  We study a mixture of spin-$1$ bosonic and spin-$1/2$ fermionic cold atoms,
e.g., $^{87}$Rb and $^{6}$Li, 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 a spontaneous quantum
Hall effect in fermions and crystalline superfluidity in bosons, both driven by
interaction.
