Orbital Kondo Effect in Ce$_x$La$_{1-x}$B$_6$: Scaling Analysis

TL;DR

This paper analyzes the orbital Kondo effect in Ce$_x$La$_{1-x}$B$_6$ using third-order scaling equations, revealing anisotropic interactions, limitations of single Kondo temperature scaling, and proposing a novel phase with unique magnetic properties.

Contribution

It introduces a third-order scaling analysis for the orbital Kondo effect in Ce$_x$La$_{1-x}$B$_6$, highlighting anisotropic interactions and a potential new phase with spin ordering without orbital order.

Findings

Scaling equations show anisotropic exchange interactions.

Single Kondo temperature scaling does not apply to resistivity and susceptibility.

A possible phase with spin order but no orbital order is proposed.

Abstract

Peculiarity of the Kondo effect in Ce$_x$La$_{1-x}$B$_6$ is investigated on the basis of the scaling equations up to third order. For the case where the $f^1$-$f^2$ charge fluctuation enters in addition to the $f^1$-$f^0$ one, the effective exchange interaction becomes anisotropic with respect to the orbital pseudospins which represent the two different orbitals in the $\Gamma_8$ ground state. Because of different characteristic energies for electric and magnetic tensors, scaling with the single Kondo temperature does not apply to physical quantities such as the resistivity and magnetic susceptibility. Possibility of a bizzare phase is pointed out where the RKKY interaction leads to the spin ordering without orbital ordering. This phase serves as a candidate of the phase IV which is observed to be isotropic magnetically.