Tunable anisotropic magnetism in trapped two-component Bose gases

We theoretically address magnetic ordering at zero and finite temperature in both homogeneous and trapped Bose-Bose mixtures in optical lattices. By using bosonic dynamical mean-field theory, we obtain the phase diagram of the homogeneous two-component Bose-Hubbard model in a three-dimensional cubic lattice, which features competing magnetic order of XY ferromagnetic and antiferromagnetic type in addition to the Mott and superfluid states. We show that these magnetic phases persist also in the presence of a harmonic trap.