Spontaneous Quantum Hall Effect in an Atomic Spinor Bose-Fermi 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 noncoplanar spin orders. The phase diagram is mapped out with varying boson tunneling and Bose-Fermi interactions. Most significantly, in one noncoplanar state the mixture is found to exhibit a spontaneous quantum Hall effect in fermions and crystalline superfluidity in bosons, both driven by interaction.