Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom

We consider bosons in a Hubbard lattice with an SU($\cal N$) pseudospin degree of freedom which is made dynamical via a coherent transfer term. It is shown that, in the basis which diagonalizes the pseudospin coupling, a generic hopping process affects the spin state, similar to a spin-orbit coupling. This results, for the system in the Mott phase, in a ferromagnetic phase with variable quantization axis. In extreme cases, it can even give rise to antiferromagnetic order.