Magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions

In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively twodimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle theta relative to the direction normal to the system's plane. Using numerical methods and the variational approximation, we demonstrate that unstable Townes solitons, created by the contact attractive interaction, may be completely stabilized (with an anisotropic shape) by the dipole-dipole interaction (DDI), in the interval theta(cr) < theta <= pi/2. The stability boundary theta(cr) weakly depends on the relative strength of the DDI, remaining close to the magic angle theta(m) = arccos(1/root 3). The results suggest that DDIs provide a generic mechanism for the creation of stable BEC solitons in higher dimensions.