The thermomagnetic tensor and the Umkehr effect in bismuth

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Abstract
From transport theory in relaxation time approximation, analytic expressions are derived for the thermomagnetic power tensor alpha (B) in terms of the magnetoconductivity tensor components and partial Seebeck coefficients for materials with multivalley Fermi surfaces. Thereby, the thermomagnetic power in bismuth is explicitly connected with the carrier densities and mobility tensor components in the two band model. To obtain these model parameters, a least mean squares procedure has been adopted to analyse experimental results of alpha 22(B) for bismuth at liquid nitrogen temperatures. The solutions found are in agreement with the model parameters computed from measurements of the twelve coefficients that describe the low field, magnetoresistivity tensor: a finding that attests to the validity of the theory developed for the thermomagnetic effects. The Umkehr effect and sign reversal observed in the thermomagnetic power of bismuth are shown to follow from the nature of the Fermi surface. Predictions are made for the occurrence of the Umkehr effect in other components of the thermomagnetic tensor.

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