We present an application of the Lorentz model in which fits to vibrational spectra or a Kramers Kronig analysis are employed along with several useful formalisms to quantify microscopic charge in unoriented (powdered) materials. The conditions under
which these techniques can be employed are discussed, and we analyze the vibrational response of a layered transition metal dichalcogenide and its nanoscale analog to illustrate the utility of this approach.
We investigated the series of temperature and field-driven transitions in LuFe$_2$O$_4$ by optical and M{o}ssbauer spectroscopies, magnetization, and x-ray scattering in order to understand the interplay between charge, structure, and magnetism in th
is multiferroic material. We demonstrate that charge fluctuation has an onset well below the charge ordering transition, supporting the order by fluctuation mechanism for the development of charge order superstructure. Bragg splitting and large magneto optical contrast suggest a low temperature monoclinic distortion that can be driven by both temperature and magnetic field.