Fermi surface of lead under homogeneous strain

Abstract

The uniaxial stress and angular shear dependence of several extremal cross sections of the Fermi surface of the simple metal lead were obtained by a simultaneous measurement of the oscillatory magnetostriction and the de Haas---van Alphen torque. For six of the seven experimentally studied orbits all the uniaxial stress derivatives were determined and their sum compares well with the directly measured hydrostatic pressure dependence of other authors. The response of the Fermi surface to homogeneous strain is discussed in terms of volume-conserving shears (tetragonal or angular) and volume changes. A theoretical study of the Fermi surface and its strain dependence, based on a local pseudopotential model, is presented. New values for the relevant pseudopotential matrix elements in the absence of strain obtained from a fit to high-precision de Haas---van Alphen frequencies are given for different sizes [(4\ifmmode\times\else\texttimes\fi{}4), (8\ifmmode\times\else\texttimes\fi{}8), (16\ifmmode\times\else\texttimes\fi{}16)] of the secular matrix. The Fermi energy and its derivatives are computed by summing over occupied states. Eight orthogonalized plane waves are required in the secular matrix in order to describe the effect of a general homogeneous deformation on the Fermi surface. The strain response of ten carefully extremalized orbits has been calculated, with the slopes of the form factor at the first two reciprocal-lattice vectors as the only free parameters. Good agreement with our uniaxial stress data, as well with the hydrostatic pressure data of Anderson et al. is found, without invoking the spin-orbit interaction as an extra free parameter.