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.