The family of hole-doped Pr-based perovskite cobaltites, Pr$_{0.5}$Ca$_{0.5}$CoO$_{3}$ and (Pr$_{1-y}$RE$_{y}$)$_{0.3}$Ca$_{0.7}$CoO$_{3}$ (where RE is rare earth) has recently been found to exhibit simultaneous metal-insulator, spin-state, and valence transitions. We have investigated magnetic-field-induced phase transitions of (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ by means of magnetization measurements at 4.2$-$100 K up to an ultrahigh magnetic field of 140 T with the chemical pressure varied by $y$ = 0.0625, 0.075, 0.1. The observed magnetic-field-induced transitions were found to occur simultaneously with the metal-insulator transitions up to 100 T. The obtained magnetic field-temperature ($B$-$T$) phase diagram and magnetization curves are well analyzed by a spin-crossover model of a single ion with interion interactions. On the other hand, the chemical pressure dependence of the experimentally obtained magnetization change during the phase transition disagrees with the single ion model when approaching low temperatures. The significant $y$ dependence of the magnetization change at low temperatures may arise from the itinerant magnetism of Co$^{3+}$ in the paramagnetic metallic phase, where the chemical pressure enhances the exchange splitting by promoting the double-exchange interaction. The observed $B$-$T$ phase diagrams of (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ are quite contrary to that of LaCoO$_{3}$, indicating that in (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ the high-field phase possesses higher entropy than the low-field phase, whereas it is the other way around in LaCoO$_{3}$.
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