A simple method for studing the electron transport properties in the magnetic tunnel junction with an arbitrary barrier shape

Based on the Slonczewski's free electron model, we present a simple method that can he used to study the electron transport properties in a magnetic tunnel junction with an arbitrary barrier shape. As examples, the TMR for three familiar barrier shapes, i.e., the trapezoidal barrier, the barrier with mirror potential taken into account, and the parabolic barrier, has been calculated.