Triplon Localization Effect in Tl_{1-x}$K_xCuCl_3

The effect of randomness on field-induced magnetic ordering was investigated through specific heat measurements in Tl${}_{1-x}$K${}_x$CuCl${}_3$ with $x\leq 0.22$\mathrm{.}TheisostructuralparentcompoundsTlCuCl$_3$andKCuCl$_3$ are coupled spin dimer systems with a gapped ground state and their field-induced antiferromagnetic ordering is described by the Bose condensation of spin triplets (triplons). Well-defined field-induced phase transitions were observed in Tl${}_{1-x}$K${}_x$CuCl${}_3$. The critical exponent $\varphi$ of the phase boundary defined by $T(H)\propto (H-H_{\mathrm{c}}{)}^{1\mathrm{/}\varphi }$ is reevaluated in TlCuCl${}_3$ as $\varphi =1.67\pm 0.07$, which is close to ${\varphi }_{\mathrm{B}\mathrm{E}\mathrm{C}}=3\mathrm{/}2$ derived from the triplon BEC theory. For $x\mathrm{\ne }0$, the exponent $\varphi$ decreases systematically with $x$. The phase boundary observed at low temperatures for $x>0.1$ is almost a linear function of temperature $T$. In the low-field region for $H<H_{\mathrm{c}}$, no magnetic ordering is observed in spite of finite susceptibility. These properties are discussed in connection with the Bose glass phase argued by Fisher {\it et al.} [Phys. Rev. B {\bf 40}, 546 (1989)].