Half-quantum vortex generation in a two-component Bose-Einstein condensate by an oscillatory magnetic obstacle

We numerically investigate the dynamics of vortex generation in a two-dimensional, twocomponent Bose-Einstein condensate subjected to an oscillatory magnetic obstacle. The obstacle creates both repulsive and attractive Gaussian potentials for the two symmetric spin-$\uparrow$ and $\downarrow$ components, respectively. We demonstrate that, as the oscillating frequency f increases, two distinct critical dynamics arise in the generation of half-quantum vortices (HQVs) with different spin circulations. Spin-$\uparrow$ vortices are nucleated directly from the moving obstacle at low f, while spin-$\downarrow$ vortices are created at high f by breaking a spin wave pulse in front of the obstacle. We find that vortex generation is suppressed for sufficiently weak obstacles, in agreement with recent experimental results by Kim et al. [Phys. Rev. Lett. 127, 095302 (2021)]. This suppression is caused by the finite sweeping distance of the oscillating obstacle and the reduction in friction in a supersonic regime. Finally, we show that the characteristic length scale of the HQV generation dynamics is determined by the spin healing length of the system.