Observation of Van Hove—type singularities in the local electron density of states by muon Knight-shift measurements in Cd andCdHgandCdMgalloys

Abstract

This paper contains a comprehensive account of positive-muon Knight-shift (${K}_{\ensuremath{\mu}}$) measurements in the hcp metal Cd and the isostructural, isovalent alloys $\mathrm{Cd}\mathrm{Hg}$ (1.23 at.% Hg) and $\mathrm{Cd}\mathrm{Mg}$ (3.38 at.% Mg) which reveal a strong and peculiar temperature dependence never observed before by NMR Knight-shift studies. Most striking are anomalies in the temperature dependence which show up as a more or less resolved structure consisting of two "dips" and a "cusplike" (logarithmic) singularity in between. In pure monocrystalline Cd an axial Knight-shift contribution is observed which changes its sign precisely at the temperature at which the "cusplike" singularity is centered. The anomalies are shown to reflect Van Hove---type singularities in the local electron density of states. The number, sequence, and topological character of the singularities can be explained in terms of a three-band model, which is essentially a replica of the three-band model which describes the bulk band structure of Cd and its Hg and Mg alloys close to the Fermi energy in the vicinity of the $K$-symmetry point in the hcp Brillouin zone. Quite unexpected and unexplained so far is the observation that, compared to the bulk band structure, the present "band states" display a reduced splitting and are considerably down-shifted relative to the Fermi energy, both effects being dependent on the alloy composition. This seems to be a new phenomenon induced locally by the presence of an interstitial and single hydrogenlike impurity.