Competing Kondo Effects in Non-Kramers Doublet Systems

TL;DR

This paper investigates the competition between magnetic and quadrupolar Kondo effects in non-Kramers doublet systems, revealing a first-order transition between non-Fermi-liquid and Fermi-liquid states and novel intermediate behaviors.

Contribution

It introduces an extended two-channel Kondo model including magnetic coupling, analyzing the competition and phase transitions using NRG, and predicts new intermediate states in Pr-based compounds.

Findings

Existence of a first-order transition between NFL and FL ground states.

Discovery of an intermediate FL state with free magnetic spins.

Singular behavior in single-particle spectra indicating complex quantum states.

Abstract

In non-Kramers Kondo systems with a quadrupolar degrees of freedom, an ordinary magnetic Kondo effect can compete with the quadrupolar Kondo effect. We discuss such competition keeping Pr$T_{2}$Zn$_{20}$ ($T$=Ir, Rh) and Pr$T_{2}$Al$_{20}$ ($T$=V, Ti) in mind, where the $\Gamma_{3}$ non-Kramers crystalline-electric-field (CEF) doublet ground state is realized in Pr$^{3+}$ ion with $(4f)^{2}$ configuration under cubic symmetry. The quadrupolar Kondo effect can be described by the two-channel Kondo model, which leads to the local non-Fermi-liquid (NFL) ground state, while the magnetic Kondo effect favors the ordinary local Fermi-liquid (FL) ground state. Based on the minimal extended two-channel Kondo model including the magnetic Kondo coupling as well, we investigate the competition and resulting thermodynamics, and orbital/magnetic, and single-particle excitation spectra by the Wilson's numerical renormalization-group (NRG) method. There exists the first-order transition between the NFL and FL ground states. In addition to these two states, the alternative FL state accompanied by a free magnetic spin appears in intermediate temperature range, which eventually reaches the true NFL ground state, as a consequence of stronger competition between the magnetic and quadrupolar Kondo effects. In this peculiar state, the magnetic susceptibility shows a Curie-like behavior, while the orbital fluctuation exhibits the FL behavior. Moreover, the single-particle spectra yield a more singular behavior. Implications to the Pr 1-2-20 systems are briefly discussed.