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Pr-containing perovskite cobaltites exhibit unusual valence transitions,coupled to coincident structural, spin-state, and metal-insulator transitions.Heteroepitaxial strain was recently used to control these phenomena in themodel (Pr$_{1-y}$Y$_y$)$_{1-x}$Ca$_x$CoO$_{3-\delta}$ system, stabilizing anonmagnetic insulating phase under compression (with a room-temperaturevalence/spin-state/metal-insulator transition) and a ferromagnetic metallicphase under tension, thus exposing a potential spin-state quantum criticalpoint. The latter has been proposed in cobaltites and can be probed in thissystem as a function of a disorder-free variable (strain). We study this herevia thickness-dependent strain relaxation in compressiveSrLaAlO$_4$(001)/(Pr$_{0.85}$Y$_{0.15}$)$_{0.70}$Ca$_{0.30}$CoO$_{3-\delta}$epitaxial thin films to quasi-continuously probe structural, electronic, andmagnetic behaviors across the nonmagnetic-insulator/ferromagnetic-metalboundary. High-resolution X-ray diffraction, electronic transport,magnetometry, polarized neutron reflectometry, and temperature-dependentmagnetic force microscopy provide a detailed picture, including abundantevidence of temperature- and strain-dependent phase coexistence. This indicatesa first-order phase transition as opposed to spin-state quantum-criticalbehavior, which we discuss theoretically via a phenomenological Landau modelfor coupled spin-state and magnetic phase transitions.

First-order phase transition vs. spin-state quantum-critical scenarios in strain-tuned epitaxial cobaltite thin films