The Magneto-Resistance Effect in Oriented Single Crystals of Germanium

This paper describes an extensive study of the magneto-resistance effect in germanium as a function of crystal orientation. Experimental measurements establish the constants involved in the dependence of the effect on orientation of magnetic field and electric current relative to the crystal axes. The measurements are internally consistent with existing phenomenological theory based on cubic crystal symmetry, in which terms involving the magnetic field to higher than the second order are neglected. It is shown that such deviations as do occur arise from higher terms in the field, since an extension of the phenomenological theory to the fourth order predicts their symmetry. Relations are established between the experimentally observed phenomenological constants and those constants appearing in existing magneto-resistance electronic theories. It is concluded that no electronic theory yet worked out is entirely consistent with experiment. The present electronic theories are special cases of a very general theory recently proposed by Shockley, and it is possible that agreement can be obtained as soon as the computational difficulties of the latter theory are overcome.