Direct Determination Of The Tomonaga-Luttinger Parameter K In Quasi-One-Dimensional Spin Systems

We test the analytical formula for the enhancement of the nuclear magnetic resonance rate T-1(-1) by the critical spin fluctuations, over the simple power-law dependence predicted for a purely one-dimensional spin system, recently derived in the random phase approximation [M. Dupont et al., Phys. Rev. B 98, 094403 (2018)]. This prediction is experimentally confirmed by excellent fits to the published temperature dependence of T-1(-1) data in the two representative spin compounds, (C7H10N)(2)CuBr4 (DIMPY) and BaCo2V2O8, providing at the same time a direct and convenient experimental determination of the Tomonaga-Luttinger-liquid parameter K, very well in agreement with theoretical predictions.