The de Haas–van Alphen effect in alkali metals

Abstract

A new method for studying the de Haas–van Alphen effect in steady magnetic fields has been developed in which the field is modulated at frequency ω and a signal at frequency 2 ω is generated in a pick-up coil round the specimen because of the non-linear field dependence of magnetization. The rectified 2 ω signal is proportional to d 2 M /dH 2 and so shows de Haas–van Alphen oscillations either when H is varied for fixed orientation or when the orientation is varied in fixed H if the Fermi surface is anisotropic. Because the phase of oscillation is very high (of order 10 4 π ) even very slight anisotropy will produce a few oscillations when the orientation is varied and the method is therefore particularly sensitive for studying very nearly spherical Fermi surfaces. From the oscillations with H , values of the frequency F were found for sodium, potassium, rubidium and caesium which were close to those predicted for a free-electron sphere containing 1 electron per atom, though some small systematic deviations of order ½ % were observed which may be significant. From detailed study of the oscillations produced by rotation of single crystals in fixed H it was found possible to describe the orientation dependence of F (proportional to the area of cross-section of the Fermi surface) for potassium and rubidium consistently by a series of cubic harmonics and hence to deduce the small departures of the Fermi surfaces from spherical shape. The deviations from a sphere were found to be of the order of 1 part in 10 3 for potassium and a little less than 1 part in 10 2 for rubidium; these deviations are compared with those predicted by band structure calculations. Preliminary results for sodium suggest that it is appreciably less anisotropic than potassium. Some results are also reported on the temperature and field dependence and the absolute amplitude of the de Haas-van Alphen effect, and it is also shown how the effect can be used to measure very small variations of field with position.