Abstract
The anomalous Hall effect due to the orbital magnetism has been investigated in a weakly doped semiconductor in the presence of a magnetic field. For a collisionless electron gas, we have calculated the conductivity tensor and (besides the usual Hall effect) we have obtained an anomalous current proportional to E × M We find that for ω = 0 no particular affect arises; for finite frequencies, we give the first non trivial term of the anomalous Hall current. We also discuss the influence of the collisions and the conditions for observing the predicted effects experimentally.
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