Electron density distribution in hexagonal cobalt: A $\gamma$-ray diffraction study

The electron density distribution of ferromagnetic hexagonal cobalt is studied at room temperature using high-quality single-crystal diffraction data measured up to $\text{sin}\theta /\lambda =1.9{\text{Å}}^{-1}$ with 316.5 keV gamma radiation. A highly anisotropic mosaic-block orientation was found. The ensuing anisotropy in secondary extinction could be fairly well described by the Thornley-Nelmes formalism, with adjusted mosaicities close to the directly observed ones. The structure factors have been analyzed by a multipole expansion model within the Hartree-Fock framework. Thermal mean-square atomic amplitudes are distinctly different along the $a$ and $c$ axes. The total $3d$ charge exhibits appreciable anisotropy with an excess of density in the singlet $a_{\text{g}}$ along the $c$ axis and a deficiency in the two doublet $e_{\text{g}}$ orbitals. The $3d$ shell in the metal shows a slight contraction of 1.2% relative to the free atom. Agreement with low-order form factors from critical-voltage electron diffraction reaches 0.1%. No difference of $d$-electron count is found between metal and atom. A $3d^7$ configuration implies incomplete filling of the majority-spin band. The directed metallic bonds are characterized in terms of the electron density topology.

Figure 1

Aspherical contributions to the static model density. Top: (110) plane $\left(8\times 6{\text{Å}}^2\right)$ with a density range from $-1.22$ to $4.76e{\text{Å}}^{-3}$; more than one unit cell is shown to illustrate the $ABAB\dots$ stacking along the $c$ axis. Bottom: basal plane of the hcp structure $\left(6\times 6{\text{Å}}^2\right)$ with a density range from 0 to $0.37e{\text{Å}}^{-3}$; the full hexagonal surrounding of one Co atom is displayed. 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 symmetric spin form factor (Ref. 20) and the radial charge form factor for $3d^7$ $\left(\kappa =1.0122\right)$ as deduced from neutron and $\gamma$-ray diffraction. The form factors are normalized to unity at $\text{sin}\theta /\lambda =0$.