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The coupled spin tube system, which is equivalent to a stackedKagome-triangular spin system, exhibits the cuboc order -- a non-coplanar spinorder with a twelve-sublattice structure accompanying spontaneous breaking ofthe translational symmetry -- in the Kagome-triangular plane. On the basis ofthe spin-wave theory, we analyze spin-wave excitations of the planarKagome-triangular spin system, where the geometric phase characteristic to thecuboc spin structure emerges. We further investigate spin-wave excitations anddynamical spin structure factors for the coupled spin tubes, assuming thestaggered cuboc order.

Spin-wave analysis for Kagome-triangular spin system and coupled spin tubes: low-energy excitation for the cuboc order