Optical properties of BiFeO$_3$ thin films and single crystal*

BiFeO$_3$ has been studied using optical and magneto-optical spectroscopy and the results are compared with first-principle calculations. The optical gap in thin films (2.7 eV) is much larger than that in the single crystal (1.3 eV), the evidence that this system has a novel transition between strongly correlated and band insulator behavior. Both magnetic field and temperature suppress the excitation between the strongly hybridized valence levels and Fe d levels near 1.5 eV. The temperature and magnetic field effects appear to scale energetically suggesting spin-charge coupling. The high energy magneto-dielectric contrast shows a jump at 18 T corresponding to the transition from toroidal to homogeneous antiferromagnetic phase.