S Uji. T. Terashima, S. Uji. National Institute for material Science. Ibaraki, Japan
... 2 A quantum spin liquid state in 2D organic Mott insulator .... Hubbard model.
Collaborators Physics
seminar at 清華大学 高等研究院
Quantum `spin-metal' phase in an organic Mott insulator with two-dimensional triangular g lattice Takasada Shibauchi 芝内 孝禎 （京都大学） Department of Physics, Kyoto University Sakyo-ku Kyoto, Sakyo-ku, Kyoto Japan
Kyoto University
Current projects in Matsuda-Shibauchi group in Kyoto Iron-pnictide superconductivity
Heavy-fermion superlattices
Nature (2012); Science (2012); PRLs (2009-12) (2009 12).
Science (2011); Nature Phys Phys. (2012); PRL (2012) (2012).
Hidden-order mystery in URu2Si2
Quantum spin liquids in triangular lattices
Science (2011); Nature Phys. (2012); PRL (2012).
Nat. Phys. (2009); Science (2010); Nat. Commun. (2012).
Collaborators
Collaborators
D. Watanabe, M. Yamashita, Y. Matsuda Department of Physics, Kyoto University Kyoto , Japan
H. M. Yamamoto, R. Kato RIKEN, Saitama, Japan
T Terashima, T. T hi S Uji S. National Institute for material Science Ibaraki, Japan
K. Behnia LPEM (CNRS-UPMC), ESPCI Paris France Paris,
I. Sheikin Grenoble High Magnetic Field Laboratory Grenoble, France Acknowledgement:
Kyoto University
N. Kawakami, Yong-Baek Yong Baek Kim, P. A. Lee, T. Senthil, and N. Nagaosa for discussions
Outline 1 Introduction 1. 2 A quantum spin liquid state in 2D organic Mott insulator 2. EtMe3Sb[Pd(dmit)2]2 with triangular lattice 3. Elementary excitations and phase diagram of the quantum spin liquid 4 Quantum spin metal: a novel phase in the Mott Insulator 4. 5 Summary 5. M.Yamashita et al., Nature Phys. 5, 44 (2009). M. Yamashita et al., Science 328, 1246 ((2010). ) D. Watanabe et al., Nature Commun. (2012).
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Introduction Quantum Liquid Q Quantum t fluctuation fl t ti prevents t conventional ti l ordering d i 4He
3He
Introduction Quantum spin liquid (QSL) A state of matter where strong quantum fluctuations melt the longrange magnetic ti order d even att absolute b l t zero ttemperature. t Spin Liquids are states which do not break any simple symmetry: neither spin-rotational symmetry nor lattice symmetry symmetry. P. W. Anderson, Mater. Res. Bull (1973), Science (1987).
Notion of QSL is firmly established in 1D 1D XXZ chain (S = 1/2) Spinon excitation (S=1/2, e=0) QSL No N LRO Gapless Algebraic spin correlation (critical phase)
Introduction QSLs in two and three dimensions Geometrical frustrations are required Classical
A large ground-state degeneracy
Quantum
Quantum fluctuation lifts the degeneracy and a QSL ground state may appear
Only a few candidate materials exist exist. Triangular lattice
3He
on graphite Organic compounds
Kagome lattice
Pyrochlore lattice
ZnCu3(OH)6Cl2 (Herbertsmithite) BaCu3V2O8(OH)2 (Vesigniete)
Na4Ir3O8 ・ ・
Introduction QSLs in two and three dimensions Geometrical frustrations are required Classical
A large ground-state degeneracy
Quantum
Quantum fluctuation lifts the degeneracy and a QSL ground state may appear
Only a few candidate materials exist exist. Triangular lattice
3He
on graphite surface
Organic compounds bulk
Introduction Organic Mott insulators with trianglar lattice κ-(BEDT-TTF)2Cu2(CN)3 EtMe3Sb[ Sb[Pd Pd((dmit) dmit)2]2
ET dmit
Strong candidates that host a QSL state
What kind of QSL is realized? Many types of QSL proposed • Resonating-valence-bond Resonating valence bond liquid • Chiral spin liquid • Quantum dimer liquid • Z2 spin liquid • Algebraic spin liquid • Spin Bose Metal • etc…
Elementary excitations S i Spinon with ith F Fermii surface f • Vison • Majorana fermions • etc…
Heisenberg spins on 2D triangular lattice Resonating Valence Bond (RVB) Liquid
Long-range order
Further fluctuations are required to realize a QSL
Superposition of different configurations Resonance between highly degenerated spin configurations leads to a liquid-like liquid like wavefunction. P. Fazekas and P. W. Anderson, Philos. Mag. (1974).
