Crystal-field states of ${\mathrm{UO}}_2$ probed by directional dependence of nonresonant inelastic x-ray scattering

Nonresonant inelastic x-ray scattering (NIXS) has been performed on single crystals of ${\mathrm{UO}}_2$ to study the directional dependence of higher-order-multipole scattering from the uranium $O_{4,5}$ edges (90–110 eV). By comparing the experimental results with theoretical calculations the symmetry of the ground state is confirmed directly as the crystal-field (CF) ${\mathrm{\Gamma }}_5$ triplet state within the $J=4$ manifold. The results demonstrate that the directional dichroism of the NIXS spectra is sensitive to the CF strength and establish NIXS as a tool for probing CF interactions quantitatively.

Figure 1

(a) Energy level diagram of the $J$ levels for the configuration ${\mathrm{U}}^{4+}5f^2$ without CF as a function of the Slater reduction factor $g_{ff}$. The gray-shaded region marks the applicable range for ${\mathrm{UO}}_2$. (b) Calculated NIXS spectra of the four cubic eigenstates as constructed by symmetry for pure $J=4$ [see Eq. (1)] for $\widehat{\mathbf{q}}\parallel \left[001\right]$ (blue), $\widehat{\mathbf{q}}\parallel \left[011\right]$ (dark yellow), and $\widehat{\mathbf{q}}\parallel \left[111\right]$ (red). The insets show the respective charge densities for two electrons. (c) and (e) Energy-level diagrams of CF states as a function of the ratio of the CF parameters $V_4=-Asin\varphi$ and $V_6=Acos\varphi$, expressed in terms of $\varphi$, for a weak and as strong CF scenario (see text). The colored dots mark selected ${\mathrm{\Gamma }}_1, {\mathrm{\Gamma }}_3$, and ${\mathrm{\Gamma }}_5$ ground states used for the direction-dependent NIXS calculations in panels (d) and (f).

Figure 2

(a) NIXS data of ${\mathrm{UO}}_2$ measured at 300 K. (b) Measured difference spectra (directional dichroism) of the two directions $\widehat{\mathbf{q}}\parallel \left[001\right]-\widehat{\mathbf{q}}\parallel \left[111\right]$ and the corresponding calculation for the weak CF case with the ${\mathrm{\Gamma }}_5$ ground state (green lines), see text.

Figure 3

Experimental pseudoisotropic spectrum of ${\mathrm{UO}}_2$ as constructed from the single-crystalline data (black dots) and calculated NIXS spectra (lines), without considering a CF (black line), with a ${\mathrm{\Gamma }}_5$ ground state in a weak CF (blue line), and with a ${\mathrm{\Gamma }}_5$ ground state in a strong CF (cyan).