  Damping in magnetization dynamics characterizes the dissipation of magnetic
energy and is essential for improving the performance of spintronics-based
devices. While the damping of ferromagnets has been well studied and can be
artificially controlled in practice, the damping parameters of
antiferromagnetic materials are nevertheless little known for their physical
mechanisms or numerical values. Here we calculate the damping parameters in
antiferromagnetic dynamics using the generalized scattering theory of
magnetization dissipation combined with the first-principles transport
computation. For the PtMn, IrMn, PdMn and FeMn metallic antiferromagnets, the
damping coefficient associated with the motion of magnetization ($\alpha_m$) is
one to three orders of magnitude larger than the other damping coefficient
associated with the variation of the N\'eel order ($\alpha_n$), in sharp
contrast to the assumptions made in the literature.
