  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.
