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

This paper contains a comprehensive account of positive-muon Knight-shift ($K_{\mu }$) 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.