Magnetocrystalline anisotropy of SmCo5and its interpretation on a crystal-field model

Results of magnetization measurements on carefully prepared single crystals of Sm${\mathrm{Co}}_5$ are presented over the temperature range 4-970 K. The contribution of the rare-earth sublattice magnetocrystalline anisotropy was evaluated using the data on Y${\mathrm{Co}}_5$ as "a blank." These results are interpreted on the basis of a singleion model. The following Hamiltonians were employed to obtain eigenvalues: $\mathcal{H}\left(\mathrm{parallel}\mathrm{to} c \mathrm{axis}\right)=\lambda \overrightarrow{\mathrm{L}}·\overrightarrow{\mathrm{S}}+{\mathcal{H}}_{\mathrm{CF}}+2\mathrm{}{\mu }_B{S}_z{H}_{\mathrm{ex}}$, $\mathcal{H}\left(\mathrm{perpendicular}\mathrm{to} c \mathrm{axis}\right)=\lambda \overrightarrow{\mathrm{L}}·\overrightarrow{\mathrm{S}}+{\mathcal{H}}_{\mathrm{CF}}+2\mathrm{}{\mu }_B{S}_x{H}_{\mathrm{ex}}$. $H_{\mathrm{ex}}$ was regarded as arising mainly from the cobalt sublattice. Contributions arising from the multiplets ${}_{}{}^6{}_{}{}^{}H_{\frac{7}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^6{}_{}{}^{}H_{\frac{9}{2}}^{}{}_{}{}^{}$ to the ground multiplet ${}_{}{}^6{}_{}{}^{}H_{\frac{5}{2}}^{}{}_{}{}^{}$ were included. The crystal field was evaluated in terms of Racah's tensor-operator technique employing $3-j$ and $6-j$ symbols. With the two sets of eigenvalues obtained from the above expressions, the anisotropy energy to rotate the magnetization direction from the axis to the plane was calculated and compared with experimental results on single crystals of Sm${\mathrm{Co}}_5$. It is shown that the sign of the crystal-field parameter predicts the correct easy direction of magnetization and that the free-energy values calculated from 4 to 970 K are in reasonable agreement with experiment.