We obtain a classical spin liquid (CSL) phase by applying a magnetic field to the J 1 -J 2 -J 3 Ising model on a kagome lattice. As we proved in the previous study [Phys. Rev. Lett. 119, 077207 (2017)], this model realizes one species of CSL, the hexamer CSL, at the zero magnetic field, which consists of macroscopically degenerate spin configurations with mixed total magnetization, M. The magnetic field selects its subset, which can be mapped to a trimer covering of the dual lattice and forms a magnetization plateau of M = 1/9. In addition 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 dual lattice.

We study a problem of interacting fractional charges with J1-J2-J3 Ising model on a checkerboard lattice under magnetic field. As a result of the interplay between repulsive interactions and particle density tuning by magnetic field, the fractional charges form a novel classical spin liquid (CSL) phase. The CSL phase is composed of degenerate spin configurations, which can be mapped to the trimer covering of dual square lattice. The CSL state shows macroscopic ground state entropy, implying the emergence of novel quantum spin liquid phase as turning on quantum fluctuation. In addition to the CSL phase, the system exhibits multiple magnetization plateaus, reflecting the fertile screening processes of dimer-monomer mixtures.

We study the dynamics of a chiral soliton lattice (CSL) in a classical one-dimensional spin chain coupled to conduction electrons under an electric field. The CSL has attracted much interest because its period can be easily controlled by an external magnetic field. We clarify the dependence of the CSL dynamics on its period. A collective coordinate and an SU(2) gauge method are used for the analysis. It turns out that the velocity of the CSL decreases as the period becomes longer. We also mention the relation between the velocity and the magnetic resistance.

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