Repulsive Tomonaga-Luttinger liquid in the quasi-one-dimensional alternating spin- 12 antiferromagnet NaVOPO4

We probe the magnetic field-induced Tomonaga-Luttinger liquid (TLL) state in the bond-alternating spin-$1/2$ antiferromagnetic (AFM) chain compound NaVOPO₄ using thermodynamic as well as local μSR and ³¹P NMR probes down to mK temperatures in magnetic fields up to 14 T. The μSR and NMR relaxation rates in the gapless TLL regime decay slowly following characteristic power-law behavior, enabling us to directly determine the interaction parameter K as a function of the magnetic field. These estimates are crosschecked using magnetization and specific heat data. The field-dependent K lies in the range of $0.4<K<1$ and indicates the repulsive nature of interactions between the spinless fermions, in line with the theoretical predictions. This renders NaVOPO₄ the first experimental realization of TLL with repulsive fermionic interactions in hitherto studied $S=1/2$ bond-alternating AFM-AFM chain compounds.