  We carry out first-principles density-functional-theory calculations to
elucidate the polarization switching mechanism in charge-ordering-induced
ferroelectrics based on the prototypical case of the
(SrVO$_3$)$_1$(LaVO$_3$)$_1$ superlattice. We find that lattice relaxation for
a specific charge ordering state can "lock" that state in, making non-adiabatic
switching to a different CO variant energetically prohibitive, and in some
cases, even making the energy barrier for adiabatic switching prohibitively
large. We classify charge-ordering materials into two types, polyhedral
breathing and off-centering displacement, based on the type of lattice mode
most strongly coupled to the charge ordering. We demonstrate that the
non-adiabatic electron hopping induced by an external electric field is
expected only in off-centering-displacement-type charge-ordering-induced
ferroelectrics. This successfully explains the different observed switching
behaviors of LuFe$_2$O$_4$ and Fe$_3$O$_4$. These results offer a new
understanding of the polarization switching mechanism in
charge-ordering-induced ferroelectrics that provides guidance for the design
and discovery of charge-ordering-induced ferroelectric materials and suggests a
strategy for realizing "electronic ferroelectricity" with polarization
switching on electronic rather than lattice time scales.
