The extraordinary Hall effect: Intuitive theory and experimental verification

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Abstract
We present a review of the theoretical literature on the extraordinary Hall effect. By using the formulation of Noziéres and Lewiner, we give an elementary presentation, stressing the physical aspects of the problem. Insight into the role of the spin‐orbit interaction in Bloch functions and in the extraordinary Hall effect is provided by the concept of the transverse displacement of a spin‐polarized electron. From this different terms of Luttinger are found and discussed on intuitive grounds. Two types of effects are distinguished: the ’’side‐displacement’’ contributions and the skew‐scattering effect. The conflicting results of various theories in the literature are compared and criticized. In the very simple case of a III‐V semiconductor the wavefunctions are well known and the calculations can be carried out exactly. We have measured the extraordinary Hall effect in such a system; by using a spin resonance method, the much larger ordinary Hall effect is circumvented as it gives no contribution to the signal. Our results provide an unambiguous test of the theory.

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