▎ 摘　　要

Within the frame of the Huang-Rhys's lattice relaxation model, we theoretically investigate the spin-flip relaxation assisted by two-phonon processes between the zeroth and first-excited Landau level in gapped graphene on different polar substrates. We give the comparisons between the spin-conserving and the spin-flip of two-phonon processes, which are composed of the surface-optical phonons and longitudinal acoustic phonons. The dependences of two-phonon processes on the energy separation, temperature and polarizability of substrates are discussed. Moreover, we find that the relaxation time of spin-flip can be tuned on a large scale by adjusting the Rashba spin-orbital coupling and internal distance between the graphene and the polar substrate.