Doped perovskite cobaltites (e.g., ${\mathrm{La}}_{1-x}{\mathrm{Sr}}_x{\mathrm{CoO}}_3$) have been extensively studied for their spin-state physics, electronic inhomogeneity, and insulator-metal transitions. Ferromagnetically interacting spin-state polarons emerge at low $x$ in the phase diagram of these compounds, eventually yielding long-range ferromagnetism. The onset of long-range ferromagnetism ($x\approx 0.18$) is substantially delayed relative to polaron percolation ($x\approx 0.05$), however, generating a troubling inconsistency. Here, Monte Carlo simulations of a disordered classical spin model are used to establish that previously ignored magnetic frustration is responsible for this effect, enabling faithful reproduction of the magnetic phase diagram.

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• Magnetic interactions
• Magnetic phase transitions
• Magnetism
• Percolation
• Complex oxides
• Monte Carlo methods
• Percolation theory
• Specific heat measurements