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An orbital-selective spin liquid in a frustrated heavy fermion spinel LiV$_2$O$_4$

The pronounced enhancement of the effective mass is the primary phenomenon associated with strongly correlated electrons. In the presence of local moments, the large effective mass is thought to arise from Kondo coupling, the interaction between itinerant and localised electrons. However, in d electron systems, the origin is not clear because of the competing Hund's rule coupling. Here we experimentally address the microscopic origin for the heaviest d fermion in a vanadium spinel LiV2O4 having geometrical frustration. Utilising orbital-selective 51V NMR, we elucidate the orbital-dependent local moment that exhibits no long-range magnetic order despite persistent antiferromagnetic correlations. A frustrated spin liquid, Hund-coupled to itinerant electrons, has a crucial role in forming heavy fermions with large residual entropy. Our method is important for the microscopic observation of the orbital-selective localisation in a wide range of materials including iron pnictides, cobaltates, manganites, and ruthnates.