-dependent nonequilibrium Green function technique. The time-averaged current ~time-averaged CISTT! is formulated in the form of a summation of dc current ~dc CISTT! multiplied by the product of Bessel functions with the energy levels shifted by m\v0. The tunneling current can be viewed to occur between the photonic sidebands of the two ferromagnets. The electrons can pass through the barrier easily under high frequencies but difficultly under low frequencies. The tunnel magnetoresistance almost does not vary with an ac field. It is found that the spin transfer torque, still being proportional to the electrical current under an ac bias, can be changed by varying frequency. Low frequencies could yield a rapid decrease of the spin transfer torque, while a large ac signal leads to a decrease of both the electrical current and the spin torque. If only an ac bias is present, the spin transfer torque is sharply enhanced at the particular amplitude and frequency of the ac bias. A nearly linear relation between such an amplitude and frequency is observed.

DOI: 10.1103/PhysRevB.68.224413 PACS number~s!: 73.40.Gk, 73.40.Rw, 75.70.Cn