Temperature dependencies of gap energies and magnon lifetimes are measured in the quasi-one-dimensional $S=1/2$ gapped quantum magnets $({\mathrm{CH}}_3{)}_2{\mathrm{CHNH}}_3{\mathrm{CuCL}}_3$ ($\mathrm{IPA}\mathrm{\text{−}}{\mathrm{CuCl}}_3$, where IPA denotes isopropyl ammonium) and ${\mathrm{Cu}}_2{\mathrm{Cl}}_4·{\mathrm{D}}_8{\mathrm{C}}_4{\mathrm{SO}}_2$ ($\mathrm{Sul}\mathrm{\text{−}}{\mathrm{Cu}}_2{\mathrm{Cl}}_4$) using inelastic neutron scattering. The results are compared to those found in literature for $S=1$ Haldane spin chain materials and to theoretical calculations for the $O(3)$- and $O(N)$- quantum nonlinear $\sigma$-models. It is found that when the $T=0$ energy gap $\Delta$ is used as the temperature scale, all experimental and theoretical curves are identical to within system-dependent but temperature-independent scaling factors of the order of unity. This quasi-universality extends over a surprising broad $T$ range, at least up to $\kappa T\sim 1.5\Delta$.

• Received 26 November 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.157204