Spin frustration and Mott criticality in triangular-lattice organics

under controlled Mottness

2013 Hangzhou Workshop on Quantum Matter, April 22, 2013

K. Kanoda, Applied Physics, Univ. of Tokyo

1. Ground states: SL vs AFM

2. Weak/strong Mott transitions from SL/AFM

3. Quantum criticality at high temperatures

(4. Doped triangular lattice)

H. Oike, T. Furukawa, Y. Shimizu (Nagoya Univ.), H. Hashiba, Y. Kurosaki, K. Umeda, K. Miyagawa,

S. Yamashita, Y. Nakazawa

M. Maesato, G. Saito (Meijo Univ.)

H. Taniguchi

Univ. of Tokyo

Kyoto Univ.

Osaka Univ.

Saitama Univ.

Outline

Mott physics in 2D organics

N. Mott (1949)

?U/W (Mottness)

Tem

pera

ture

AF/SLSC

Mott insulator Metal

Anderson (1973)

Mott transition

Criticality ?

Charge

Frustration

AF or Spin Liq. ?

SpinSuperconductivity

Pairing origin ?

Charge/Spin

Onnes (1911)

All in one material

-(ET)2X; quasi-triangular lattice systems

ET+0.5

t’

t t

t’

t t

t’

t t

t’

t t

Ab initio Kandpal et al.(2009)Nakamura et al.(2009)

0.687.2Metal (SC)Cu[N(CN)2]Br

0.757.5Mott ins.Cu[N(CN)2]Cl

6.5

6.6

6.8

6.8

8.2

U/t

0.58Metal (SC)I3

0.60Metal (SC)Ag(CN)2 H2O

0.68Metal (SC)Cu(CN)[N(CN)2]

0.84Metal (SC)Cu(NCS)2

1.06Mott ins.Cu2(CN)3

t’/tX-

0.687.2Metal (SC)Cu[N(CN)2]Br

0.757.5Mott ins.Cu[N(CN)2]Cl

6.5

6.6

6.8

6.8

8.2

U/t

0.58Metal (SC)I3

0.60Metal (SC)Ag(CN)2 H2O

0.68Metal (SC)Cu(CN)[N(CN)2]

0.84Metal (SC)Cu(NCS)2

1.06Mott ins.Cu2(CN)3

t’/tGround state

at ambient pressureX-

0.687.2Metal (SC)Cu[N(CN)2]Br

0.757.5Mott ins.Cu[N(CN)2]Cl

6.5

6.6

6.8

6.8

8.2

U/t

0.58Metal (SC)I3

0.60Metal (SC)Ag(CN)2 H2O

0.68Metal (SC)Cu(CN)[N(CN)2]

0.84Metal (SC)Cu(NCS)2

1.06Mott ins.Cu2(CN)3

t’/tX-

0.687.2Metal (SC)Cu[N(CN)2]Br

0.757.5Mott ins.Cu[N(CN)2]Cl

6.5

6.6

6.8

6.8

8.2

U/t

0.58Metal (SC)I3

0.60Metal (SC)Ag(CN)2 H2O

0.68Metal (SC)Cu(CN)[N(CN)2]

0.84Metal (SC)Cu(NCS)2

1.06Mott ins.Cu2(CN)3

t’/tGround state

at ambient pressureX-

0.80

0.44

X-1

Mott phase diagrams of quasi-triangular lattices

QSL FLSC

Critical endpoint

P (MPa)

T(K

)

QSL FLSC

Critical endpoint

P (MPa)

T(K

)

P (MPa)

T (K)

AFI

Critical endpoint

FLSC

P (MPa)

T (K)

