Spin-orbit coupling stabilizing half-quantum spin defect in spin-1 Bose-Einstein condensates

Abstract

Quantum topological defects usually are excited on density. In this study, we extend the topological defect to another dimensionality: the spin. We indicate that the spin singularity, where the spin density |S| vanishes locally, occurs commonly in the two-dimensional spin-1 Bose-Einstein condensates. We assume a coreless half-quantum vortex solution in the spin-1 Bose-Einstein condensates according to the spin singularity. This half-quantum vortex can further induce a half-quantum spin defect, which is similar to the general half-quantum Skyrmion but its centre proposes singularity on the spin density. We use the variational method to obtain a possible stable solution under the combined interaction of the spin-orbit coupling and the external magnetic field. Our calculation shows that the isotropic spin-orbit coupling provides local energy minimum to stabilize the coreless half-quantum vortex and the corresponding singular half-quantum spin texture excitation. The combined restriction of the isotropic spin-orbit coupling and the perpendicular magnetic field is a key factor to obtain this kind of excitation. Our study also provides the stability phase diagram and the most possible size of the half-quantum vortex. Furthermore, our analysis shows that adjusting of the spin interaction hardly affects the stability of the half-quantum vortex.