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We investigate the phase diagrams of the spin-orbital $d^9$ Kugel-Khomskiimodel for a bilayer and a monolayer square lattice using Bethe-Peierls-Weissmethod. For a bilayer we obtain valence bond phases with interlayer singlets,with alternating planar singlets, and two entangled spin-orbital (ESO) phases,in addition to the antiferromagnetic and ferromagnetic order. Possibility ofsuch entangled phases in a monolayer is under investigation at present.

Entangled Spin-Orbital Phases in the d$^9$ Model