Tunneling of holes through a trilayer structure made of two diluted magnetic semiconductors, (Ga,Mn)As, separated by a thin layer of nonmagnetic AlAs is investigated. The problem is treated within the $6\times 6$ Luttinger-Kohn model for valence bands with the split-off band included. The influence of the spin-orbit coupling is pronounced as the spin-splitting ${\Delta }_{\mathit{ex}}$ is comparable with the split-off ${\Delta }_{\mathit{SO}}$ splitting. It is assumed that direct tunneling is the dominant mechanism due to the high quality of the tunnel junctions. Our theoretical results predict the correct order of magnitude for the tunneling magnetoresistance ratio, but various other effects, such as scattering on impurities and defects, should be included in order to realize a quantitative agreement with experiment.

• Received 3 June 2005

DOI:https://doi.org/10.1103/PhysRevB.72.125350