Ripple state in the frustrated honeycomb-lattice antiferromagnet

Rich nontrivial magnetic structures in multiple-q states have attracted much attention these days. One of the most celebrated example might be a skyrmion-lattice state known as a triple-q state with forming periodic vortex-crystal structure. We have found a new type of multiple-q state, a "ripple state" in the J₁-J₂ classical honeycomb-lattice Heisenberg antiferromagnet by means of extensive Monte Carlo simulations. This honeycomb model has been known to have an infinite ring-like degeneracy in the ground state. In the ripple state, surprisingly, order-by-disorder mechnism does not work and all wavevectors on the degenerate ring equally contribute to its order. The real-space spin texture of the ripple state does not form a crystal in spite of the breaking of the translational symmetry and seems to be like a "water ripple" observed when we throw a stone on the surface of water. We will talk about the detail of the intringuing properties of the ripple state and discuss the possible realization in the honeycomb-lattice spin-liquid material, Bi₃Mn₄O₁₂(NO₃).