  There is little doubt that the magnetization dynamics of ferromagnetic
systems is governed by the Landau-Lifshitz-Gilbert equation or its
generalization with various spin torques. In contrast, there are several sets
of dynamic equations for two-sublattice antiferromagnets (AFMs) in literature
that have different forms of dissipative torques and no proper dynamic
equations for multi-sublattice AFMs and ferrimagnets in general. Here we
introduce the general Rayleigh dissipation functional into the Lagrange
equation and derive the proper form of the dissipative torques in the
phenomenological equations for the AFMs with multiple sublattices. A new type
of dissipative torque arising from inter-sublattice drag effect is discovered
that has important influences on magnon lifetime and domain wall motion. In
particular, our theory unifies different dynamic equations of AFMs in
literature.
