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 $x\leq 0.22$. The isostructural parent compounds TlCuCl$_3$ and KCuCl$_3$ 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 $\phi$ of the phase boundary defined by $T(H) \propto (H-H_{\rm c})^{1/\phi}$ is reevaluated in TlCuCl$_3$ as $\phi=1.67 \pm 0.07$, which is close to $\phi_{\rm BEC} =3/2$ derived from the triplon BEC theory. For $x \neq 0$, the exponent $\phi$ 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 $H<H_{\rm c}$, 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)].