Elementary excitations of the S=1/2 one-dimensional antiferromagnet KCuGaF_6 were investigated by inelastic neutron scattering in zero and finite magnetic fields perpendicular to the (1, 1, 0) plane combined with specific heat measurements. KCuGaF$_6$ exhibits no long-range magnetic ordering down to 50 mK despite the large exchange interaction J/k_B=103 K. At zero magnetic field, well-defined spinon excitations were observed. The energy of the des Cloizeaux and Pearson mode of the spinon excitations is somewhat larger than that calculated with the above exchange constant. This discrepancy is mostly ascribed to the effective XY anisotropy arising from the large Dzyaloshinsky-Moriya interaction with an alternating D vector. KCuGaF_6 in a magnetic field is represented by the quantum sine-Gordon model, for which low-energy elementary excitations are composed of solitons, antisolitons and their bound states called breathers. Unlike the theoretical prediction, it was found that the energy of a soliton is smaller than that of the first breather, although the energy of the first breather coincides with that observed in a previous ESR measurement.
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