  Optimal materials to induce bulk photovoltaic effects should lack inversion
symmetry and have an optical gap matching the energies of visible radiation.
Ferroelectric perovskite oxides such as BaTiO$_3$ and PbTiO$_3$ exhibit
substantial polarization and stability, but have the disadvantage of
excessively large band gaps. We use both density functional theory and
dynamical mean field theory calculations to design a new class of Mott
multiferroics--double perovskite oxides $A_2$VFeO$_6$ ($A$=Ba, Pb, etc). While
neither perovskite $A$VO$_3$ nor $A$FeO$_3$ is ferroelectric, in the double
perovskite $A_2$VFeO$_6$ a `complete' charge transfer from V to Fe leads to a
non-bulk-like charge configuration--an empty V-$d$ shell and a half-filled
Fe-$d$ shell, giving rise to a polarization comparable to that of ferroelectric
$A$TiO$_3$. Different from nonmagnetic $A$TiO$_3$, the new double perovskite
oxides have an antiferromagnetic ground state and around room temperatures, are
paramagnetic Mott insulators. Most importantly, the V $d^0$ state significantly
reduces the band gap of $A_2$VFeO$_6$, making it smaller than that of
$A$TiO$_3$ and BiFeO$_3$ and rendering the new multiferroics a promising
candidate to induce bulk photovoltaic effects.
