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The crystal structure of Lanthanum Cerium Oxide (La$_2$Ce$_2$O$_7$) is investigated using textit{ab initio} density functional theory (DFT) calculations. The relative stability of fluorite- and pyrochlore-like structures is studied through comparison of their formation energies. These formation energies show the pyrochlore structure to be favored over the fluorite structure, apparently contradicting the conclusions based on experimental neutron and X-ray diffraction (XRD). By calculating and comparing XRD spectra for a set of differently ordered and random structures, we show that the pyrochlore structure is consistent with diffraction experiments. For these reasons, we suggest the pyrochlore structure as the ground state crystal structure for La$_2$Ce$_2$O$_7$. %we show that among the structures considered in this work, the pyrochlore geometry is clearly favorable over the disordered fluorite geometry.
The oxide pyrochlore Bi$_2$Ti$_2$O$_7$ is in some ways analogous to perovskite PbTiO$_3$, in that Bi$_2$Ti$_2$O$_7$ has two cations, Bi$^{3+}$ and Ti$^{4+}$ in oxidation states that are normally associated with a propensity to off-center. However, un
Both amorphous and crystalline materials frequently exhibit low temperature specific heats in excess of what is predicted using the Debye model. The signature of this excess specific heat is a peak observed in $C/T^3$ textit{versus} $T$. To understan
The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives r
Terbium titanate (Tb$_2$Ti$_2$O$_7$) is a spin-ice material with remarkable magneto-optical properties. It has a high Verdet constant and is a promising substrate crystal for the epitaxy of quantum materials with the pyrochlore structure. Large singl
The search for quantum spin liquids (QSL) -- topological magnets with fractionalized excitations -- has been a central theme in condensed matter and materials physics. While theories are no longer in short supply, tracking down materials has turned o