Quantum critical behavior in the highly random systemTl1−xKxCuCl3probed by zero- and longitudinal-field muon spin relaxation

Abstract

Zero-and longitudinal-field muon-spin-relaxation ͑LF-SR͒ measurements were carried out on the randomness-introduced quantum spin system Tl 1−x K x CuCl 3 . The relative temperature change in the muon-spinrelaxation rate in longitudinal-fields, which corresponds to the wave-vector integration of the generalized dynamical susceptibility, was deduced from LF-SR measurements. Peak structure in the relative temperature change of for x = 0.60 is observed at T ϳ 3 K in 3950 G, and the temperature where the peak is observed decreases with decreasing the magnetic field. This behavior is interpreted as the soft mode of spin waves in the vicinity of the quantum critical point.

Low-energy spin dynamics in randomness-introduced spin-gap systemsTl1−xKxCuCl3Suzuki1, Yamada2, Yamada3 et al. 2010Phys. Rev. BSelf Cite

“…1 with solid lines. For all samples in this study, the temperature dependence of ␤ shows almost the same tendency as reported for x = 0.51 and 0.60, 33 namely, ␤ is ϳ1.5 at 8-10 K, decreases with decreasing temperature, and saturates to 0.5-0.6. In the case of x = 0.60 and 0.65, the time spectrum becomes to show a faster relaxation down to 3 K, and below 3 K, the relaxation changes to be slower with decreasing temperature.…”

“…33 The observed soft mode suggests that the system has strong spin fluctuations toward a magnetic phase transition. However, it is obscure at this stage whether or not this mode is headed for the BG phase, because the strong randomness could cause the transition to a magnetically ordered state.…”

“…The LF-SR measurements are suitable for this purpose. 33,[38][39][40] Thus, to obtain the microscopic information about the appearance of the BG phase and of other magnetic phases, we carried out ZFand LF-SR measurements in the wide region of x from 0.40 to 0.65.…”

Bose-Einstein condensation in quantum magnets

“…Thus Bose glass behavior occurs in the intermediate regime of magnetic field for which the spin gaps for some magnetic ions have been suppressed to zero but not others. Bose glass behavior due to bond doping has been studied in several materials including IPA-CuCl 3−x Br x (Saito et al, 2006;Adachi et al, 2007;Manaka, Kolomiets, and Goto, 2008;Manaka et al, 2009;Hong et al, 2010), Tl 1−x K x CuCl 3 (Shindo and Tanaka, 2004;Suzuki et al, 2009Suzuki et al, , 2010Yamada et al, 2011), and DTN (Yu et al, 2012;Wulf et al, 2013).…”

“…The atomic physics counterpart of this phenomenon is the transition between BECs of atoms and diatomic molecules that may occur whenever the interatomic interaction is attractive. Moreover, the same S ¼ 1 model on frustrated lattices, such as triangular or face centered cubic, contains a phase in which crystal or Ising-like ordering coexists with a BEC of pairs or spin-nematic ordering for large enough anisotropy (Boninsegni and Prokof'ev, 2005;Heidarian and Damle, 2005;Wessel and Troyer, 2005;Suzuki and Kawashima, 2007) (see discussion at the end of Sec. IV).…”