Theory of the magnetic ordering and lattice internal rearrangement transition in UO2

The first-order antiferromagnetic transition in fluorite structure U${\mathrm{O}}_2$ coincides with a lattice transition to a transverse internal rearrangement (TIR). In the TIR, the oxygen planes have a periodic internal shear relative to the undistorted fcc uranium sublattice. We have investigated the selection mechanism that causes the TIR to occur in preference to other distortions. The driving mechanism that causes some distortion to occur is the splitting of the ${\Gamma }_5$ cubic crystal-field ground state and consequent lowering of crystal-field energy. Our detailed calculations, involving consideration of a number of "candidate" distortional modes, verify that the TIR occurs because the lattice is relatively soft for such a distortion. This elastic energy advantage more than makes up for the advantage of a competing conventional (homogeneous) internal distortion in lowering the crystal-field energy more for a given size relative distortion. Our calculations incorporate experimental elastic effects by using parameters from a rigid-ion model fit to the phonon behavior. We find a low-temperature oxygen displacement of approximately 0.021 Å in close agreement with the experimental 0.014 Å.