Magnetic form factor of terbium in Tb(OH)3

The magnetic form factor of terbium in Tb(OH${)}_3$ has been measured from single crystals with polarized neutrons in both the paramagnetic (90°K) and ferromagnetic (2.6°K) states. The atomic parameters of the crystal structure were obtained from a refinement of Bragg intensities measured with unpolarized neutrons, and are in agreement with the parameters determined for other rare-earth hydroxides. This refinement indicated severe extinction effects, but corrections to both the unpolarized and polarized data were applied successfully with the simple Zachariasen formula, and with the same extinction parameter in each case. After correcting for extinction the experimental results essentially fall on a smooth curve as a function of $\frac{sin\theta }{\lambda }$. At both temperatures the best fit to the experimental smooth curve is with a magnetic form factor intermediate between that derived from the nonrelativistic wave functions of Freeman and Watson, and that found experimentally for terbium metal. However, the experimental form factor is in good agreement with recent relativistic mixed-configuration Dirac-Fock wave functions calculated by Desclaux and Freeman. An examination of certain Bragg reflections that have no contribution from the terbium atom shows that the magnitude of the net spin transferred to the ligand sites is less than 0.01${\mathrm{\mu }}_{\mathrm{B}}$ in the ferromagnetic state when the terbium moment is 8.90${\mathrm{\mu }}_{\mathrm{B}}$/Tb atom.