Electronic structure of ${\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x{\mathrm{Rh}}_2{\mathrm{S}}_4$ and ${\mathrm{CuRh}}_2{\mathrm{Se}}_4$: Band-structure calculations, x-ray photoemission, and fluorescence measurements

The electronic structure of spinel-type ${\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x{\mathrm{Rh}}_2{\mathrm{S}}_4$ $(x=0.0,$ 0.1, 0.3, 0.5, 1.0) and ${\mathrm{CuRh}}_2{\mathrm{Se}}_4$ compounds has been studied by means of x-ray photoelectron (XPS) and fluorescent spectroscopy. Cu $L_3,$ Ni $L_3,$ S $L_{2,3},$ and Se $M_{2,3}$ x-ray emission spectra (XES) were measured near thresholds at Beamline 8.0 of the Lawrence Berkeley Laboratory’s Advanced Light Source. XES measurements of the constituent atoms of these compounds, reduced to the same binding energy scale, are found to be in excellent agreement with XPS valence bands. The calculated XES spectra which include dipole matrix elements show that the partial density of states reproduce experimental spectra quite well. States near the Fermi level ${(E}_F)$ have strong Rh d and S(Se) p character in all compounds. In ${\mathrm{NiRh}}_2{\mathrm{S}}_4$ the Ni $3d$ states contribute strongly at $E_F,$ whereas in both Cu compounds the Cu $3d$ bands are only $\sim 1$ eV wide and centered $\sim 2.5$ eV below $E_F,$ leaving very little $3d$ character at $E_F.$ The density of states at the Fermi level is less in ${\mathrm{NiRh}}_2{\mathrm{S}}_4$ than in ${\mathrm{CuRh}}_2{\mathrm{S}}_4.$ This difference may contribute to the observed decrease, as a function of Ni concentration, in the superconducting transition temperature in ${\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x{\mathrm{Rh}}_2{\mathrm{S}}_4.$ The density of states of the ordered alloy ${\mathrm{Cu}}_{0.5}{\mathrm{Ni}}_{0.5}{\mathrm{Rh}}_2{\mathrm{S}}_4$ shows behavior that is more “split-band”-like than “rigid-band”-like.