Electron density distribution in paramagnetic and antiferromagnetic NiO: A $\gamma$-ray diffraction study

High-accuracy single-crystal structure factor data sets, complete up to $\sin \theta ∕\lambda =1.6{\mathrm{\AA }}^{-1}$, have been measured from paramagnetic NiO at $550\mathrm{K}$ and in the antiferromagnetic state at $10\mathrm{K}$ using $316.5\mathrm{keV}$ gamma radiation. In the rhombohedral low-temperature phase, monodomain formation was enforced by application of moderate stress. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. Pronounced asphericity is found in the nickel valence region which, unexpectedly, is not significantly influenced by the magnetic order. NiO thus exhibits a radically different behavior than that found for MnO or CoO. Similarly, very different charge responses of the $e_g$ and $t_{2g}$ subshells in the paramagnetic states are observed, supporting a prediction from theory. The $3d$ charge distribution is contracted by about 3% relative to the free atom; the total number of $d$ electrons on nickel amounts to 7.65(1). From the $3d$ population analysis, unquenched orbital angular momentum is derived, in quantitative accordance with magnetic x-ray measurements. Electronic properties at the bond critical points reveal the Ni-O interactions as purely ionic. Methodological issues such as the importance of high momentum data and the influence of the wave-function quality are also discussed.

Figure 1

Aspherical contributions to the static model density in the cubic (100) plane. Top: paramagnetic NiO with a density range from $-7.10\text{to}1.78e{\mathrm{\AA }}^{-3}$. Bottom: antiferromagnetic NiO with a density range from $-6.19\text{to}1.57e{\mathrm{\AA }}^{-3}$. Ni is located in the center and the corners of the maps. Solid lines represent positive regions, dashed lines represent negative regions in steps of $0.05e{\mathrm{\AA }}^{-3}$. The zero contour is omitted. The densities are truncated at $\pm 0.25e{\mathrm{\AA }}^{-3}$.

Figure 2

Aspherical contributions to the static model density in the cubic (110) plane. Top: paramagnetic NiO with a density range from $-6.98\text{to}4.72e{\mathrm{\AA }}^{-3}$. Bottom: antiferromagnetic NiO with a density range from $-6.10\text{to}4.25e{\mathrm{\AA }}^{-3}$. Ni is located in the center of the map. Contours as in Fig. 1.

Figure 3

Relative deviation, in percent, of the ordinary nonrelativistic (FF) and relativistic (RFF) form factors from the modified form factor for nickel.

Figure 4

The refined population $P_{40}\left(\mathrm{Ni}\right)$ at HT as a function of increasing momentum cutoff values.