Resistivity of heavy-fermion systems in the presence of a crystalline electric field.

Abstract

In this paper a systematic study of the effect of a crystalline electric field (CEF) in heavy-fermion systems has been undertaken, in particular, the spin-flip scattering of electrons by the Kondo term and by a pair of RKKY-type adjacent magnetic impurities in the presence of a CEF. A competition between elastic and inelastic scattering of an electron determines the anomalous temperature dependence of the resistivity. In the absence of CEF splitting (\ensuremath{\delta}\ensuremath{\rightarrow}0), the Kondo resistivity ${\ensuremath{\rho}}_{K}$ approaches the usual single-impurity behavior and ${\ensuremath{\rho}}_{\mathrm{RKKY}}$ yields a dependence reciprocal in temperature. For finite CEF's \ensuremath{\delta} the resistivities ${\ensuremath{\rho}}_{K}$ and ${\ensuremath{\rho}}_{\mathrm{RKKY}}$ reveal an interesting temperature dependence. In Kondo resistivity, as we increase CEF (\ensuremath{\delta}), it is suppressed. However, the Kondo resistivity-versus-temperature behavior reverses the sign of the curvature at low temperatures for \ensuremath{\delta} between 50 and 100 K. It is more interesting to see that minima or maxima in resistivity are a clear-cut manifestation of the presence of CEF depending upon whether the RKKY coupling between two impurities is positive or negative. The formalism presented here is valid for cerium-based heavy-fermion systems.