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An intriguing idea of spin-orbit Mott insulator has been proposed to explainmagnetic insulating behavior in various iridates. This scenario relies on thestrength of the spin-orbit coupling being comparable to electroniccorrelations, and it is not a priori obvious whether this picture is valid forall iridates. In particular, Sr3Ir2O7 exhibits a small charge gap and magneticmoment compared to Sr2IrO4, questioning the validity of such hypothesis. Tounderstand the microscopic mechanism for magnetism in Sr3Ir2O7, we construct atight binding model taking into account the full t2g- orbitals, the staggeredrotation of the local octahedra, and the bilayer structure. The bands near theFermi level are mainly characterized by the total angular momentum Jeff = 1/2,except below the {\Gamma} point, supporting a reasonably strong spin-orbitcoupling picture. A first order transition to a collinear antiferromagnet viamulti-orbital Hubbard interactions is found within the mean fieldapproximation. The magnetic moment jump at the transition is consistentlysmaller than Sr2IrO4, originated from the underlying band structure of a barelyband insulator. Given the small charge gap and moment observed in Sr3Ir2O7, thesystem is close to a magnetic transition. A comparison to a spin-model ispresented and connection to the Mott insulator is also discussed.

Microscopic theory of magnetism in Sr3Ir2O7