[en] Motivated by the recent experimental observation of a large magneto-optical Kerr effect and direct imaging of magnetic domains in the non-collinear antiferromagnet (AFM) Mn₃Sn, we formulate a scheme to study spin dynamics in non-collinear AFMs having complex spin configurations. Our scheme is based on the multipole expansion of the magnetic structure, in which we define multipole moment for a cluster of atoms. We find that the moment, which we call cluster multipole, is a convenient order parameter for a systematic derivation of a low-energy effective model. By applying the present approach to Mn₃Sn, we find that the spin dynamics is accurately described in terms of the cluster magnetic octupole. Interestingly, the domain wall in Mn₃Sn has a high maximum velocity without showing the Walker breakdown, and the coherent precession has a tunable frequency ranging from sub-THz to THz. These results indicate that Mn₃Sn is a promising material for future applications of antiferromagnetic spintronics. (author)