Asymmetric tunneling of holes through a semiconductor junction in an arbitrary magnetization configuration

In this paper, we investigate the asymmetry of holes tunneling through GaMnAs/GaAs/GaMnAs heterostructures in the cases general, where the magnetization of the two electrodes are not colinear and their magnitude are not equal. The six-bands $\textbf{k.p}$ Hamiltonian is employed to describe the holes in the GaAs and GaMnAs layers, taking into account both spin-orbit and exchange interactions. The multi-band transfer-matrix formalism is applied for numerically solving the Schrodinger equation to derive the hole wave transmission. We then calculate the transmission asymmetry and discuss its dependence on the right electrode magnetization magnitude, as well as the angles determining relatively the orientation of two magnetization vectors. The study may provide the insights into dynamic of Anomalous Tunneling Hall current during magnetization switching process which are important in spintronics technology for device design and measurement.