Magnetic specific-heat contributions from linear vis-à-vis nonlinear excitations in the one-dimensional antiferromagnet (${\mathrm{C}{\mathrm{H}}_3)}_4$NMn${\mathrm{Cl}}_3$ (TMMC)

Low-temperature specific-heat data obtained in a single crystal of (${\mathrm{C}{\mathrm{H}}_3)}_4$NMn${\mathrm{Cl}}_3$ (TMMC) are presented. The experiments were performed in a variety of magnetic field strengths between 0 and 10 T. For magnetic fields oriented parallel to the chain axis, linear excitations were found to adequately describe the magnetic specific heat. When the magnetic field was perpendicular to the chain axis, these excitations alone were not sufficient and the addition of nonlinear (solitonlike) excitations were required. At low field the sine-Gordon model appears to be adequate but not the simple ideal soliton-gas phenomenology which, with the neglecting of the interaction terms, is not realistic in the temperature range where the specific-heat peak occurs. At high field ($H>\mathrm{}5\mathrm{}$ T) the sine-Gordon model is no longer adequate for TMMC, which is now described by a model with small deviations from the axial symmetry. For the latter model, numerical transfer-matrix calculations are presented which are in reasonable agreement with the experimental data. The influence of the quantum effects is also discussed.