Polarized-neutron study of the coherent paramagnetic scattering amplitude of metallic erbium

Polarized-neutron techniques have been used to measure the coherent paramagnetic scattering amplitude of high-purity single crystals of metallic erbium at 300 K. The angular dependence of the coherent-scattering amplitude has been determined with the external magnetic field ($H=22\mathrm{}$ kOe) applied parallel as well as perpendicular to the $c$ axis of the crystal. It has been found that the angular dependence of the scattering amplitude for $\overrightarrow{H}\parallel \overrightarrow{\mathrm{c}}$ as well as $\overrightarrow{H}\parallel \overrightarrow{\mathrm{c}}$ is in good agreement, except at small scattering angles, with the $4f$-electron magnetic form factor calculated using relativistic Dirac-Fock wave functions. At small scattering angles the experimental points were found to be systematically higher than the theoretical curves obtained by least-square fitting of the calculated $4f$-electron form factor to the large-angle experimental points. This small-angle contribution, attributed to the polarization of the conduction bands of erbium, has an unusual angular dependence; it is different from either a $5d$ or $6s$ atomic form factor and exhibits a non-negative oscillatory character.