Band gap hierarchy of single crystal CoFe$_2$O$_4$ thin films from optical absorption spectroscopy

Thin film materials have a wide variety of applications and also serve as an useful bridge between bulk single crystals and the nanoscale. In this work, we report temperature-dependent optical absorption spectroscopy of single crystal CoFe$_2$O$_4$ thin-films along with complimentary electronic structure analysis. This magnetic insulator has one of the highest Curie temperature among complex oxides and potentially useful in areas such as spintronics. Similar to its Nickel analogue,\footnote{Q.C. Sun, H. Sims, D.Mazumdar, J.X.Ma, B. Holinswoth, K.O'Neal, G.Kim, W.H.Butler, A.Gupta, and J.Musfeldt (accepted to Phys. Rev. B).} our work reveals CoFe$_2$O$_4$ to be an indirect band gap material (1.2 eV) with a direct gap much higher (2.8eV) at 300K. These gap values are robust down to 4.2K. Electronically, both chemical tuning and inversion fraction are found to be important factors in lowering of the band gap compared to NiFe$_2$O$_4$.