3-sublattice Néel order ((120°structure)) D. Huse and V. Elser, PRL (1988). L. Caprioti, A. E.E. Trumper, S. Sorella, PRL (1999). B. Bernu, C. Lhuillier, L. Pierre, PRL (1992).
Quantum spin liquid on a 2D triangular lattice H i Heisenberg b model d l ffor a ttriangular i l llattice tti 4 spin ring exchange model
P1234 = (s1 ⋅ s 2 )(s 3 ⋅ s 4 ) + (s1 ⋅ s 4 )(s 3 ⋅ s 2 ) − (s1 ⋅ s 3 )(s 2 ⋅ s 4 )
?
When J4>0
?
?
4-spin ring exchange yields a strong frustration
?
?
θ1−θ2+θ3−θ4=π
?
?
?
?
? ?
?
?
G. Misguich et al., PRB (1999). W. W LiMing, LiMing G. G Misguish, Misguish P. P Sindzingre, Sindzingre C. C Luhuiller, Luhuiller PRB (2000). (2000)
QSL with gapped excitations
?
? ?
Quantum spin liquid on a 2D triangular lattice Hubbard model
Non on--Magnetic Insulating phase near M M--I transition (Quantum spin liquid)
Morita-Watanabe-Imada, JPSJ (2002).
t’/t = 1
Metal
NMI
120⁰ Néel
Kyung-Tremblay, PRL (2006). Yoshioka-Koga-Kawakami, PRL (2010).
Energy resolutions of these calculations are not enough to discuss low energy excitations (E~J/100)
κ-(BEDT-TTF)2Cu2(CN)3 H
S
Spin 1/2
C
BEDT TTF molecule BEDT-TTF l l bis(ethylendithio)-tetrathiafulvalence
dimer Viewed from the top
Layer of BEDT-TTF Layer of anion (nonmagnetic)
J~250 K t /t = 1.06 t’/t 1 06 (Hückel Method)
Mott insulator : t~54.5 t 54 5 meV, meV tt’~57.5 57 5 meV and U~448 U 448 meV (U/t~8.2) (U/t 8 2)
κ-(BEDT-TTF)2Cu2(CN)3 1H
Spin 1/2
NMR
No internal magnetic field Y. Shimizu et al., PRL (2003).
dimer Layer of BEDT-TTF Layer of anion
J~250 K t /t = 1.06 t’/t 1 06 (Hückel Method)
μSR
F. L. Pratt et al., Nature (2011).
κ-(ET)2Cu2(CN)3 : inhomogeneity or phase separation 13C
NMR
8
LF-μSR T = 50 mK
Asym mmetry (%)
6
4
2
0 0
Y. Shimizu et al. PRB 73, 140407 (2006).
Relaxation curve below 300 mK two components
3950G 100G 50G 30G 20G 10G 7G 5G 3G ZF
S. Nakajima et al. ArXiv 1204.1785 3
6 Time (μs)
9
12
Microscopic phase separation between gapped and gapless regions
NMR recovery curve shows stretched exponential singlet region α> a ~ 1 nm More than 1000 times longer than the interspin distance!!
Itinerant excitation Homogeneous Extremely long correlation length
Spin liquid
κspin Residual R id l κ/T /T at T→0 K
M. Yamashita et al., Science 328, 1246 (2010).
Elementary excitations : gapless or gapped? 1 ΔT Q =κ l Wt
Thermal conductivity Quantum spin p liquid q conducts heat very well, as good as brass.
Brass ((Cu0.7+Zn0.3)) Spin liquid 5 yyen coin
Brass M. Yamashita et al., Science 328, 1246 (2010).
What kind of QSL state in EtMe3Sb[Pd(dmit)2]2 ? Gapless elementary excitations Remaining key question
Are they magnetic?
Spin-spin correlation function 1D S=1/2 Heisenberg
Haldane system (S = 1)
CuCl2∙2N(C5D5) Mag gnetization n
NENP
Gapless Power law (algebraic)
Kyoto University
Gap p Exponential
What kind of QSL state in EtMe3Sb[Pd(dmit)2]2 ? Gapless elementary excitations Remaining key question
Are they magnetic?
Uniform susceptibility and magnetization at low temperatures Magnetic torque+ESR (down to 30 mK up to 32 T) SQUID (Only down to ~4 K due to Curie contribution)
•Isotropic contribution from impurities is cancelled. cancelled Torque picks up only anisotropic components. •High sensitivity. Measurements on a tiny single crystal are possible.
