Degenerate Anderson-impurity model with finite on-site Coulomb interaction: An analytical approach.

Abstract

We discuss here thermodynamic properties and bremsstrahlung-isochromat-spectroscopy (BIS) spectra that originate with degenerate Anderson impurities embedded in a metal. The finite on-site Coulomb interaction U on impurity sites is accounted for within the slave-boson formalism and the diagrammatic noncrossing approximation. With both the incorporation of an approximate scheme in which only spin fluctuations are considered and an analytical treatment of the vertex correction, simple spectral functions for the empty, single- and double-occupied f-electron states are developed; also, the f occupancies, specific heat ${\mathit{C}}_{\mathit{V}}$ and magnetic susceptibility \ensuremath{\chi} are calculated as functions of the temperature for typical ${\mathrm{Ce}}^{3+}$ and ${\mathrm{Yb}}^{3+}$ parameters. The BIS spectral functions are also calculated. The computations are greatly reduced by our analytical approach. We show that ${\mathit{C}}_{\mathit{V}}$(T) and \ensuremath{\chi}(T)/\ensuremath{\chi}(T=0) as functions of the reduced temperature T/${\mathit{T}}_{0}$(U) are almost independent of U [${\mathit{T}}_{0}$(U) being the Kondo temperature]. The theory developed here has good quantitative accuracy for T\ensuremath{\lesssim}${\mathit{T}}_{0}$(U) and it is convenient for analysis of experimental data. We also propose here an accurate analytical expression for the Kondo temperature ${\mathit{T}}_{\mathit{c}}$(U). At zero temperature our theory fully reproduces the Gunnarsson-Sch\onhammer variational results.