  We theoretically investigate, using non-perturbative strong correlation
techniques, Mott insulating phases and magnetic ordering of two-component
fermions in a two-dimensional double-well optical lattice. At filling of two
fermions per site, there are two types of Mott insulators, one of which is
characterized by spin-1 antiferromagnetism below the Neel temperature. The
super-exchange interaction in this system is induced by the interplay between
the inter-band interaction and the spin degree of freedom. A great advantage of
the double-well optical lattice is that the magnetic quantum phase diagram and
the Neel temperature can be easily controlled by tuning the orbital energy
splitting of the two-level system. Particularly, the Neel temperature can be
one order of magnitude larger than that in standard optical lattices,
facilitating the experimental search for magnetic ordering in optical lattice
systems.
