Time-Dependent Spin-Polarized Transport Through a Resonant Tunneling   Structure with Multi-Terminal
  The spin-dependent transport of the electrons tunneling through a resonant tunneling structure with ferromagnetic multi-terminal under dc and ac fields is explored by means of the nonequilibrium Green function technique. A general formulation for the time-dependent current and the time-averaged current is established. As its application the systems with two and three terminals in noncollinear configurations of the magnetizations under dc and ac biases are investigated, respectively. The asymmetric factor of the relaxation times for the electrons with different spin in the central region is uncovered to bring about various behaviours of the TMR. The present three-terminal device is different from that discussed in literature, which is coined as a spin transistor with source. The current-amplification effect is found. In addition, the time-dependent spin transport for the two-terminal device is studied. It is found that the photonic sidebands provide new channels for the electrons tunneling through the barriers, and give rise to new resonances of the TMR, which is called as the photon-asisted spin-dependent tunneling. The asymmetric factor of the relaxation times is observed to lead to additional resonant peaks besides the photon-asisted resonances. 
Zhen-Gang Zhu, Gang Su, Qing-Rong Zheng and Biao Jin