Molecular-field theory of moment reduction in Kondo systems with crystal-field effects

Several dense Kondo compounds have a low-temperature ordered phase in which the magnetic moments are reduced with respect to the values expected for the crystal-field (CEF) ground state. In the present work the phenomenon of moment reduction is studied within a molecular-field theory combined with a variational solution of the one-impurity Anderson model with CEF effects. The calculated zero-temperature magnetization and susceptibility agree well with available exact results; the present method is easily applied to systems of any symmetry. We first study the f ¹ configuration in cubic symmetry, for small values of the ratio T _K/Δ between Kondo temperature and CEF splitting. With a Γ _∞ ground state and a field along a 〈100〉 direction, an inflection point occurs in the magnetization curve, which gives rise to a first order transition in the zero-temperature phase diagram. This feature is not found for a field along 〈110〉 or 〈111〉, for which the transition is second order. For a Γ ₇ ground state and small values of T _K/Δ, the magnetic-nonmagnetic transition is second order for all field directions. On increasing T _K/Δ an inflection point in the magnetization curve appears first for a field along 〈111〉. The theory is applied to a study of cubic CeAg, CeAl₂, CePb₃, CeIn₃, CeTe, and hexagonal CePd₂Ga₃. The bare value of the moment is found to be strongly increased by exchange coupling to excited CEF states, and the amount of Kondo reduction is found to be substantial, confirming the importance of the Kondo effect in these compounds.