Competing Kondo Effects in Non-Kramers Doublet Systems

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.

9 pages, 18 figures, 1 table

References in corpus (6)

• The numerical renormalization group method for quantum impurity systems
• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Non-Fermi Liquid and Fermi Liquid in Two-Channel Anderson Lattice Model: Theory for Pr$A_2$Al${}_{20}$ ($A$=V, Ti) and PrIr${}_2$Zn${}_{20}$
• Resolution of Entropy $\ln \sqrt{2}$ by Ordering in Two-Channel Kondo Lattice
• Mean-field description of odd-frequency superconductivity with staggered ordering vector
• Competition between Quadrupole and Magnetic Kondo Effects in Non-Kramers Doublet Systems

Cited by in corpus (8)

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• Channel-selective non-Fermi liquid behavior in the two-channel Kondo lattice model under a magnetic field
• Evolution of non-Kramers Doublets in Magnetic Field PrNi${}_2$Cd${}_{20}$ and PrPd${}_2$Cd${}_{20}$
• New quantum number for the many-electron Dirac-Coulomb Hamiltonian
• Optical and magnetic excitations in the underscreened quasi-quartet Kondo lattice
• L-point quadrupole order under magnetic field in cubic PrIr${}_2$Zn${}_{20}$