Magnetostriction and Magnetoelastic Quantum Oscillations in $p-\mathrm{PbTe}$

A detailed experimental and theoretical study of quantum oscillations in the magnetostriction and Young's modulus of $p-\mathrm{PbTe}$ is presented. The valence band of PbTe is approximated by a spheroidal nonparabolic model in which the effects of strain on the valence-band parameters are described by a deformation potential model. Using appropriate thermodynamic derivatives of the modified Lifshitz-Kosevich expression for the oscillatory part of the electronic free energy, it is shown that both types of oscillations arise mainly from relative shifts of the valence-band maxima due to shear strains, accompanied by intervalley charge transfer. Band parameters derived from the periods, phases, and spin splitting of the oscillations are in generally good agreement with values reported by other workers. A detailed comparison is made of the experimentally observed oscillation amplitudes with those predicted by theory, and satisfactory agreement is found. The ratio of the amplitudes of the two effects yiends a value of the valence-band deformation potential ${\Xi }_u^v=7.9\mathrm{}\pm 1.3$ eV in good agreement with a value found from piezoresistance experiments by Burke.