Theory of the magnetization and exchange-enhanced susceptibility of alloys. I. Zero-temperature susceptibility of paramagnetic alloys in the random-phase approximation

A new theoretical treatment of the magnetic susceptibility of substitutionally disordered alloys is presented. This treatment goes beyond the existing treatments of the susceptibility of alloys in several important respects, although in the present paper (I of this series) it is confined to zero temperature and the random-phase approximation (RPA). Unlike treatments based on the single-site approximation, it yields results for the exchange-enhanced local susceptibilities ${\chi }_{\mathrm{ij}}$(ω) as a function of the local environment of sites i and j. Specifically, it includes the strong effects of the nonlinearity of the dependence of the ${\chi }_{\mathrm{ij}}$(ω) on local environments and the effects of short-range order on the uniform susceptibility χ(0,ω). This treatment goes beyond all previous cluster treatments of the susceptibility by treating exactly the embedding of a cluster in a given effective medium. Even more important, it is the first cluster theory to include exchange-enhancement effects in the embedding medium. Disorder in the exchange enhancement and in the local band susceptibility are treated on an equal footing. Finally, the formal connection between alloy band theory and the random-phase-approximation theory of alloy susceptibilities is elucidated. In particular, the problem of choosing the best self-consistency condition for the determination of the susceptibility χ¯(q,ω) of the effective medium is considered in detail in light of the known results of alloy band theory. In the following two papers of this series, the theory presented here is extended to treat the local magnetization of alloys and the susceptibility in the presence of moments, and to include the effects of quantum and thermal spin fluctuations in a manner consistent with the results of renormalization-group theory.