Attractive Tomonaga-Luttinger Liquid in a Quantum Spin Ladder

We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines we determine the phase boundary and the order parameter of the low-temperature (3-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1 T^(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1