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The behaviour of a harmonically trapped dipolar Bose-Einstein condensate withits dipole moments rotating at angular frequencies lower than the transverseharmonic trapping frequency is explored in the co-rotating frame. We obtainsemi-analytical solutions for the stationary states in the Thomas-Fermi limitof the corresponding dipolar Gross-Pitaevskii equation and utilise linearstability analysis to elucidate a phase diagram for the dynamical stability ofthese stationary solutions with respect to collective modes. These results areverified via direct numerical simulations of the dipolar Gross-Pitaevskiiequation, which demonstrate that dynamical instabilities of the co-rotatingstationary solutions lead to the seeding of vortices that eventually relax intoa triangular lattice configuration. Our results illustrate that rotation of thedipole polarization represents a new route to vortex formation in dipolarBose-Einstein condensates.

Vortex Lattice Formation in Dipolar Bose-Einstein Condensates via Rotation of the Polarization