Magneto-optical investigation of the field-induced spin-glass insulator to ferromagnetic metallic transition of the bilayer manganite (La$_{0.4}$Pr$_{0.6}$)$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$

We measured the magneto-optical response of (La$_{0.4}$Pr$_{0.6}$)$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$ in order to investigate the microscopic aspects of the magnetic field driven spin-glass insulator to ferromagnetic metal transition. Application of a magnetic field recovers the ferromagnetic state with an overall redshift of the electronic structure, growth of the bound carrier localization associated with ferromagnetic domains, development of a pseudogap, and softening of the Mn-O stretching and bending modes that indicate a structural change. We discuss field- and temperature-induced trends within the framework of the Tomioka-Tokura global electronic phase diagram picture and suggest that controlled disorder near a phase boundary can be used to tune the magnetodielectric response. Remnants of the spin-glass insulator to ferromagnetic metallic transition can also drive 300 K color changes in (La$_{0.4}$Pr$_{0.6}$)$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$.