Ripple State in the Frustrated Honeycomb-Lattice Antiferromagnet

We discover a new type of multiple-q state, a "ripple state," in a frustrated honeycomb-lattice Heisenberg antiferromagnet under magnetic fields. The ground state has an infinite ringlike degeneracy in the wave vector space, exhibiting a cooperative paramagnetic state, a "ring-liquid" state. We elucidate that the system exhibits the ripple state as a new low-temperature thermodynamic phase via a second-order phase transition from the ring-liquid state, keeping the ringlike spin structure factor. The spin texture in real space looks like a "water ripple" and can induce a giant electric polarization vortex. A possible relationship to the honeycomb-lattice compound, Bi_{3}Mn_{4}O_{12}(NO_{3}), is discussed.