We report the results of dc magnetization, thermal expansion, and magnetostriction measurements of the Kondo semiconductor ${\mathrm{CeOs}}_4{\mathrm{Sb}}_{12}$. These results provide a magnetic-field–temperature phase diagram for the three principal axes of the cubic crystal [100], [110], and [111] and reveal the magnetic anisotropy of the three ordered phases A, B, and C. The magnetic anisotropy of the transition temperature $T_{\mathrm{C}}$ from the paramagnetic phase to the C phase is $T_{\mathrm{C}}^{\left[111\right]}>T_{\mathrm{C}}^{\left[110\right]}>T_{\mathrm{C}}^{\left[100\right]}$. At low temperatures, the magnetization has a distinct magnetic anisotropy in high magnetic fields: $M^{\left[100\right]}>M^{\left[110\right]}>M^{\left[111\right]}$. This ratio of magnetization is in good agreement with that of the magnetically anisotropic ${\mathrm{\Gamma }}_{67}$ quartet. The observation indicates that the crystalline electric field ground state is a ${\mathrm{\Gamma }}_{67}$ quartet and that the $c\text{−}f$ hybridization effect is nearly isotropic. In addition, comparison of the present experimental results with numerical calculations of a two-sublattice model using the mean-field approximation suggests that the C phase is a ${\mathrm{\Gamma }}_5$-type antiferroquadrupolar ordered state despite the presence of strong $c\text{−}f$ hybridization effects. In this case, the increase in $T_{\mathrm{C}}$ due to the external field is mainly caused by the ${\mathrm{\Gamma }}_2$-type antiferro-octupolar interaction.

• Received 4 October 2021
• Revised 11 November 2021
• Accepted 16 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.195144