Optical Properties and Magnetic Field-Induced Phase Transitions in the   Ferroelectric State of Ni$_3$V$_2$O$_8$
  We use a combination of optical spectra, first principles calculations, and energy dependent magneto-optical measurements to elucidate the electronic structure and to study the phase diagram of Ni$_3$V$_2$O$_8$. We find a remarkable interplay of magnetic field and optical properties that reveals additional high magnetic field phases and an unexpected electronic structure which we associate with the strong magneto-dielectric couplings in this material over a wide energy range. Specifically, we observed several prominent magneto-dielectric effects that derive from changes in crystal field environment around Ni spine and cross-tie centers. This effect is consistent with a field-induced modification of local structure. Symmetry-breaking effects are also evident with temperature. We find Ni$_3$V$_2$O$_8$ to be an intermediate gap, local moment band insulator. This electronic structure is particularly favorable for magneto-dielectric couplings, because the material is not subject to the spin charge separation characteristic of strongly correlated large gap Mott insulators, while at the same time remaining a magnetic insulator independent of the particular spin order and temperature. 
R. C. Rai, J. Cao, S. Brown, J. L. Musfeldt, D. Kasinathan, D. J.   Singh, G. Lawes, N. Rogado, R. J. Cava, and X. Wei