Competition between quadrupole and magnetic Kondo effects in non-Kramers doublet systems

Abstract

We discuss possible competition between magnetic and quadrupole Kondo effects in non-Kramers doublet systems in cubic symmetry. The quadrupole Kondo effect leads to non-Fermi-liquid (NFL) ground state, while the magnetic one favors ordinary Fermi-liquid (FL) ground state. In terms of the j-j coupling scheme, we argue that the orbital fluctuation must develop in the vicinity of the NFL-FL boundary. A change of temperature dependence of the f-electron entropy in both the FL and NFL regimes is demonstrated by the Wilson's numerical renormalization-group (NRG) method on the basis of the extended two-channel Kondo exchange model. We present implications to PrT2X20 (T=Ti, V, Ir; X=Al, Zn) systems which exhibit both quadrupole ordering and peculiar superconductivity. We discuss how the magnetic field lifts the non-Kramers degeneracy. Our model also represents the alternative FL state accompanied by a free magnetic spin, as a consequence of stronger competition between the magnetic and the quadrupole Kondo effects.