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The series expansion method is used to study magnon spectra of the kagomesystem with nearest-neighbor exchange interaction $J$ and out-of-planeDzyaloshinskii-Moriya (DM) interaction $D^{\parallel}$, which is a minimalmodel for Cs$_{2}$Cu$_{3}$SnF$_{12}$. Compared to the magnon spectra by thelinear spin wave (LSW) theory, we find that dispersions at high energy partsuffer downward deformation, which is similar to the triangle lattice case, inaddition to the reduction of the energy scale of about 40\% as pointed out in aneutron-scattering study by Ono {\it et al.} Using a reliable estimation$J=20.7$ meV in a previous study on the magnetic susceptibility ofCs$_{2}$Cu$_{3}$SnF$_{12}$, we use $D^{\parallel}$ as the fitting parameter toreproduce the experimental magnon spectra and obtain $D^{\parallel}=0.12J$. Wealso report that a roton-like minimum occurs at the M point and a maximum atpoints somewhat away from the $\Gamma$ point. Compression of the LSW magnonband is commonly seen in the kagome and triangular-lattice systems, which maybe viewed as being pushed from above by the spinon continuum.

journal of the physical society of japan

A Series Expansion Study for Large Negative Quantum Renormalization of  Magnon Spectra in the $S=1/2$ Kagome-Lattice Heisenberg Antiferromagnet  Cs$_{2}$Cu$_{3}$SnF$_{12}$