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Using micromechanical force magnetometry, we have measured the magnetizationof the strong-leg spin-1/2 ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_2$ attemperatures down to 45 mK. Low-temperature magnetic susceptibility as afunction of field exhibits a maximum near the critical field H_c at which themagnon gap vanishes, as expected for a gapped one-dimensional antiferromagnet.Above H_c a clear minimum appears in the magnetization as a function oftemperature as predicted by theory. In this field region, the susceptibility inconjunction with our specific heat data yields the Wilson ratio R_W. The resultsupports the relation R_W=4K, where K is the Tomonaga-Luttinger-liquidparameter.

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