Lateral Shifts for Spin Electrons in a Hybrid Magnetic-Electric-Barrier Nanostructure Modulated by Spin-Orbit Couplings

We theoretically investigate how to modulate spin-dependent lateral shifts by the spin-orbit coupling (SOC) in a hybrid magnetic-electric-barrier (MEB) nanostructure, which can be experimentally realized by depositing a ferromagnetic (FM) stripe and a Schottky metal (SM) stripe on the top and bottom of the semiconductor heterostructure, respectively. Two kinds of ROCs, Rashba SOC (RSOC) and Dresselhaus SOC (DSOC), are taken into account fully. The Schrödinger equation of the spin electron in the hybrid MEB nanostructure is exactly solved by using the improved transfer-matrix method (ITMM), and the lateral shift and its spin polarization are numerically calculated with the help of the stationary phase method (SPM). Theoretical analysis indicates that the spin polarization effect in the lateral shift still exists in the hybrid MEB nanostructure when the SOCs are considered. Numerical simulations show that both magnitude and sign of the spin polarization effect in lateral shifts vary strongly with the strengths of RSOC and DSOC. These interesting features may offer an effective means to control the behavior of spin-polarized electrons in the semiconductor nanostructure, and such a hybrid MEB nanostructure serves as a SOC-manipulable spatial spin splitter for spintronic applications.