  Compared with ferromagnetic counterparts, antiferromagnetic materials are
considered as the future of spintronic applications since these materials are
robust against the magnetic perturbation, produce no stray field, and display
ultrafast dynamics. There are (at least) two sets of magnetic moments in
antiferromagnets (with magnetization of the same magnitude but antiparallel
directions) and ferrimagnets (with magnetization of the different magnitude).
The coupled dynamics for the bipartite collinear antiferromagnets is modeled by
a coupled system of Landau-Lifshitz-Gilbert equations with an additional term
originated from the antiferromagnetic exchange, which leads to femtosecond
magnetization dynamics. In this paper, we develop three Gauss-Seidel projection
methods for micromagnetics simulation in antiferromagnets and ferrimagnets.
They are first-order accurate in time and second-order in space, and only solve
linear systems of equations with constant coefficients at each step.
Femtosecond dynamics, N\'{e}el wall structure, and phase transition in presence
of an external magnetic field for antiferromagnets are provided with the
femtosecond stepsize.
