Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

By means of nuclear spin-lattice relaxation rate T₁^-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 NiCl₂-4SC(NH₂)₂ and the spin-ladder system (C₅H₁₂N)₂CuBr₄. 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, T₁^-1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T₁^-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.