Wilson Ratio of a Tomonaga-Luttinger Liquid in a Spin-1/2Heisenberg Ladder

Using micromechanical force magnetometry, we have measured the magnetization of the strong-leg spin-$1/2$ ladder compound $({\mathrm{C}}_7{\mathrm{H}}_{10}\mathrm{N}{)}_2{\mathrm{CuBr}}_2$ 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.