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Many correlated metallic materials are described by Landau Fermi-liquidtheory at low energies, but for Hund metals the Fermi-liquid coherence scale$T_{\text{FL}}$ is found to be surprisingly small. In this Letter, we study thesimplest impurity model relevant for Hund metals, the three-channelspin-orbital Kondo model, using the numerical renormalization group (NRG)method and compute its global phase diagram. In this framework, $T_{\text{FL}}$becomes arbitrarily small close to two new quantum critical points (QCPs) whichwe identify by tuning the spin or spin-orbital Kondo couplings into theferromagnetic regimes. We find quantum phase transitions to a singularFermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phaseshows frustrated behavior involving alternating overscreenings in spin andorbital sectors, with universal power laws in the spin ($\omega^{-1/5}$),orbital ($\omega^{1/5}$) and spin-orbital ($\omega^1$) dynamicalsusceptibilities. These power laws, and the NRG eigenlevel spectra, can befully understood using conformal field theory arguments, which also clarify thenature of the non-Fermi-liquid phase.

Global phase diagram of a spin-orbital Kondo impurity model and the suppression of Fermi-liquid scale