Tunneling times in double spin-filter junctions

Abstract

Based on the free electronic model and Winful's theory about tunneling times, the dwell times and the phase times in NM/SF/I/SF/NM double spin filter junctions are investigated, where the NM denotes the normal metal, SF the insulator barrier with spin filter effects and I the nonmagnetic insulator barrier. There are three different cases which are analyzed in detail:1) the dependences of dwell time and phase time on the energy of the incident electron; 2) the dependences of dwell time and phase time on the heights of the barrier; 3) the dependences of dwell time and phase time on the width of the barrier and the molecular field in the spin filter layer. The numerical results show that for the first case, when the electrons have low incident energy (smaller than the barrier height), as the influence of the spin-dependent self-interfere term, the phase times are always larger than the dwell times for electrons with different spinorientations. But when the electrons have high incident energy (higher than the barrier heights), the influence of the self-interfere term disappears and the differences between the phase time and dwell time for electrons with different spin orientations disappear also. For case 2, the numerical results show that the variation of nonmagnetic insulator barrier height has little influence on the dwell time and phase time in NM/SF/I/SF/NM double spin filter junctions. But when the nonmagnetic insulator barrier height is lower than the barrier height of spin filter layer, the quantum well will appear and the resonant tunneling can be induced to lead to the peaks in the dependences of dwell and phase times on the insulator barrier height. The variation of spin-filter barrier height has obvious influence on the dwell time and phase time in NM/SF/I/SF/NM double spin filter junction. With increasing the height of spin-filter barrier, the dwell times and phase time both first increase and then decrease. For case 3, the influences of the widths of the nonmagnetic insulator barrier layer and spin filter layer on the dwell time and phase time are little. But when the barrier height of nonmagnetic insulator barrier is lower than that of spin-filter layer, the variation of width of insulator barrier can lead to the resonant tunneling and the peaks in dwell and phase times. Unlike the influence of width of barrier, the influences of molecular field in the spin filter layer on the dwell time and phase time are obvious. For the up-spin electrons, dwell time and phase time decrease with increasing the molecular fields, which is contrary to the scenario for the down-spin electrons.