Structures of magnetic excitations in the spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> kagome-lattice antiferromagnets <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Cs</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>SnF</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Rb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>SnF</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ is a spin-1/2 antiferromagnet on a nearly uniform kagome lattice with an exchange interaction of $J=20.7$ meV. This compound undergoes magnetic ordering at ${T}_{\mathrm{N}}=20.2$ K with the $\mathbit{q}=0$ structure and positive chirality, which is mainly caused by the large Dzyaloshinskii-Moriya interaction. ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ is a spin-1/2 antiferromagnet on a modified kagome lattice with a $2a\ifmmode\times\else\texttimes\fi{}2a$ enlarged chemical unit cell at room temperature resulting in four kinds of nearest-neighbor exchange interaction, the average of which is ${J}_{\mathrm{avg}}=15.6$ meV. Its ground state is a pinwheel valence bond solid (VBS) with an excitation gap. Here, we show the structures of magnetic excitations in ${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ and ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ investigated by inelastic neutron scattering in wide energy and momentum ranges. For ${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$, four single-magnon excitation modes were observed. Three low-energy modes are assigned to be transverse modes and the high-energy fourth mode is suggested to be an amplitude mode. It was confirmed that the energy of single-magnon excitations arising from the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ point in the extended Brillouin zones is largely renormalized downwards. It was found 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, as well as the results of the recent theories based on the fermionic approach of spinon excitations from the spin liquid ground state, strongly suggest spinon excitations as elementary excitations in ${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$. In ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$, 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 $2.6{J}_{\mathrm{avg}}$. The characteristics of the high-energy excitation continuum are common to both ${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ and ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$, irrespective of their ground states. The experimental results strongly suggest that the spin liquid component remains in the ground state as quantum fluctuations in ${\mathrm{Cs}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$ and ${\mathrm{Rb}}_{2}{\mathrm{Cu}}_{3}{\mathrm{SnF}}_{12}$.

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