AFI

Critical endpoint

FLSC

0.33

>10

1

R/Rc

-(ET)2Cu2(CN)3 t’/t=0.80-1.0

-(ET)2Cu[N(CN)2]Cl t’/t=0.44-0.75

t’

t t

t’

t t

t’

t t

t’

t t

Similar QC behavior at high T

Dissimilar at low T

frustrated less frustrated

-(ET)2Cu2(CN)3 t’/t ~ 0.80-1.06

AFIAFIAFI

-(ET)2Cu[N(CN)2]Cl t’/t ~ 0.44-0.75Kagawa et al., Nature 2005 , PRL 2004; PRB 2004,

Kurosaki et a., PRL 2005, Furukawa et al.unpublished

Spin liquid

Separation of charge localization and spin ordering on triangular lattice

Highly correlated particles

Uncorrelated waves

AF insulator Metal/SC

(U/W)Mott

AF insulator Metal/SCSpin liq.

U/W

Frustrated lattice

correlated particle/wave

Thermodynamic anomaly at 6K in -(ET)2Cu2(CN)3

Specific heat S. Yamashita et al., Nature Phys. 4 (2008) 459

Thermal expansion coefficient Manna et al., PRL 104 (2010) 016403

Thermal conductivity M. Yamashita et al., Nature Phys. 5 (2009) 44

NMR Relaxation rate Shimizu et al., PRB 70 (2006) 060510

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10Temperature (K)

(a)

13C NMRrelaxation rate

Inhomogeneous relaxation0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10Temperature (K)

(a)

13C NMRrelaxation rate

Inhomogeneous relaxation0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7 8 9 10Temperature (K)

(a)

13C NMRrelaxation rate

Inhomogeneous relaxation

BBBBBBBBBBBBBBBBBBBBB

BBBB

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B

BB

JJJJJJJJJJJJJJJJJJJJJ

JJJJ

JJJJJJJJJJJJJJJJ

JJJJ

J

J

J

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30

TEMPERATURE (K)

BBBBBBBBBBBBBBBBBBBBBBBBB

BBBBBBBBBBBB

BBBBBB

BBB

B

B

BB

JJJJJJJJJJJJJJJJJJJJJJJJJ

JJJJJJJJJJJJJJJJJJJJJ

J

J

JJ

11111111111111111111111

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

TEMPERATURE (K)

13C NMR under a parallel field

B

-400 -200 0 200 400 600 800SHIFT from TMS (ppm)

20 K

18 K

16 K

14 K

12 K

10 K

8 K

6 K

4 K

2 K

-ET2Cu2(CN)3Magic Angle

a axis

line shift

line width

a decrease in local

line broadeningField-induced spin texture ?

6K

Degenerate spinons (Motrunich, P.A. Lee, Senthil)

Spin liquid in -(ET)2Cu2(CN)3; Gapless or marginally gapped

0

25

50

75

100

125

150

0 1 2 3 4 5 6

■　 0T

▼ 　 1T

● 　 4T

◆ 　 8T

■　 0T

▼ 　 1T

● 　 4T

◆ 　 8T

CPT

-1 /

mJ

K-2

mol

-1

T2 (K2)

Spin liquid -(E

T) 2Cu 2

(CN) 3

AF insulator -(ET) 2

X, ’-(ET) 2

ICl 2

S. Yamashita et al., , Nature Phys. 4 (2008) 459

Specific heat gapless (= 13-14 mJ/K2mol)

0

50

T2 (K2)

Thermal conductivity gapped; 0.46 K

M. Yamashita et a., Nature Phys. 5 (2009) 44

-(ET)2Cu2(CN)3

= 13-14 mJ/K2mol

Nuclear Shottky

Criticalpoint

Mott Insulator

Metal

Criticalpoint

Mott Insulator

Metal

Kagawa et al., Nature 436 (2005) 534

Conductivity

Strong Mott transition from antiferromagnet

Resistance

-(ET)2Cu[N(CN)2]Cl

AFIAFIAFI

-(ET)2Cu2(CN)3

Senthil et al., PRB (2008) and pfreprint

Weak Mott transition from spin liquid

Spin liquid

Phase diagram

11K

9K

7K

5K

1~10 h/e2

Resistivityjump

Quantum Mott transition from spin liquid

T P

T-dependence of P-dependence of

~8h/e2

-m=cf(zv/T)

zv =0.68

P(MPa)T(K)

