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No single material yet combines both at room temperature.","posed_since":"","precise":"Identify a single-phase compound with ferroelectric polarization above about $3 \\times 10^{3}\\ \\mathrm{statC}/\\mathrm{cm}^{2}$ and net magnetization above $10\\ \\mathrm{emu}/\\mathrm{cm}^{3}$ at $T = 300\\ \\mathrm{K}$, in which an electric field deterministically reverses (or rotates by $90\\ \\text{degrees}$) the magnetization. An answer is a material with measured $P$, $M$ and demonstrated electric-field reversal of $M$ at $300\\ \\mathrm{K}$ without a ferromagnetic overlayer.","problem_ref":"0e680aca51fd9a8975b25f9fede761b6f8f047a2098feb8a511013e11c28bedb","references":"","settled_by":"Synthesis and measurement of a single-phase compound showing 300 K polarization and magnetization hysteresis plus electric-field-driven magnetization reversal imaged by XMCD-PEEM or magnetic force microscopy.","status_note":"Deterministic switching at $300\\,\\mathrm{K}$ so far uses $\\mathrm{BiFeO_3}$ coupled to a ferromagnetic layer (Heron et al., Nature 2014).","title":"A single-phase room-temperature multiferroic with strong magnetoelectric 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