Kitaev interactions of the spin-orbit coupled magnet UO2

Abstract

Uranium dioxide, UO$_2$, is a canonical example of a magnetic material with strong spin-orbit coupling. Here, we present a study of the magnetic diffuse scattering measured on a polycrystalline sample of UO$_2$, which we interpret in terms of its magnetic interactions between U$^{4+}$ magnetic moments. By refining values of the magnetic interaction parameters to magnetic diffuse-scattering data measured above the magnetic ordering transition temperature, we show that the dominant magnetic coupling in UO$_2$ is a bond-dependent interaction analogous to the Kitaev model of honeycomb magnets. We compare our experimental results with published theoretical predictions and experimental measurements of the magnetic excitation spectrum. Our results suggest that magnetic materials with $f$-electron magnetic ions, particularly actinides, may be promising candidates for realising Kitaev magnetism, and highlight the role that magnetic diffuse-scattering data can play in identifying such materials.

Figures (3)

• Figure 1: (a) Kitaev model on the honeycomb lattice. (b) Kitaev model on the face-centered cubic lattice. In (a) and (b), the Kitaev interaction couples the $z$ components of spins connected by red solid lines, the $x$ components of spins coupled by the green dashed lines, and the $y$ components of spins coupled by the blue dotted lines. (c) Transverse triple-$\mathbf{k}$ magnetic structure of UO$_{2}$, showing U$^{4+}$ ions as grey spheres, O$^{2-}$ ions shown as red spheres, and spin directions as arrows. Different colours of the spins are used to show the four $\langle111\rangle$ directions along which spins are aligned in this non-coplanar magnetic structure.
• Figure 2: Magnetic diffuse scattering data (black circles) and model fits (lines), showing (a) 32.5 K data only, and (b) data measured at 35 K to 250 K, with successive temperatures vertically offset by 0.15 units for clarity. Temperatures are labelled above each curve and a data set measured at 300 K has been subtracted from every data set shown. Green dashed lines show model fits to all data for isotropic interactions up to fourth neighbours, allowing an intensity scale factor to vary separately for each data set. Red dotted lines show model fits to all data for the $J$-$K$-$\Gamma$-$J_{3}$ model (Eq. (\ref{['eq:JK_model']})), allowing an intensity scale factor to vary separately for each data set (Model 1A in Table \ref{['tab:param_values']}). Blue solid lines show model fits to data measured between 32.5 K and 50 K for the $J$-$K$-$\Gamma$-$J_{3}$ model (Eq. (\ref{['eq:JK_model']})), allowing a common intensity scale factor for all data sets (Model 2A in Table \ref{['tab:param_values']}). Fits for Model 2A and Model 2B resemble fits for Model 1A and Model 1B, respectively, and are not shown.
• Figure 3: Magnetic excitations in UO$_2$, where r.l.u. denotes reciprocal-lattice units. (a) Previously published dispersion relation for UO$_{2}$, reproduced from Ref. Caciuffo_1999. (b) Calculated inelastic neutron-scattering intensity for the $J$-$K$-$\Gamma$-$J_{3}$ model (Model 1A in Table \ref{['tab:param_values']}). (c) Calculated inelastic neutron-scattering intensity for the same model as (b), except a biquadratic interaction $J_{\mathrm{bq}}=10$ K is assumed.