Competition between Quadrupole and Magnetic Kondo Effects in Non-Kramers Doublet Systems

TL;DR

This paper investigates the competition between magnetic and quadrupole Kondo effects in non-Kramers doublet systems, revealing how this interplay influences ground states, entropy behavior, and implications for specific Pr-based compounds.

Contribution

It introduces an extended two-channel Kondo model to analyze the competition, highlighting the role of orbital fluctuations near the NFL-FL boundary and implications for experimental systems.

Findings

Demonstrates change in f-electron entropy near the NFL-FL boundary.

Shows the model explains coexistence of quadrupole order and superconductivity.

Predicts a FL state with a free magnetic spin due to strong competition.

Abstract

We discuss possible competition between magnetic and quadrupole Kondo effects in non-Kramers doublet systems under cubic symmetry. The quadrupole Kondo effect leads to non-Fermi-liquid (NFL) ground state, while the magnetic one favors ordinary Fermi liquid (FL). In terms of the $j$-$j$ coupling scheme, we emphasize that the orbital fluctuation must develop in the vicinity of the NFL-FL boundary. We demonstrate a change of behavior in the f-electron entropy by the Wilson's numerical renormalization-group (NRG) method on the basis of the extended two-channel Kondo exchange model. We present implications to extensively investigated PrT$_{2}$X$_{20}$ (T=Ti, V, Ir; X=Al, Zn) systems that exhibit both quadrupole ordering and peculiar superconductivity. We also discuss the magnetic-field effect which lifts weakly the non-Kramers degeneracy. Our model also represents the FL state accompanied by a free magnetic spin as a consequence of stronger competition between the magnetic and the quadrupole Kondo effects.