Polarized-Neutron Study of the Induced Magnetic Moment in TmSb

The magnetic form factor of the induced moment in TmSb has been measured with polarized neutrons. Thulium antimonide is a singlet-ground-state system, i.e., it has no spontaneous magnetic moment, but under the conditions of the experiment the magnetization develops through the mixing of the ground state with the first excited state. The experiments were performed on a single crystal at 5 °K and an applied field of 12.5 kOe. Measurements were taken with $\overrightarrow{\mathrm{H}}\parallel 〈100〉$ and $\overrightarrow{\mathrm{H}}\parallel 〈110〉$. The theoretical magnetic form factor has been derived using the tensor-operator technique of Johnston, Lovesey, and Rimmer, and the nonrelativistic wave functions of Freeman and Watson. The experimental form factor with $\overrightarrow{\mathrm{H}}\parallel 〈100〉$ is essentially a smooth curve as a function of $\frac{sin\theta }{\lambda }$, while for $\overrightarrow{\mathrm{H}}\parallel 〈110〉$ considerable anisotropy is observed at high scattering angles. This anisotropy arises from the nature of the ground state and is determined by the crystal field acting on the rare-earth ion. The present technique may therefore be useful in investigating the ground states of the many compounds with unquenched orbital moments and appreciable crystal field interactions. The experimentally observed anisotropy is in complete agreement with theory. Previous polarized-neutron experiments on rare-earth metals indicate that the spatial extent of the $4f$ electrons is more expanded than given by the nonrelativistic calculations. The observed form factor in TmSb does not agree with the form factor calculated with nonrelativistic wave functions. Good agreement is obtained by using the $4f$ radial distribution as determined from polarized-neutron measurements on thulium metal. A set of $〈r^n〉$ integrals has been derived from the experimental radial densities.