Direct determination of the Tomonaga-Luttinger parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> in quasi-one-dimensional spin systems
M. Horvatić, M. Klanjšek, E. Orignac
Abstract
We test the analytical formula for the enhancement of the nuclear magnetic resonance rate ${T}_{1}^{\ensuremath{-}1}$ 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 ${T}_{1}^{\ensuremath{-}1}$ data in the two representative spin compounds, ${({\mathrm{C}}_{7}{\mathrm{H}}_{10}\mathrm{N})}_{2}{\mathrm{CuBr}}_{4}$ (DIMPY) and ${\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, 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.