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

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 the model (Pr$_{1-y}$Y$_y$)$_{1-x}$Ca$_x$CoO$_{3-\delta}$ system, stabilizing a nonmagnetic insulating phase under compression (with a room-temperature valence/spin-state/metal-insulator transition) and a ferromagnetic metallic phase under tension, thus exposing a potential spin-state quantum critical point. The latter has been proposed in cobaltites and can be probed in this system as a function of a disorder-free variable (strain). We study this here via thickness-dependent strain relaxation in compressive SrLaAlO$_4$(001)/(Pr$_{0.85}$Y$_{0.15}$)$_{0.70}$Ca$_{0.30}$CoO$_{3-\delta}$ epitaxial thin films to quasi-continuously probe structural, electronic, and magnetic behaviors across the nonmagnetic-insulator/ferromagnetic-metal boundary. High-resolution X-ray diffraction, electronic transport, magnetometry, polarized neutron reflectometry, and temperature-dependent magnetic force microscopy provide a detailed picture, including abundant evidence of temperature- and strain-dependent phase coexistence. This indicates a first-order phase transition as opposed to spin-state quantum-critical behavior, which we discuss theoretically via a phenomenological Landau model for coupled spin-state and magnetic phase transitions.