Effects of Zeeman field on the dynamical instability of flat states for spin-2 Bose-Einstein condensates in an optical lattice

We investigate the effects of Zeeman field on the dynamical instability of flat states for F=2 spinor Bose-Einstein condensates in an optical lattice. The instability criteria for the ferromagnetic, uniaxial nematic, biaxial nematic-like and cyclic-like states are obtained analytically. It is shown that the linear Zeeman splitting shift only changes the dynamical instability of the biaxial nematic-like phase, but the quadratic Zeeman splitting shift can stabilize or induce additional dynamical instability to all the phases except the first-type ferromagnetic phase. The interaction strength of the spin-singlet pair term can change the dynamical instability of the cyclic-like state only when the quadratic Zeeman splitting is included. We also provide the experimental parameters to observe these interesting phenomena in future experiments.