  We study in this paper the parallel spin current in an antiferromagnetic
semiconductor thin film where we take into account the interaction between
itinerant spins and lattice spins. The spin model is an anisotropic Heisenberg
model. We use here the Boltzmann's equation with numerical data on cluster
distribution obtained by Monte Carlo simulations and cluster-construction
algorithms. We study the cases of degenerate and non-degenerate semiconductors.
The spin resistivity in both cases is shown to depend on the temperature with a
broad maximum at the transition temperature of the lattice spin system. The
shape of the maximum depends on the spin anisotropy and on the magnetic field.
It shows however no sharp peak in contrast to ferromagnetic materials. Our
method is applied to MnTe. Comparison to experimental data is given.
