Title: Magnetically induced Ferroelectricity in Bi$_2$CuO$_4$,
Abstract: The tetragonal copper oxide Bi$_2$CuO$_4$ has an unusual crystal structure
with a three-dimensional network of well separated CuO$_4$ plaquettes. This
material was recently predicted to host electronic excitations with an
unconventional spectrum and the spin structure of its magnetically ordered
state appearing at T$_N$ $\sim$43 K remains controversial. Here we present the
results of detailed studies of specific heat, magnetic and dielectric
properties of Bi$_2$CuO$_4$ single crystals grown by the floating zone
technique, combined with the polarized neutron scattering and high-resolution
X-ray measurements. Our polarized neutron scattering data show Cu spins are
parallel to the $ab$ plane. Below the onset of the long range antiferromagnetic
ordering we observe an electric polarization induced by an applied magnetic
field, which indicates inversion symmetry breaking by the ordered state of Cu
spins. For the magnetic field applied perpendicular to the tetragonal axis, the
spin-induced ferroelectricity is explained in terms of the linear
magnetoelectric effect that occurs in a metastable magnetic state. A relatively
small electric polarization induced by the field parallel to the tetragonal
axis may indicate a more complex magnetic ordering in Bi$_2$CuO$_4$.