Tunnel Magneto-resistance in GaMnAs: going beyond Julli\`{e}re formula

The relation between tunnel magneto-resistance (TMR) and spin polarization is explored for GaMnAs/GaAlAs/GaMnAs structures where the carriers experience strong spin-orbit interactions. TMR is calculated using Landauer approach. The materials are described in the 6 band $\bf {k}\cdot \bf{p}$ model which includes spin orbit interaction. Ferromagnetism is described in the virtual crystal mean field approximations. Our results indicate that TMR is a function of of spin polarization and barrier thickness. As a result of the stong spin orbit interactions, TMR also depends on the the angle between current flow direction and the electrode magnetization. These results compromise the validity of Julliere formula.