Electron density distribution in ferromagnetic nickel: A $\gamma$-ray diffraction study

High-accuracy single-crystal structure factors, complete up to $\text{sin}\theta /\lambda =1.9{\text{Å}}^{-1}$, have been measured from ferromagnetic nickel at 295 K using 316.5-keV gamma radiation. The experimental uncertainty of the structure factors is of the order of 10 millielectrons per atom for all data. A detailed description of the electron density distribution is presented in terms of a multipolar atomic deformation model. Achievement of a reliable Debye-Waller factor is of vital importance in this context. The charge asphericity is due to an excess $e_g$ orbital occupancy of 43.4(2)%. The $3d$ shell in the metal is contracted by 2.07(5)% relative to the free atom. The results are discussed and compared with earlier experimental and theoretical works. In contrast to bcc Cr and Fe, solid-state effects are less pronounced in fcc Ni. Clear disentanglement between the $3d$ and $4s$ valence electrons could be accomplished for the first time. The general expectation that the number of $3d$ electrons in the metal should be increased as compared to the atom was confirmed in the case of iron by combining spin and charge-density data. In the case of nickel, it is rejected as revealed by the $\gamma$-ray data alone. Only with the $d^8$ configuration, consistency is achieved between observed and refined mosaic widths of the sample crystal. A $3d^8$ configuration implies that the majority-spin $d$ band cannot be full. Strong support is lent to a localized atomic character of the valence electrons.

Figure 1

Aspherical contributions to the static model density. Top: (100) plane $\left(4\times 4{\text{Å}}^2\right)$ with a density range from $-0.45$ to $1.78e{\text{Å}}^{-3}$. Bottom: (110) plane $\left(5\times 5{\text{Å}}^2\right)$ with a density range from $-1.19$ to $1.78e{\text{Å}}^{-3}$. Solid lines represent regions of excessive density and dashed lines represent depleted regions in steps of $0.1e{\text{Å}}^{-3}$. The zero contour is omitted. The densities are truncated at $\pm 0.5e{\text{Å}}^{-3}$.

Figure 2

The difference between the spherically averaged spin form factor ($={⟨j_o⟩}_{\text{obs}}$ from Ref. 27) and the radial charge form factors for $3d^9$ $\left(\kappa =1.021\right)$ and $3d^8$ $\left(\kappa =1.020\right)$ as deduced from neutron and $\gamma$-ray diffraction. The form factors are normalized to unity at $\text{sin}\theta /\lambda =0$.