Spin-dependent tunnelling through a symmetric barrier

The problem of electron tunnelling through a symmetric semiconductor barrier based on zinc-blende-structure material is studied. The $k^3$ Dresselhaus terms in the effective Hamiltonian of bulk semiconductor of the barrier are shown to result in a dependence of the tunnelling transmission on the spin orientation. The difference of the transmission probabilities for opposite spin orientations can achieve several percents for the reasonable width of the barriers.