Temperature-Dependent Knight Shift in Cadmium: A Theoretical Study

Abstract

Experimentally the Knight shift in Cd is characterized by (1) an increase in the nuclear resonance frequency of more than 70% in the temperature range from 0 to 594°K (melting point), (2) an increase of 33% in the isotropic Knight shift at the melting point, and (3) an increase in the anisotropic Knight shift from a small negative value at $T=0\mathrm{}°$K to a fairly large positive value at high temperatures. We find that this temperature dependence is theoretically accounted for by including the effects of lattice vibrations into the electronic structure which we have investigated by means of an empirical pseudopotential. The effect of the lattice vibrations is to decrease the strength of the pseudopotential. This makes the energy bands more free-electron-like, and the $s$ character of the wave functions of the Fermi surface increases. It also destroys the cancellation of the contributions of the various $p$ parts of the wave function to the anisotropic Knight shift, thus increasing the anisotropy as well. Many-body corrections were included by means of a temperature-independent enhancement factor and were determined empirically for $T=0\mathrm{}°$K. The trend of the variation of the Knight shift with temperature, both isotropic and anisotropic, is explained.