Bose-Einstein condensation with magnetic dipole-dipole forces

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of, e.g., chromium $\left(6\mathrm{}{\mu }_B\right),$ and a typical value of the scattering length, all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region, the ground-state wave functions show internal structures that we believe have not been seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.