Temperature Dependent Atomic Structure of LuFe$_{\mathrm{2}}$O$_{\mathrm{4}}$

The LuFe$_{\mathrm{2}}$O$_{\mathrm{4}}$ system has been studied intensively as a novel material with charge ordered driven ferroelectricity. However, the existence and origin of electric polarization and it coupling to the magnetic structure are open questions still to be addressed. We have studied the structure on LuFe$_{\mathrm{2}}$O$_{\mathrm{4}}$ on multiple length scales using X-ray diffraction, temperature and orientation dependent Raman spectroscopy, temperature dependent X-ray and neutron pair distribution function measurements and DFT modeling. The stable space groups on different length scales are being determined. This work is supported by DOE Grant DE-FG02-07ER46402.