#### Abstract

By means of nuclear spin-lattice relaxation rate ${T}_{1}^{-1}$, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system ${\mathrm{NiCl}}_{2}\mathrm{\text{\u2212}}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2}$ and the spin-ladder system $({\mathrm{C}}_{5}{\mathrm{H}}_{12}\mathrm{N}{)}_{2}\mathrm{Cu}{\mathrm{Br}}_{4}$. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, ${T}_{1}^{-1}$ exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for ${T}_{1}^{-1}$, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

- Received 29 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.177206

© 2012 American Physical Society