Neutron diffraction study of UO2: Antiferromagnetic state

The elastic neutron magnetic scattering cross section from the ${\mathrm{U}}^{4+}$ ions in antiferromagnetic U${\mathrm{O}}_2$ has been measured at 4.2 K. The measurements included all reciprocal-lattice points for which $\frac{\left(sin\theta \right)}{\lambda }=\frac{\kappa }{4\pi }\le 0.83$ ${\mathrm{\AA }}^{-1\mathrm{}}$. The values of $\mu f\left(\overrightarrow{\kappa }\right)$, obtained from the measurements, fall on a smooth curve at small $\kappa$, but show considerable anisotropy for $\frac{\left(sin\theta \right)}{\lambda }>0.5\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. The ordered magnetic moment is $(1.74\mathrm{}\pm 0.02){\mu }_B$ per uranium atom at 4.2 K. Theoretical calculations of the magnetic cross section from a number of possible states (including the effects of intermediate coupling and $J$ mixing) are unable to reproduce the experimental data at large $\kappa$. Subtracting the calculated magnetic cross section from the observed scattering cross section, we have determined that additional scattering is present only for reflections with $h$, $k$ even and $l$ odd. The additional intensity is a result of a small (0.014 Å) shift of the oxygen atoms from their equilibrium position. These shifts are examined within the framework of Allen's microscopic theory for U${\mathrm{O}}_2$. An analysis in terms of the homogeneous deformations proposed by Allen cannot explain the neutron results. However, when Allen's concepts are extended to include inhomogeneous deformations, corresponding to a zone-boundary $q=\left(\frac{2\pi }{a}\right) \mathrm{}(1,0,0)\mathrm{}$ phonon, excellent agreement is obtained between theory and experiment. The oxygen displacement is 0.014 Å from the fluorite lattice positions and, in addition, the inhomogeneous deformation $T_{2g}-T_{1g}$ does not require a corresponding change in the unit-cell dimensions. The dominance of this deformation mode in the spin-lattice interactions suggests the presence of a noncollinear magnetic structure in U${\mathrm{O}}_2$.