Emerging quantum critical phase in a cluster spin-glass

The study of strong electron correlations has significantly advanced the frontiers of condensed matter physics, especially in relation to correlation-driven quantum phase transitions (QPTs). In the vicinity of QPTs, quantum critical fluctuations of multiple degrees of freedom enable the emergence of exotic many-body states and quantum critical behaviours beyond the Landau paradigm. Recently, magnetic frustration, traditionally associated with insulating magnets, has been recognized as pivotal to investigating new phases of matter in correlation-driven Kondo breakdown QPTs that are not clearly associated with broken symmetry. The nature of these new phases, however, remains underexplored. Here, we report quantum criticalities emerging from a cluster spin-glass in the heavy-fermion metal TiFe_xCu_{2x - 1}Sb, where frustration originates from intrinsic disorder. Specific heat and magnetic Grüneisen parameter measurements under varying magnetic fields exhibit quantum critical scaling, indicating a quantum critical point (QCP) near 0.13 Tesla. As the magnetic field increases, the cluster spin-glass phase is progressively suppressed. Upon crossing the QCP, resistivity and Hall effect measurements reveal enhanced screening of local moments and an expanding Fermi surface, consistent with the Kondo breakdown scenario. Our findings uncover a new family of iron-based heavy-fermion metals with intricate interplay of multiple degrees of freedom, enabling the exploration of unconventional excitations and exotic quantum critical states and behaviours.