Wilson ratio of a Tomonaga-Luttinger liquid in a spin-1/2 heisenberg ladder

Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-1/2 ladder compound (C ₇H ₁₀N) ₂CuBr ₂ at temperatures down to 45 mK. Low-temperature magnetic susceptibility as a function of field exhibits a maximum near the critical field H _c at which the magnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet. Above H _c a clear minimum appears in the magnetization as a function of temperature, as predicted by theory. In this field region, the susceptibility in conjunction with our specific-heat data yields the Wilson ratio R _W. The result supports the relation R _W=4K, where K is the Tomonaga-Luttinger-liquid parameter.