Kondo temperature and crystal field levels of Ce systems within a finite U Non-Crossing Approximation

TL;DR

This paper develops a simplified finite U Non-Crossing Approximation method to accurately compute the Kondo temperature and crystal-field levels in Ce systems, aligning well with experimental data.

Contribution

It introduces an approximation to the vertex function and combines it with ab initio data to improve predictions of Kondo temperatures and crystal field splittings in Ce compounds.

Findings

Accurate calculation of $T_K$ and crystal-field levels for CeIn$_3$ and CeSn$_3$

The vertex function approximation improves $T_K$ predictions

Ground state symmetries match experimental observations

Abstract

We calculate the Kondo temperature ($T_K$) and crystal-field levels of strongly correlated multiorbital systems solving the Anderson Impurity Model with the finite U Non-Crossing Approximation (UNCA) in its simplest scheme, that is, considering the self energies at lowest order in the 1/N diagrammatic expansion. We introduced an approximation to the vertex function that includes the double energy dependence and investigate its effect on the values of $T_K$ for simple electronic models. We also analyze the competition between the two spin flip mechanisms, involving virtual transitions to empty and doubly occupied states, in the determination of the ground state symmetry by including an extra diagram of higher order in $1/N.$ We finally combine the resulting simple formalism with {\it ab initio} calculated electronic structures to obtain $T_K$'s, ground states, and crystal field splittings in excellent agreement with experimental results for two particular Ce compounds, namely CeIn$_3$ and CeSn$_3$.