  We report the results of direct measurement of remanent hysteresis loops on
nanochains of BiFeO$_3$ at room temperature under zero and $\sim$20 kOe
magnetic field. We noticed a suppression of remanent polarization by nearly
$\sim$40\% under the magnetic field. The powder neutron diffraction data reveal
significant ion displacements under a magnetic field which seems to be the
origin of the suppression of polarization. The isolated nanoparticles,
comprising the chains, exhibit evolution of ferroelectric domains under dc
electric field and complete 180$^o$ switching in switching-spectroscopy
piezoresponse force microscopy. They also exhibit stronger ferromagnetism with
nearly an order of magnitude higher saturation magnetization than that of the
bulk sample. These results show that the nanoscale BiFeO$_3$ exhibits
coexistence of ferroelectric and ferromagnetic order and a strong
magnetoelectric multiferroic coupling at room temperature comparable to what
some of the type-II multiferroics show at a very low temperature.
