Triplon Localization Effect in Tl₁₋ₓKₓCuCl₃

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The effect of randomness on field-induced magnetic ordering was investigated through specific heat measurements in Tl₁₋ₓKₓCuCl₃ with x≤ 0.22. The isostructural parent compounds TlCuCl₃ and KCuCl₃ 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 Tl₁₋ₓKₓCuCl₃. The critical exponent ϕ of the phase boundary defined by T(H) ∝ (H-H c)¹/ϕ is reevaluated in TlCuCl₃ as ϕ=1.67 ± 0.07, which is close to ϕ BEC =3/2 derived from the triplon BEC theory. For x ≠ 0, the exponent ϕ 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 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 et al. [Phys. Rev. B 40, 546 (1989)].