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Motivated by the recent discovery of high temperature antiferromagnetSrRu$_2$O$_6$ and its potential to be the parent of a new superconductor, weconstruct a minimal $t_{2g}$-orbital model on a honeycomb lattice to simulateits low energy band structure. Local Coulomb interaction is taken into accountthrough both random phase approximation and mean field theory. Experimentallyobserved Antiferromagnetic order is obtained in both approximations. Inaddition, our theory predicts that the magnetic moments on three$t_{2g}$-orbitals are non-collinear as a result of the strong spin-orbitcoupling of Ru atoms.

t2g-orbital model on a honeycomb lattice: application to antiferromagnet SrRu2O6