Green's-Function Theory of an Induced Moment System Containing Impurities: Paramagnetic Phase

An induced moment system containing a substitutional impurity is studied using the Green's-function method in the random phase approximation. All the ions are assumed to have a singlet crystal field ground state and a singlet excited state. We focus our attention on the paramagnetic phase, without local polarization, in this paper. Two $s$-type modes are predicted in a lattice with only nearest-neighbor exchange interactions. The energies of the impurity modes have been calculated as functions of the impurity parameters and the temperature for a simple-cubic lattice. Similar to an ordinary impure magnetic system, local modes can appear above the energy band of the host and/or in the energy gap. The spectral weight function at the impurity site is discussed. Local susceptibilities, which are proportional to the temperature-dependent part of the NMR Knight shift, are calculated and compared with predictions of the molecular-field theory. The experimental situation is also reviewed.