In order to improve the magnetic properties of permanent magnet films, based on the theory of micromagnetism, we have studied the magnetization properties of Ce_1.66Mg_1.34Co₃ and α″-Fe₁₆N₂ exchange coupled multilayer gradient films by using software OOMMF, and the influence of magnetic crystal anisotropy gradient on the properties of multilayer films systematically. We analyze the changes of remanence, coercivity, hysteresis loop and energy during magnetization reversal process. We find that the coercivity and residual magnetization of the films can be effectively increased by decreasing the anisotropic gradient of magnetic crystals or increasing the anisotropy difference at the interface, so as to improve the magnetic properties. A magnetic vortex state is found by calculating the magnetic moment distribution, and the generation of this magnetic vortex state is accompanied by the increase of system energy.

Based on Gross-Pitaevskii equation, we studied numerically ground-state density distribution of Bose-Einstein condensates trapped in a combined potential of a spin-dependent optical lattice potential and an infinite deep potential. We discuss specifically the influence of propagation directions and the ratio of wave numbers (l) of the two lasers, which produce the spin-dependent optical lattice on the ground-state of the Bose-Einstein condensate. As the wave number is small, two beams of light spread forward to each other. The two components exhibit continuous stripes with l < 2. And with l≥2 both components show discontinuous stripes. As the two beams of light propagate vertically, with the increase of l, component 1 changes gradually from continuous to discontinuous stripes, and component 2 behaves oppositely. The number of ground state density fringes increases with the increase of wave number, while the number of vortices remains unchanged.