Rb-NMR study of the quasi-one-dimensional competing spin-chain compound Rb2Cu2Mo3O12

A Rb-NMR study has been performed on the quasi-one-dimensional competing spin chain $\mathrm{R}{\mathrm{b}}_{2}\mathrm{C}{\mathrm{u}}_{2}\mathrm{M}{\mathrm{o}}_{3}{\mathrm{O}}_{12}$ with ferromagnetic and antiferromagnetic exchange interactions on nearest-neighboring and next-nearest neighboring spins, respectively. The system changes from a gapped ground state at zero field to a gapless state at ${H}_{\mathrm{C}}\ensuremath{\simeq}2\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, where the existence of magnetic order below 1 K was demonstrated by a broadening of the NMR spectrum, associated with a critical divergence of $1/{T}_{1}$. In the higher-temperature region, ${T}_{1}^{\ensuremath{-}1}$ showed a power-law-type temperature dependence, from which the field dependence of the Luttinger parameter $K$ was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.