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A Note on the Hall and Magneto-Resistance Effects

Published online by Cambridge University Press:  24 October 2008

D. Shoenberg
D. Shoenberg*
Affiliation:
Coutts Trotter Student, Trinity College
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Extract

Recently Kohler, on the basis of some experiments by Verleger, has questioned the validity of the usual assumption that the linear Hall effect is entirely perpendicular to the current. The available experimental data are however contradictory, so a simple magneto-resistance experiment with a bismuth crystal was made, which suggested that the usual assumption was, after all, valid. The disymmetry of the Hall effect is discussed, and some of Kohler's results are generalized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 31 , Issue 2 , April 1935 , pp. 271 - 276
Copyright
Copyright © Cambridge Philosophical Society 1935

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References

* Kohler, M., Ann. der Phys, 20 (1934), 878 and 891.CrossRefGoogle Scholar

† Voigt, W., Lehrbuch der Kristallphysik (Teubner, 1928).Google Scholar

‡ The summation convention is used throughout this paper.

* Shoenberg, D., Proc. Cambridge Phil. Soc. 31 (1935), 265.CrossRefGoogle Scholar

† The main cleavage plane is normal to the trigonal axis.

‡ Verleger, H.. Z. f. Phys. 76 (1932), 760.CrossRefGoogle Scholar

* The Hall effect is no longer linear for this rather high field, but this does not substantially alter the argument, since the Hall effect for this field is certainly of the same order of magnitude as would be obtained by extrapolation from lower fields. The non-linearity may be described by taking account of cubic and higher order terms in H. and it is easily seen that these would also cause a reversible change of resistance effect in addition to (11) if the perpendicularity hypothesis is rejected.

* Since in R iklm i, k and l, m commute, the tensor can be abbreviated in the conventional way to R αβ;, where α, β; vary from 1 to 6.

* This idea fits in with the observation of Lownds ( Ann. der Phys. 9 (1902), 677 Google Scholar) that the disymmetry is much larger at very low temperatures than at room temperatures, since it is well known that the magneto-resistance increases enormously with decrease of temperature.