Structures of magnetic excitations in spin-1/2 kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$.

We show the structures of magnetic excitations in spin-1/2 kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$ investigated by inelastic neutron scattering in wide energy and momentum ranges. For Cs$_2$Cu$_3$SnF$_{12}$, four single-magnon excitation modes were observed. Low-energy three modes are assigned to be transverse modes and the high-energy fourth mode is suggested to be an amplitude mode composed of bound spinons. It was found that the high-energy single-magnon excitations near the zone boundary significantly broaden out, and that the broad excitation continuum without a marked structure spreads in a wide energy range from $0.15J$ to approximately $2.5J$ in contrast to the clearly structured excitation continuum observed in the spin-1/2 triangular-lattice Heisenberg antiferromagnet. These findings strongly suggest spinon excitations as elementary excitations in Cs$_2$Cu$_3$SnF$_{12}$. In addition, weak excitations arising from M points were observed. In Rb$_2$Cu$_3$SnF$_{12}$, singlet--triplet excitations from the pinwheel VBS state and their ghost modes caused by the enlargement of the chemical unit cell were clearly confirmed. It was found that the excitation continuum is structured in the low-energy region approximately below $J_{\mathrm{avg}}$ and the almost structureless high-energy excitation continuum extends to approximately $2.6J_{\mathrm{avg}}$. The characteristics of the high-energy excitation continuum are common to both Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$, irrespective of their ground states. The experimental results, as well as recent theory based on a fermionic approach of spinon excitations from the spin liquid ground state, strongly suggest that the spin liquid component remains in the ground state as quantum fluctuations in Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$.