Spin-flip scattering contribution to resonant-tunneling current in semimagnetic semiconductor heterostructures

Abstract

We calculate the characteristic current-voltage curve of a tunneling device based on semimagnetic semiconductor materials. The device is a heterostructure with layers of Cd1,xMnxTe in which the magnetic ions Mn 2+ interact strongly with the conducting electrons via the s-d exchange interaction. Thermal uctuations of Mn 2+ magnetic moments cause spin-dependent electron scattering that modi es the characteristic current-voltage curve. Our calculation shows how this electron-ion scattering is expected to a ect the spin dynamics in transport measurements. I IntroductionRecent advances in the growth of semimagnetic semiconductor SMS quantum structures have renewed the interest in the long-standing study of carriers interacting with magnetic ions. 1 SMS quantum structures are versatile systems in which to conduct such study because they make possible the adjust of the spatial overlap between the carrier wave functions and the magnetic ions. 2Optical spectroscopy with polarized light h a ve contributed greatly to the understanding of the carrier spin dynamics in undoped SMS quantum structures. 3 That is because angular momentum conservation at the absorption of a polarized photon allows creation of carriers in de nite spin states. Furthermore, detection of the polarization of the luminescence reveals the spin states of the carriers at the moment they recombine; from this it is possible to study the role of di erent spin relaxation mechanisms on the spin population initially photoexcited. On the other hand, most of the transport measurements do not give access to the spin state of the conducting carriers, which complicates the study of the spin dynamics. Also, such measurements usually require doped SMS samples that only recently have been grown with reliable quality. Despite these di culties, preliminary investigations have shown interesting behaviors that are attributed to the spin polarization of the conducting carriers. 4In this work we i n vestigate a tunneling device made out of layers of Cd 1,x Mn x Te materials, where the magnetic moments arise from the half-lled d shell of the ions Mn 2+ . An external magnetic eld B is applied along the growth axis z-axis to align the localized moments and to create a magnetization proportional the average ion spin hS z i, which acts on the electrons via the s-d exchange interaction. This e ect can be seen, in the mean-eld approximation, as a change in the potential pro les; electrons with spins up see a di erent potential than electrons with spins down. 2 Several devices have been proposed 5 based on this di erence in potential pro les to create tunneling current with some degree of spin polarization.II Spin-dependent potential pro lesThe coupling between electrons and the magnetic ions is given by the s-d exchange interaction term P i J s,d b S i in the electron Hamiltonian, where b is the electronspin operator, S i 's are the ion spins, and J s,d the exchange coupling constant. As discussed above, in the mean-eld approximation, the Hamiltonian can be written as