Coreless vortex ground state of the rotating spinor condensate

We study the ground state of the rotating spinor condensate and show that for slow rotation the ground state of the ferromagnetic spinor condensate is a coreless vortex. While the coreless vortex is not topologically stable, we show that there is an energetic threshold for the creation of a coreless vortex. This threshold corresponds to a critical rotation frequency that vanishes as the system size increases. Also, we demonstrate the dramatically different behavior of the spinor condensate with the antiferromagnetic interactions. For antiferromagnetic spinor condensate the angular momentum as a function of rotation frequency exhibits the familiar discrete staircase behavior, but in contrast to an ordinary condensate the first step is to the state with angular momentum of $1/2$ per particle.