Spin excitation spectra of spin–orbit coupled bosons in an optical lattice*
Li Ruo-Yana), He Liangb), Sun Qingc)†, Ji An-Chunc)‡, Tian Guang-Shana)
       
(a) Spin configuration of the 2×2 spin vortex phase, where i denotes the magnetic primitive cell and μ is the sublattice index. (b) The spin is rotated from the z axis to a new direction ( θ , ϕ ) in the spin-wave theory.