Thermoelectric power of cerium and ytterbium intermetallics

Abstract

The temperature dependence of the thermoelectric power (TEP) of metallic systems with cerium and ytterbium ions exhibits characteristic features which we explain by the Coqblin-Schrieffer model (CSM). We specify a given system by the degeneracy and splitting of the crystal-field (CF) levels, the strength of the exchange and potential scattering, and the number of f electrons or f holes; for cerium and ytterbium ions we assume ${n}_{f}l~1$ and ${n}_{f}^{\mathrm{hole}}l~1,$ respectively. The Kondo temperature ${T}_{K}$ is then generated by the ``poor man's scaling''; it separates a local-moment (LM) from a Fermi-liquid (FL) regime. In the LM regime $(Tg~{T}_{K})$ we calculate the TEP by a renormalized perturbation expansion, in which the exchange coupling J is also renormalized by the poor man's scaling. This gives the TEP with a large peak at high temperatures and a sign change at ${T}_{x}\ensuremath{\simeq}\ensuremath{\alpha}{T}_{K},$ where for parameters used in this paper we have $\ensuremath{\alpha}$ between roughly 2.5 and 10. For ${n}_{f}\ensuremath{\simeq}1$ and large CF splitting, we find a broad temperature range ${T}_{K}\ensuremath{\ll}Tl~{T}_{x},$ in which the TEP of the CSM is negative. In the FL regime $(Tl~{T}_{K})$ we neglect the excited CF states, reduce the CSM to an effective spin-degenerate exchange model, map it on an effective spin-degenerate Anderson model, and calculate the TEP by an expansion in terms of $U\ensuremath{\propto}1/J.$ For cerium ions ${(n}_{f}l~1)$ we obtain in this way the TEP which follows for $T\ensuremath{\ll}{T}_{K}$ a linear FL law, attains at about ${T}_{K}/2$ a positive maximum, and changes sign above ${T}_{K}.$ The results pertaining to ytterbium ions ${(n}_{f}^{\mathrm{hole}}l~1)$ are obtained by reflecting the ${n}_{f}l~1$ curves on the temperature axis. The overall results obtained for the CSM in such a way explain the essential features of the temperature, pressure, and doping dependence of the TEP in cerium and ytterbium systems. Unfortunately, neither our high-temperature nor the low-temperature expansion provide the details or locate the minimum of the negative TEP which we find in the transition region between the FL and LM regimes.