On theory of anomalous hall effect in semiconductors

The anomalous Hall effect in semiconductors is calculated. This effect is specified by asymmetry of dispersion of the polarized electrons due to their spin-orbital interaction with the crystal field of the lattice in the third Born approximation. The effect is mainly defined by the corrections to the collision integral. In the non-compensated semiconductors this effect differs from zero in the second Born approximation. When electrons are scattered on positive or negative centers, the effect is the same in its absolute opposite in direction. In compensated semiconductors the non-zero effect is traced only in the third Born approximation. Its absolute value is less than in the non-compensated semiconductors and direction coincides with the direction observed during electron scattering on negative centers. When the kinetic energy of the electrons is low and the Born parameter is absent, the effect may be evaluated using the phase method. Calculations are given for InSb with parameters corresponding to those employed in the experimental work (J.-N. Chazslviel, I. Solomon. Phis.Rev.Lett., 29, 1676, 1972), which was thoroughly discussed and compared with the given theory