Distribution of Magnetic Moment in Metallic Gadolinium

Neutron-diffraction experiments with both polarized and unpolarized neutrons have been carried out on single-crystal specimens of ${}_{}{}^{160}{}_{}{}^{}\mathrm{Gd}$ in order to measure the magnetic-moment distribution in the metal. Data have been obtained in the ferromagnetic state at 96 °K for all ($\mathrm{hk}0\mathrm{}$) reflections out to $\frac{\left(sin\theta \right)}{\lambda }=1.275\mathrm{}$ and nearly all ($0kl$) peaks to $\frac{\left(sin\theta \right)}{\lambda }=1.04\mathrm{}$. Measurements have been made as well at a temperature above the Curie point. The shape of the spin distribution appears to be identical at the elevated temperature (313 °K) to that observed at 96 °K. The form-factor data can logically be separated into diffuse and localized components, which may be identified with the conduction electrons and $4f$ electrons, respectively. The $4f$ density is spherically symmetric, and it has a radial dependence which is significantly expanded relative to Hartree-Fock wave functions for the free trivalent ion. Good agreement can be achieved with theoretical form factors based on relativistic Hartree-Fock-Slater wave functions. The diffuse density does not have the distribution expected for $5d$ or $6s$ orbitals: It is long range and oscillatory, however, as one expects for conduction electrons in the rare earths. Measurements of the form factor of ${\mathrm{Gd}}^{+3\mathrm{}}$ in paramagnetic ${\mathrm{Gd}}_2$ ${\mathrm{O}}_3$ have also been made, and the results are in excellent agreement with the free-ion calculations, except at very small scattering angles.