Room-temperature coexistence of large electric polarization and magnetic order in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Bi</mml:mi><mml:mi mathvariant="normal">Fe</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>single crystals

From an experimental point of view, room-temperature ferroelectricity in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is raising many questions. Electric measurements made a long time ago on solid solutions of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ with $\mathrm{Pb}(\mathrm{Ti},\mathrm{Zr}){\mathrm{O}}_{3}$ indicate that a spontaneous electric polarization exists in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ below the Curie temperature ${T}_{C}=1143\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Yet in most reported works, the synthesized samples are too conductive at room temperature to get a clear polarization loop in the bulk without any effects of extrinsic physical or chemical parameters. Surprisingly, up to now there has been no report of a $P(E)$ (polarization versus electric field) loop at room temperature on single crystals of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$. We describe here our procedure to synthesize ceramics and to grow good quality sizeable single crystals by a flux method. We demonstrate that $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is indeed ferroelectric at room temperature through evidence by piezoresponse force microscopy and $P(E)$ loops. The polarization is found to be large, around $60\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{C}∕{\mathrm{cm}}^{2}$, a value that has only been reached in thin films. Magnetic measurements using a superconducting quantum interference device magnetometer and M\"ossbauer spectroscopy are also presented. The latter confirms the results of nuclear magnetic resonance measurements concerning the anisotropy of the hyperfine field attributed to the magnetic cycloidal structure.