Localized $5d^2$ electrons in a cubic crystal field possess multipoles such as electric quadrupoles and magnetic octupoles. We studied the cubic double perovskite ${\mathrm{Ba}}_2{\mathrm{CaOsO}}_6$ containing the ${\mathrm{Os}}^{6+}$ ($5d^2$) ions, which exhibits a phase transition to a ‘‘hidden order’’ below $T^{*}\sim$ 50 K, by x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) at the Os $L_{2,3}$ edge. The cubic ligand-field splitting between the $t_{2g}$ and $e_g$ levels of Os $5d$ was deduced by XAS to be $\sim 4\mathrm{eV}$. Ligand-field multiplet calculation under fictitious strong magnetic fields indicated that the exchange interaction between nearest-neighbor octupoles should be as strong as $\sim 1.5\mathrm{meV}$ if a ferro-octupolar order is stabilized in the hidden-ordered state, consistent with the exchange interaction of $\sim 1\mathrm{meV}$ previously predicted theoretically using model and density functional theory calculations. The temperature dependence of the XMCD spectra is consistent with a $\sim 18\mathrm{meV}$ residual cubic splitting of the lowest $J_{\mathrm{eff}}=$ 2 multiplet state into the non-Kramers $E_g$ doublet ground state and the $T_{2g}$ triplet excited state.

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• Magnetic order
• Spin state transition
• Spin-orbit coupling
• Mott insulators
• Crystal-field theory
• X-ray magnetic circular dichroism