When symmetry in a system is broken, topological defects may form, with the possible defects determined by the nature of the broken symmetry.   Topological defects in an atomic Bose-Einstein condensate (BEC), such as vortices, therefore can serve as a laboratory for studying the physics of broken symmetry.  By engineering the system such that the broken symmetry changes over some boundary, one may also study the physics of topological interfaces.  In this talk I will discuss the energetic stability of vortices in spin-1 atomic BECs, identified by numerically minimizing the free energy functional, as well as proposed scheme accessible to current experiments which realizes a topological interface.

The spin-1 BEC exhibits two phases of the ground state manifold, polar and ferromagnetic (FM), with different broken symmetries.  I will present the core structures of the energetically stable singular vortices in both phases and discuss how these may be understood in terms of an energetic hierarchy of length scales.  I will then discuss recent results which show how the stable vortex structures change when the conservation of longitudinal magnetization is explicitly imposed, such as the stability of a nonsingular FM vortex when atomic interactions favor the polar phase.  Finally, I will discuss stable vortices which cross a boundary between polar and FM BECs, corresponding to a topological interface.