Surface Effects on the Spin Susceptibility of Paramagnetic Metals; A Simple Model

Abstract

The purpose of this paper is to study the effect of a surface on the spin susceptibility of simple models of paramagnetic metals. We first formally derive the form of the random-phase-approximation (RPA) equation satisfied by the dynamic susceptibility of a single tight-binding band of electrons that interact via a local intra-atomic Coulomb interaction. We then find an explicit expression for the dynamic susceptibility appropriate to a simple cubic metal with a (100) surface, in the absence of interactions. Special limiting forms of this function are studied, and in particular the magnitude of the magnetic moment induced in the surface layer by a static, spatially uniform field is calculated as a function of the position of the Fermi level. In a final section, we use a simplified form of the RPA equations to obtain analytic expressions for the static, wave-vector-dependent susceptibility in the limit that exchange enhancement of the host becomes large. The static correlation length between spins in the surface layer remains finite in our model even when the Stoner factor $1\ensuremath{-}\overline{I}$ vanishes. The form of the static correlation function is weakly dependent on ($1\ensuremath{-}\overline{I}$) when this parameter is small, but we find a rather strong dependence on the strength of the intra-atomic Coulomb interaction in the surface layer. A number of features of this result are discussed and compared with an earlier molecular-field theory of static spin correlations near the surface of the Heisenberg paramagnet.