Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning the material to a quantum critical point using a control parameter such as the magnetic field, pressure, or chemical composition. Our high precision magnetization measurements of the ultrapure f-electron based superconductor {beta}-YbAlB4 demonstrate a scaling of its free energy indicative of zero-field quantum criticality without tuning in a metal. The breakdown of Fermi-liquid behavior takes place in a mixed-valence state, in sharp contrast with other known examples of quantum critical f-electron systems that are magnetic Kondo lattice systems with integral valence.
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