Theoretical study of magnetic properties of the triangulated kagome lattice - Magnons in the Heisenberg model and their quantum effects

The Holstein-Primakoff spin-waves for Heisenberg spin states on the triangulated Kagome lattice are obtained by the Bogoliubov transformation. The calculation is made on the basis of the Heisenberg model with the nine-sublattice system proposed by Mekata for the compound Cu9Cl2(cpa)(6). xH(2)O. According to the behavior of the dispersion of magnons, obtained modes can be assigned in correspondence to those in triangular antiferromagnets. Because obtained modes for this system have both characters of triangular and Kagome antiferromagnetic lattices, remarkable features can be found in the behavior of magnons: as well as "the flat mode" with zero-energy excitation corresponding to that in the Kagome lattice, two "dispersionless modes" with finite energy appear. The obtained quantum effect by the zero-point vibration of magnons to the ground-state energy is also discussed.