Spontaneous quantum Hall effect in an atomic spinor Bose-Fer mi mixture

We study a mixture of spin-1 bosonic and spin-1/2 fermionic cold atoms, e.g., Rb-87 and Li-6,confined in a triangular optical lattice. With fermions at 3/4 filling, Fermi surface nesting leads to spontaneous formation of various spin textures of bosons in the ground state, such as collinear, coplanar and even non-coplanar spin orders. The phase diagram is mapped out with varying boson tunneling and Bose-Fermi interactions. Most significantly, in one non-coplanar state the mixture is found to exhibit spontaneous quantum Hall effect in fermions and crystalline superfluidity in bosons, both driven by interaction.