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

RIKEN Accel. Prog. Rep. 55 (2022)

RIKEN Accel. Prog. Rep. 55 (2022)

μ+ SR Knight shift of the Mott insulator κ-(ET)4 Hg2.78 Cl8D. P. Sari,∗1,∗2 Y. Cai,∗3,∗4 M. -V. deToro Sanchez,∗5,∗4 K. Kojima,∗3,∗4 I. Watanabe,∗2 Y. Ishii,∗1 andH. Taniguchi∗6The hole-doped organic superconductor κ(ET)4 Hg3-δ Br8 , (κ-HgBr), where δ = 11% and ET= bis (ethylenedithio) tetrathiafulvalene, has been thekey to bridge the knowledge gap between half-ﬁlled organics and doped cuprate systems, as the well-known
Mott-Hubbard model in the laboratory. Usually, organic superconductivity appears under pressure when
the ratio of Hubbard interaction and bandwidth, U/W,
is larger than 1. Nonetheless, the triangular lattice oforganics, unlike the square lattice in cuprates, provides
extensive geometrically control through nearest, t, andnext-nearest, t , transfer integrals between sites. In thecase of geometrically triangular frustration (t ∼ t ),the Mott insulating state cannot be magnetically ordered down to the miliKelvin (mK) order, becoming
a Mott quantum spin liquid.1) Speciﬁcally, both holedoped superconductors have a region corresponding toa strange metallic state at which resistivity exhibits alinear temperature dependence, ρ ∝ T , which is not a
Fermi-liquid (FL) behavior.1–3)
In 2015, an important model to study strange metal
was developed by Sachdev-Ye-Kitaev (SYK).4,5) It
consists of Majorana fermions with random all-toall interactions, leading to quantum information science and quantum many-body physics. Although therealization of the SYK-strange metal remains complex, Tsuji-Werner theoretically found an SYK-strange
metal region after an out-of-time-order correlation
treatment of a multi-band Hubbard model.6) In thestrange metal region, the electron behaves as a systemhaving a non-FL electronic scattering rate with ρ ∝ T .
In this region, the spin ﬂuctuates strongly while adjusting the competition between the localized spin in
the Mott insulating state and the itinerant one in theFL state, and U/W should be close to unity, which
is known as a quantum critical point (QCP).6) Cha etal. further showed that when the itinerant spin-1/2
fermions interact via onsite U and random inﬁniteranged spin-spin interaction, the QCP appears withquantum spin liquid dynamics, identical to that of
SYK-local spin dynamics.7) On the other hand, thegrowth of antiferromagnetic spin ﬂuctuations (AFSFs)
towards low temperature without any long-range order can lead to the QCP at which a non-FL behavior
is observed, like in the heavy fermion system.1)
Our experiment8) showed that the time-reversal∗1∗2∗3∗4∗5∗6

College of Engineering, Shibaura Institute of Technology
RIKEN Nishina Center
SBQM Institute, University British Columbia
CMMS, TRIUMF
School of Physics and Astronomy, University of Edinburg
Department of Physics, Saitama University

symmetry is preserved in the superconducting stateof κ-HgBr down to 0.3 K, narrowing the similarity
down to that of cuprates despite the triangular lattice. To seek evidence of strong AFSFs towards theMott spin-liquid ground state, we also study the sister insulating compound, which has a diﬀerent doping
content yet slightly higher U/W than that of κ-HgBr,
κ-(ET)4 Hg3-δ Cl8 (κ-HgCl), with δ = 22%. It shows ametal-insulator transition at TMI = 20 K and ambientpressure.
The signature of strong AFSFs has been observed in
κ-HgBr, in which the temperature dependence of μ+
Knight shift, K(T ), is not proportional to that of susceptibility, χ(T ) in the low-temperature region below
50 K, unlike in other κ-type organic superconductors;
this signature is often found in heavy-fermion system.1)
One possible reason is that μ+ probes a hyperﬁne coupling constant diﬀerent from itinerant electrons in thehigh-T region and localized electrons. From the linear
part of the K -χ plot from 50 to 300 K, the hyperﬁnecoupling constant, Ahf , in κ-HgBr was reported to be
166 Oe/μB . If this deviation is a signature of such a
diﬀerent hyperﬁne coupling constant, we naively expect a larger Ahf in κ-HgCl.
We have followed the same experimental condition
to measure the μ+ Knight shift in κ-HgCl with thatof κ-HgBr.9) The measurement was performed using
DC muon beam on the NuTime spectrometer in M15
beamline, TRIUMF Canada, in a ﬁeld of 6 T. Figure 1shows the measured μ+ SR time spectra after Fouriertransforming. From 300 down to 2 K, the central peakis gradually shifted to the positive side, and a prominent shift was detected below TMI . K(T ) follows Curie-Fig. 1. Fourier transform of μ+ SR time spectra in the ﬁeldof 6 T in κ-(ET)4 Hg2.78 Cl8 measured at several temperatures, represented by colorful lines, from 276–2 K.

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

RIKEN Accel. Prog. Rep. 55 (2022)

Weiss paramagnetic behavior well while χ(T ) has abroad peak at 70 K. From the linear region of the K -χplot above 100 K, our preliminary analysis obtained
Ahf = 230(20) Oe/μB . The value is about 40% larger
than that of κ-HgBr. Next, we are going to study thespin dynamics of κ-HgCl down to the mK order.
References
1) H. Oike et al., Nat. Commun. 8, 756 (2017).
2) B. Keimer et al., Nature 518, 179 (2015).
3) H. Taniguchi et al., J. Phys. Soc. Jpn. 76, 113709(2007).
4) S. Sachdev, J. Ye, Phys. Rev. Lett. 70, 3339 (1993).
5) A. Kitaev, J. Suh, J. High Energy Phys. 183 (2018).
6) N. Tsuji, P. Werner, Phys. Rev. B 99, 115132 (2019).
7) P. Cha et al., Proc. Natl. Acad. Sci. U.S.A. 31, 18341(2020).
8) D. P. Sari, RIKEN Accel. Prog. Rep. 54, S30 (2021).
9) K. Satoh et al., Physica B 404, 597 (2009).

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