Spin-dependent delay time and the Hartman effect in tunneling through diluted-magnetic-semiconductor/semiconductor heterostructures

Abstract

We investigate spin-dependent group delay and dwell time in diluted-magnetic-semiconductor/semiconductor (DMS/S) heterostructures, where the $sp\text{\ensuremath{-}}d$ exchange interaction gives rise to a giant spin splitting when an external magnetic field applied along the growth direction of the heterostructures. It is found that both the group delay and the dwell time strongly depend not only on the incident energy and the structural configuration, but also on spin orientations. In the spectra of both the group delay and the dwell time, there are some sharp peaks with larger peak-to-valley ratios for spin-up electrons through the DMS/S heterostructures with a single or double DMS layers, while the curves become more smoothed for spin-down ones through the same heterostructure. The difference of the group delay or of the dwell time between spin-up and spin-down cases reaches its maximum when resonant tunneling occurs. The numerical results indicate that the spin-up and spin-down processes are separated on the time scales. Further, for spin-down electrons, the group delay can be negative at low energy under some magnetic fields.