In this talk, We consider the convergence of the system of the Allen-Cahn equations to the weak solution for the multi-phase mean curvature flow in the sense of Brakke. The Landau-Lifshitz equation in this talk can be regarded as a system of Allen-Cahn equations with the Lagrange multiplier, which is a phase field model of the multi-phase mean curvature flow. We show that the family of the varifolds derived from the singular limit of energies is a Brakke flow, under an assumption for the limit of the energies.