Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 47 (2014)

Disappearance of gapped Mott insulating phase neighboring
Boseglass phase in Tl1−x Kx CuCl3 detected by longitudinal-field muon
spin relaxation†

†

∗1
∗2
∗3
∗4

Condensed from the article submitted to J. Phys. Soc. Jpn.
College of Engineering, Shibaura Institute of Technology
RIKEN Nishina Center
Faculty of Science and Technology, Sophia University
Department of Physics, Tokyo Institute of Technology- 250 -

Corrected Asymmetry

1.0
LF 65 G0.8

182 mK72 mK
25 mK

0.60.40.20031.0t (µs)

69LF 200 G
182 mK
72 mK
25 mK

0.8
0.6
0.4

Corrected Asymmetry

Corrected Asymmetry

TlCuCl3 and KCuCl3 are isostructural, and arethree-dimensionally coupled Cu 3d S =1/2 spin dimer
systems. The ground states are spin singlets with excitation gaps of ∆ = 7.5 K in TlCuCl3 and 31 K in
KCuCl3 , originating from strong intradimer antiferromagnetic interaction J. Applying magnetic ﬁelds to
the gapped state, the spin gap is collapsed, and a magnetically ordered state appears, which is qualitativelywell described by the magnon Bose-Einstein condensation (BEC) theory1) . Describing the magnetic statesby magnon motions, the spin singlet state corresponds
to the gapped Mott Insulating (MI) phase.
By introducing randomness in the intradimer interaction, a new phase, Bose glass (BG) phase wastheoretically predicted to appear at T = 0 neighboring the magnon BEC phase2) . In the mixed system
Tl1−x Kx CuCl3 , the randomness of the local chemical
potential is introduced spatially, because the value ofthe dominant intradimer interaction J, which corresponds to the local potential of magnons, is diﬀerent
between TlCuCl3 and KCuCl3 3) . Recently, Yamada
et al. performed electron-spin resonance (ESR) measurements on Tl1−x Kx CuCl3 with x = 0.22 and 0.44
in resonance ﬁelds close to the critical ﬁeld of BEC
transition which is conﬁrmed by speciﬁc heat measurements, and reported the change of the spectrum
shape from Lorentzian shape to the intermediate shape
between Gaussian and Lorentzian4) . This result suggests the localization of magnons at suﬃciently lowtemperature, and suggest the appearance of the BG
phase adjacent to the BEC phase. According to thetheoretical prediction, the BG phase appears between
the gapped MI phase and the BEC phase, and there
exist a quantum phase transition point HB from theBG phase to the gapped MI phase with decreasing themagnetic ﬁeld. However, magnetization measurementssuggest HB =0. Thus, whether or not the gapped MIphase neighboring the Bose glass phase disappears inthe zero-ﬁeld limit is a controversial problem. The purpose of this study is to microscopically investigate thisproblem using LF - µSR technique.
Figure 1 shows temperarature dependence of LF µSR time spectrum of Tl1−x Kx CuCl3 with x = 0.40
down to 25 mK in various longitudinal ﬁelds. All time
spectra are analyzed using the stretched exponential

Corrected Asymmetry

T. Suzuki,∗1,∗2 H. Guo,∗2 I. Kawasaki,∗2 I. Watanabe,∗2 T. Goto,∗3 K. Katayama,∗4 and H. Tanaka∗40.2
003t (µs)

691.0
LF 100 G
320 mK110 mK25 mK

0.80.60.4
0.2003t (µs)

691
LF 500 G182 mK72 mK
25 mK

0.80.60.40.2003t (µs)

69Fig. 1. Temperature dependence of LF-µSR time spectrumof Tl1−x Kx CuCl3 with x = 0.40.

function A(t) = A0 exp(−λt)β , and are well ﬁtted asshown with solid lines. A0 is the initial asymmetry
and λ is the muon spin relaxation rate. Fitted results of β are almost constant for all spectra in a rangeof β = 0.8 ± 0.06, which is consistent with the previous data for x = 0.40 in longitudinal ﬁelds. LF-µSRtime spectra shows an exponential like decay, and themuon spin-relaxation rate does not has a signiﬁcanttemperature dependence down to 25 mK. As a ﬁtted
result, λ, which corresponds to a low frequency dynamical susceptibility, is almost constant down to 25
mK although slight changes in λ are observed. The
low frequency spectrum seems to be a white spectrum,
because λ in each ﬁeld is ﬁnite below 500 gauss. These
results mean that internal magnetic ﬁelds at the muonsites are ﬂuctuating by low frequencies below ∼ 1 MHz
down to 25 mK. When the spin system has a tendency
toward a magnetic phase transition, λ is expected toincrease with decreasing temperature in the zero-ﬁeldlimit below 500 gauss. Thus, in this case, a magnetic
ordered state is not experimentally expected, and theground state is a spin ﬂuctuating state. It is suggested
that the theoretically predicted quantum phase transition point from the Bose glass phase to the gapped
Mott insulating phase disappears, i.e. HB =0.
References
1) A. Oosawa, M. Ishii, and H. Tanaka, J. Phys. Condens.
Matter 11 (1999) 265.
2) O. Nohadani, S. Wessel, and S. Haas, Phys. Rev. Lett.
95 (2005) 227201.
3) A. Oosawa and H. Tanaka, Phys. Rev. B 65, (2002)
184437.
4) F. Yamada, H. Tanaka, T. Ono, And H. Nojiri, Phys.
Rev. B 83 (2011) 020409(R).