Specific heat study of the field-induced magnetic ordering in the spin-gap system ${\mathrm{TlCuCl}}_3$

Specific heat measurements have been performed in the coupled dimer system ${\mathrm{TlCuCl}}_3,$ which has a singlet ground state with the excitation gap $\Delta \simeq 7.5$ K. The cusplike anomaly indicative of the three-dimensional magnetic ordering was clearly observed in magnetic fields higher than the critical field $H_{\mathrm{g}}$ corresponding to the gap $\Delta .$ The phase boundary determined by the present specific heat measurements coincides with that determined by previous magnetization measurements. The phase boundary can be described by the power law $\left[H_{\mathrm{c}}\mathrm{}\right(T\left)\mathrm{}-H_{\mathrm{g}}\right]\propto T^{\phi }$ with $\phi =2.1\mathrm{}\left(1\right).$ This result supports the magnon Bose condensation picture for the field-induced magnetic ordering in ${\mathrm{TlCuCl}}_3$ [Nikuni et al., Phys. Rev. Lett. 84, 5868 (2000)].