Spin-dependent delay time in ferromagnet/insulator/ferromagnet heterostructures

We study theoretically spin-dependent group delay and dwell time in ferromagnet/insulator/ferromagnet (FM/I/FM) heterostructure. The results indicate that, when the electrons with different spin orientations tunnel through the FM/I/FM junction, the spin-up process and the spin-down process are separated on the time scales. As the self-interference delay has the spin-dependent features, the variations of spin-dependent dwell-time and spin-dependent group-delay time with the structure parameters appear different features, especially, in low incident energy range. These different features show up as that the group delay times for the spin-up electrons are always longer than those for spin-down electrons when the barrier height or incident energy increase. In contrast, the dwell times for the spin-up electrons are longer (shorter) than those for spin-down electrons when the barrier heights (the incident energy) are under a certain value. When the barrier heights (the incident energy) exceed a certain value, the dwell times for the spin-up electrons turn out to be shorter (longer) than those for spin-down electrons. In addition, the group delay time and the dwell time for spin-up and down electrons also relies on the comparative direction of magnetization in two FM layers and tends to saturation with the thickness of the barrier.