Observation of a multiferroic critical end point

The study of abrupt increases in magnetization with magnetic field known as metamagnetic transitions has opened a rich vein of new physics in itinerant electron systems, including the discovery of quantum critical end points with a marked propensity to develop new kinds of order. However, the electric analogue of the metamagnetic critical end point, a metaelectric critical end point has not yet been realized. Multiferroic materials wherein magnetism and ferroelectricity are cross-coupled are ideal candidates for the exploration of this novel possibility using magnetic-field (emph{H}) as a tuning parameter. Herein, we report the discovery of a magnetic-field-induced metaelectric transition in multiferroic BiMn$_{2}$O$_{5}$ in which the electric polarization (emph{P}) switches polarity along with a concomitant Mn spin-flop transition at a critical magnetic field emph{H}$_{rm c}$. The simultaneous metaelectric and spin-flop transitions become sharper upon cooling, but remain a continuous crossover even down to 0.5 K. Near the emph{P}=0 line realized at $mu_{0}$emph{H}$_{rm c}$$approx$18 T below 20 K, the dielectric constant ($varepsilon$) increases significantly over wide field- and temperature (emph{T})-ranges. Furthermore, a characteristic power-law behavior is found in the emph{P}(emph{H}) and $varepsilon$(emph{H}) curves at emph{T}=0.66 K. These findings indicate that a magnetic-field-induced metaelectric critical end point is realized in BiMn$_2$O$_5$ near zero temperature.