Kyoto University
Magnetic torque measurements in EtMe3Sb[Pd(dmit)2]2
Uniform susceptibility and magnetization of QSL Susceptibility χ⊥plane
Magnetization M⊥plane 30 mK
T-independent and remains finite at TÆ0K
increases linearly with H
Gapless magnetic excitations (absence of spin gap)
Δ ∝ ξ −1
( ξ: magnetic correlation length, Δ: spin gap )
Divergence of ξ , i.e. i e QSL is in a critical state S z (r ) S z (0) ∝ r −η
Algebraic spin liquid
Uniform susceptibility and magnetization of QSL H How th QSL changes the h when h th the d degree off ffrustration t ti varies? i ? Deuteration Cation layer X = EtMe3Sb,
Three Me groups are deuterated
h9-dmit: pristine d9-dmit :deuterated
h9-dmit: d it Cp / T ~ 20 mJ/K J/K2moll d9-dmit : Cp / T ~ 40 mJ/K2mol
d9-dmit: dmit: h9-dmit:
Deuteration changes the low temperature specific heat. Presumably it reduces t’/t. S. Yamashita et al., Nature Commun. (2011).
Uniform susceptibility and magnetization of QSL Susceptibility χ⊥plane
Magnetization M⊥plane 30 mK
Deuteration changes the degrees of geometrical frustration.
Uniform susceptibility and magnetization of QSL Susceptibility χ⊥plane
Magnetization M⊥plane 30 mK
Deuteration changes the degrees of geometrical frustration.
Both h9- and d9-dmit dmit systems exhibit essentially the same paramagnetic behavior with gapless magnetic excitations.
B h systems are iin a critical Both i i l state d down to kBT~J/10,000
Phase diagram of the QSL Case-I
Case-II
d9-dmit h9-dmit
Quantum critical ‘phase’
D W D. Watanabe t b ett al., l Nature N t C Commun. 3 1090 (2012) 3, (2012).
Both h9-dmit and d9-dmit with different degrees of frustration exhibit essentially the same paramagnetic behavior with gapless magnetic excitations.
An extended quantum critical phase, rather than a QCP.
What kind of spin liquid is realized in dmit? Resonating-Valence-Bond theory
Spin liquid with spinon Fermi surface
Algebraic spin liquid
Quantum Dimer Model
Z2 spin liquid
Spin Bose Metal
Chiral spin liquid
What kind of spin liquid is realized in dmit? Gapless Spin Liquid
Gapped Spin Liquid
Gapless Fermionic spinon or spin Bose metal
Resonating-Valence-Bond theory
Spin liquid with spinon Fermi surface Quantum critical ‘phase’
Spin Bose Metal
Algebraic spin liquid
Gapped Bosonic spinon
Spin liquid with spinon Fermi surface?
Quantum critical iti l ‘‘phase’ h ’
A simple thermodynamic test assuming 2D Fermion with Fermi surface Pauli susceptibility
Specific heat coefficient C/T
γ~20mJ/K2 mol (experimental value)
Fermi temperature (exp. value)
These values are (semi-)quantitatively consistent with the theory of the QSL that possesses a spinon Fermi surface.
A new phase in a Mott insulator
Metal
Quantum `spin-metal’ phase
D. F. Mross and T. Senthil, PRB (2011).
Spin excitation behave as in Pauli paramagnetic metals with Fermi surface, even though the charge degrees of freedom are frozen.
Spin liquid with spinon Fermi surface? More direct methods to detect the spinon Fermi surface
Thermal Hall effect
Quantum oscillation
H. Katsura, N. Nagaosa and P. A. Lee, PRL (2010). O I. O. I Mitrunich, Mitrunich PRB (2006). (2006)
tanθH=κxy/κxx
κxy thermal Hall conductivity 0.23 K
M⊥(μB/diimer)
30 mK up to 35 T
1K D. Watanabe et al., Nature Commun. (2012).
No discernible oscillation M. Yamashita et al., Science (2010).
No discernible thermal Hall effect
The coupling between the magnetic field and the gauge flux may be weak. Z2 spin liquid with pseudo-Fermi surfaces? Barkeshli, Yao, Kivelson (2012).
Summary Ground state and phase diagram of the QSL in 2D organic Mott insulator EtMe3Sb[Pd(dmit)2]2 with triangular lattice Distinct residual thermal conductivity and paramagnetic susceptibility in the zero temperature limit. The QSL is an algebraic spin liquid with a magnetically gapless ground state, i.e. a critical state with infinite magnetic correlation length.
Essentially the same results in the deuterated sample with a different degree of geometrical frustration The emergence of an extended `quantum spin-metal phase' in the Mott insulator, in which the low-energy spin excitations behave as in Pauli paramagnetic metals with Fermi surface.
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M.Yamashita et al.,, Nature Phys. y 5,, 44 (2009). ( ) M. Yamashita et al., Science 328, 1246 (2010). D. Watanabe et al., Nature Commun. 3, 1090 (2012).
