In four classes of materials, the layered copper-oxides, organics, iron-pnictides and heavy-fermion compounds, an unconventional superconducting state emerges as a magnetic transition is tuned toward absolute zero temperature, that is, toward a magnetic quantum-critical point (QCP). In most materials, the QCP is accessed by chemical substitutions or applied pressure. CeCoIn5 is one of the few materials that are born as a quantum-critical superconductor and, therefore, offers the opportunity to explore the consequences of chemical disorder. Cadmium-doped crystals of CeCoIn5 are a particularly interesting case where Cd substitution induces long-range magnetic order, as in Zn-doped copper-oxides. Applied pressure globally supresses the Cd-induced magnetic order and restores bulk superconductivity. Here we show, however, that local magnetic correlations, whose spatial extent decreases with applied pressure, persist at the extrapolated QCP. The residual droplets of impurity-induced magnetic moments prevent the reappearance of conventional signatures of quantum criticality, but induce a heterogeneous electronic state. These discoveries show that spin droplets can be a source of electronic heterogeneity in classes of strongly correlated electron systems and emphasize the need for caution when interpreting the effects of tuning a correlated system by chemical substitution.
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