Calculation of the Spin Susceptibility of Disordered Binary Alloys: Application to Pt-Pd, Rh-Pd, Ni-Rh, and Ni-Pd

Abstract

Recently the spin susceptibility $\chi$ of a one-band model for a disordered binary alloy with intraatomic Coulomb interactions and short-range scattering potentials was calculated using the coherent-potential approximation (CPA). The formal expression for $\chi$, which is applicable to alloys of arbitrary concentration and potential-scattering strengths, was found to reduce to previously obtained expressions for the susceptibility in the dilute-alloy limit and to contain as a special case the uniform-enhancement model for $\chi$. In the present paper this theory for the spin susceptibility is applied to several binary Ni, Rh, and Pd alloys. Good agreement with experiment is obtained for $\chi$ as a function of $x$ in ${\mathrm{Pt}}_x{\mathrm{Pd}}_{1-x}$, ${\mathrm{Rh}}_x{\mathrm{Pd}}_{1-x}$, ${\mathrm{Ni}}_x{\mathrm{Rh}}_{1-x}$, and ${\mathrm{Ni}}_x{\mathrm{Pd}}_{1-x}$ when a simple "steeple model" for the density of $d$-electron states is used. The sign of the potential-scattering parameter is obtained from renormalized-atom calculations; its magnitude is allowed to vary arbitrarily. Good agreement between theory and experiment makes it possible to determine the physical mechanisms which govern the behavior of $\chi$ in the four alloy systems considered. It is shown that potential-scattering effects which change the density of states at the Fermi energy in the alloy from the value in the pure crystals must be included in calculations of $\chi$ in ${\mathrm{Pt}}_x{\mathrm{Pd}}_{1-x}$. A uniform-enhancement model, in which the alloy is replaced by a periodic crystal at each site of which the Coulomb interaction energy is given by the average of the intra-atomic Coulomb energies, is found to approximate the calculated spin susceptibility in ${\mathrm{Pt}}_x{\mathrm{Pd}}_{1-x}$ to within an accuracy of 10%. For ${\mathrm{Rh}}_x{\mathrm{Pd}}_{1-x}$ alloys it is concluded that it is more likely that the nonmonotonic $x$ dependence of $\chi$ is due to a relatively large contribution to the susceptibility associated with Rh sites than to a rigid-band density-of-states effect. This conclusion is in agreement with recent NMR data. The theoretically determined spin susceptibility in ${\mathrm{Ni}}_x{\mathrm{Rh}}_{1-x}$ alloys for $x<~0.50$ may be approximated to within an accuracy of 10% by a uniform-enhancement model, providing the density of states at the Fermi energy is calculated self-consistently at each concentration $x$ using the CPA. Thus both the Ni and Rh atoms may be viewed as participating equally in the ferromagnetic phase transition in ${\mathrm{Ni}}_x{\mathrm{Rh}}_{1-x}$ which takes place for $x>~0.63$. By contrast, for ${\mathrm{Ni}}_x{\mathrm{Pd}}_{1-x}$ alloys in which it is found that the Ni sites make a relatively large contribution to the susceptibility, the Ni atoms appear to be mainly responsible for the ferromagnetic phase transition which occurs at very low Ni concentrations $x>~0.022$.