Motivated by the discovery of a new family of 122 iron-based superconductors,we present the theoretical results on the ground state phase diagram,spin wave,and dynamic structure factor obtained from the extended J_1-J_2 Heisenberg model.In the reasonable physical parameter region of K_2Fe_4Se_5,we find that the block checkerboard antiferromagnetic order phase is stable.There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase,which have analytic expressions at the high-symmetry points.To further compare the experimental data on neutron scattering,we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.
