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We obtain a classical spin liquid (CSL) phase by applying a magnetic field in$J_1$-$J_2$-$J_3$ Ising model on a kagome lattice. As we proved in the previousstudy [Phys. Rev. Lett. {\bf 119}, 077207 (2017)], this model realizes onespecies of CSL, the hexamer CSL, at zero magnetic field, which consists ofmacroscopically degenerate spin configurations with mixed total magnetization,$M$. The magnetic field selects its subset, which can be mapped to a trimercovering of the dual lattice, and forms a magnetization plateau of $M=1/9$. Inaddition to this CSL, we find two other magnetization plateaus at $M=5/9$ and$17/27$, which are ascribed to the "multimer" superstructures on a duallattice.

Field-selective classical spin liquid and magnetization plateaus on kagome lattice