shown in Fig. \[fig5\](b) with $q_\textrm{mag}[\textrm{L}]=(\pi,0,0)$. By the reduction in $\Delta_{\textrm{M}\sigma}^0$, we indeed find a crucial difference: The dimer-type AF insulating (AFI) state within the L orbital discussed above \[filled symbol in Fig. \[fig6\](a)\] stabilized in the wide range of parameters in the room-$T$ case is not seen, and different AF metallic (AFM) states appear in Figs. \[fig6\](b) and \[fig6\](c), owing to the mixing between the L and M$\sigma$ orbitals.

In Fig. \[fig7\], we show the $U_{\textrm{L}}$ dependence of site occupation number for the three kinds of orbitals together with the spin moments on the L and M$\sigma$ orbitals. Figures \[fig7\](a)-7(c) correspond to the cases in Figs. \[fig6\](a)-6(c), respectively. The right and left panels in Figs. \[fig7\](b) and 7(c) are data along different traces in the ($U_{\textrm{M}}$, $U_{\textrm{L}}$) plane, i.e., for $U_{\textrm{M}}=U_{\textrm{L}}$ and $U_{\textrm{M}}=2U_{\textrm{L}}$, respectively.

### Room-temperature structure {#subsubsec311}

The phase diagram in Fig. \[fig6\](a) shows no dependence on $U_{\textrm{M}}$; this is because the M$\sigma$ orbital is always nearly unoccupied, as shown in Fig. \[fig7\](a). As $U_{\textrm{L}}$ is increased, the system varies as PM $\rightarrow$ AFM $\rightarrow$ AFI states. Since only L sites possess magnetic moments, the magnetic phases are represented as L-AFM and L-AFI in Fig. \[fig7\](a).

These results 