# Internal structure and stability of vortices in a dipolar spinor Bose-Einstein condensate

## TL;DR

This paper explores how dipolar interactions influence vortex structures and stability in spinor Bose-Einstein condensates, revealing new core behaviors, spin textures, and effects of anisotropy and magnetic fields.

## Contribution

It introduces a detailed analysis of vortex core structures in dipolar spinor BECs, highlighting the role of dipolar physics and anisotropy in vortex stability and spin textures.

## Key findings

- Dipolar interactions restrict vortex core size in ferromagnetic phases.
- Competition between interactions can enlarge vortex cores in polar phases.
- Magnetic fields induce symmetry-breaking and spin-domain wall formation.

## Abstract

We demonstrate how dipolar interactions can have pronounced effects on the structure of vortices in atomic spinor Bose-Einstein condensates and illustrate generic physical principles that apply across dipolar spinor systems. We then find and analyze the cores of singular vortices with non-Abelian charges in the point-group symmetry of a spin-3 $^{52}$Cr condensate. Using a simpler model system, we analyze the underlying dipolar physics and show how a characteristic length scale arising from the magnetic dipolar coupling interacts with the hierarchy of healing lengths of the s-wave scattering, and leads to simple criteria for the core structure: When the interactions both energetically favor the ground-state spin condition, such as in the spin-1 ferromagnetic phase, the size of singular vortices is restricted to the shorter spin-dependent healing length. Conversely, when the interactions compete (e.g., in the spin-1 polar phase), we find that the core of a singular vortex is enlarged by increasing dipolar coupling. We further demonstrate how the spin-alignment arising from the interaction anisotropy is manifest in the appearance of a ground-state spin-vortex line that is oriented perpendicularly to the condensate axis of rotation, as well as in potentially observable internal core spin textures. We also explain how it leads to interaction-dependent angular momentum in nonsingular vortices as a result of competition with rotation-induced spin ordering. When the anisotropy is modified by a strong magnetic field, we show how it gives rise to a symmetry-breaking deformation of a vortex core into a spin-domain wall.