Weyl type spin-orbit coupled ferromagnetic Bose-Einstein condensates under rotation

We investigate the ground state of ferromagnetic Bose-Einstein condensates with Weyl type spin-orbit coupling and rotation. When the spin-orbit coupling is strong, the ground state of the system exhibits square lattice phase for the non-rotation case, while two half-skyrmion chains can occur, which is perpendicular to each other, for the rotation case. For the weak spin-orbit coupling case, half-skyrmion displays the symmetrical arrangement around Mermin-Ho vortex at the center of condensates as the rotation frequency is increased. Moreover, the effects of spin-independent and spin-dependent interactions on the ground state are also studied.