Paramagnetic $\mathrm{Ni}\mathrm{Cu}$ Alloys: Electronic Density of States in the Coherent-Potential Approximation

The coherent-potential approximation (CPA) is extended to study general band shapes and systems having orbital degeneracy. This permits its application to realistic systems, in particular the $\mathrm{Ni}\mathrm{Cu}$ alloys. The effects of alloying on a highly asymmetric model density of states characteristic of some of the features of the density of states in fcc transition metals are considered in detail. A model Hamiltonian for paramagnetic $\mathrm{Ni}\mathrm{Cu}$ is constructed using a basis of orthogonalized plane waves and tight-binding $d$ functions. Orbital degeneracy and hybridization are treated as in paramagnetic Ni. Effects of alloying are assumed to be restricted to the diagonal elemensts of the $d-d$ block. The model is applicable to the Ni-rich alloys, as is the approximation used to obtain simple solutions of the full CPA equations. The results are consistent with recent photoemission data on $\mathrm{Ni}\mathrm{Cu}$, and with the "minimum polarity" hypothesis used by Lang and Ehrenreich. They are incompatible with the rigid-band model because the scattering potential of the random alloy is strong compared to the peak widths. Rather than a rigid shift of the density of states, the calculated concentration dependence shows that the main peaks remain stationary while changing magnitude and shape. Decomposition of the total density of states into Ni and Cu contributions confirms that, for the expected position of the Fermi level, the $d$ holes are located primarily on Ni sites.