$xy$, $x^2-y^2$, $(1/\pi)\Delta/((\epsilon-7)^2+\Delta^2)$ for $yz$, $zx$, and $(1/\pi)\Delta/((\epsilon-8.5)^2+\Delta^2)$ for $3z^2-r^2$, with energies in units of eV and $\Delta=2.5$ eV. This arbitrary assumption for the DOS form may be justified by the fact that the RXS spectra is not sensitive to the assumption.

The second term of eq. (\[eq.crystal\]), which arises from the buckling of sheets of B and C atoms, gives rise to a small modification on the $5d$ band. Although the actual modulation of the $5d$ states may come through the hybridization to the $s$ and $p$ states of B and C atoms, such effects can be included into the second term. This term makes the local symmetry twofold.

Dy$^{3+}$ ion is approximately in the $4f^9$-configuration ($^6$H$_{15/2}$). Equation (\[eq.crystal\]) is now applied to the subspace of $J=15/2$. Since the $4f$ states are much localized than the $5d$ states, the crystal field is much smaller here than that on the $5d$ states. The coefficient $D_f$ of the first term is expected to be positive from the analysis of magnetic susceptibility.[@Yamauchi] This leads to the lowest energy states $|\pm\frac{1}{2}\rangle$ and the next energy states $|\pm\frac{3}{2}\rangle$, both of which form Kramers’ doublets ($|M\rangle$ represents the state of $J_z=M$). The axial symmetry is 