R(ohm)

P(MPa)T(K)

R(ohm)

P

Mott transition seen in spin degrees of freedom

-(ET)2Cu[N(CN)2]Cl t’/t=0.44-0.75

less frustrated

-(ET)2Cu2(CN)3 t’/t=0.80-1.0

frustrated

-1

0

1

2

3

4

5

79.07 79.12 79.17 79.22 79.27 79.32

Frequency [MHz]

5MPa

110MPa

155MPa

175MPa

190MPa

79.279.1 79.3

-1

0

1

2

3

4

5

79.07 79.12 79.17 79.22 79.27 79.32

Frequency [MHz]

5MPa

110MPa

155MPa

175MPa

190MPa

79.279.1 79.3

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200Pressure [MPa]

5K

2K

P

NMR

NMR spectra

NMR spectra

Mott trans

metal

insulator

Mott trans

Holon-doublon pair excitation costs more in AF than in SL

AF

SL

J

U-V(r) +8J

U-V(r) +JExotic charge excitations in spin liquid state fermionic; Ng & P.A. Lee, PRL 99 (2007) 156402. bosonic; Qi & Sachdev: PRB 77 (2008) 165112

Miyagawa et al., PRL89 (2002) 017003

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 10 100Temperature (K)

-(ET)2Cu

2(CN)

3 13C NMR

0 kbar (inner)

4.3 kbar (3.5 T)

4.3 kbar (2.0 T)

~T3

TC

Not pseudo-gapped

Not pseudo-gapped nearby spin liq.

EEEEEEEEEEEEEEEEEEEEE

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JJJJJJJJJJJJJ

BBB

BBBBBBBB

B

BB

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EEEEEEEE

0.005

0.01

0.1

1

1 10 100 1000TEMPERATURE (K)

J

JJJJ

JJJJJJJ

JJJJ

JJJJJJJJJJJJJ

0

0.01

0.02

0.03

0.04

0.05

0.06

0 5 10 15 20 25 30TEMPERATURE (K)

13C NMR

TC

H // conducting layer

13C NMR

(a)

(b)Pseudo-gapped

AFIAFIAFI

Pseudo-gapped nearby AFM

13C NMR 1/T1T

Spin liquid

Deuterated -Br

Shimizu et al., PRB 81 (2010) 224508

-Cu2(CN)312K

3-4 K

Pseudo-gap　killed　by　field　and　pressure

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II

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0

0.5

1

1.5

2

0 10 20 30 40 50 60Temperature (K)

TC

11THH

13C-NMR H // b axis

15.5T

pseudogap

0.9T3.8T

00.010.020.030.040.050.060.070.080.090.1

0.11

0 5 10 15 20 25 30 35 40 45 50 55 60 65T[K]

1/T1

T[sec

-̂1]

04MPa20MPa50MPa100MPaAmbient(*1)

Tc1/T

1T(1

/sK

)

Pressure

Field dependence Pressure dependence

PG has connection with superconductivity as well as spin fluctuations

Ground　states　of　　　　　　　　　　　　　　　　　with　half-filling

AF

SL

SC

Metal

t’

t t

t’

t t

t’

t t

t’

t t

Mottness (U/W)

Fru

stra

tion

(t’/

t)

Strong Mott from AFPseudo-gappedHigh Tc

Weak Mott from SLgapless

Not pseudo-gappedlow Tc

e-

e- e-

e-

e-

-

- -

-

e-

e- e-

e-

e-

-

- -

-

e-

e- e-

e-

e-

-

- -

-

e-

e- e-

e-

e-

-

- -

-t’/t =1

t’/t <1

gapless-(ET)2Cu2(CN)3

-(ET)2Cu[N(CN)2]Cl

tow

ard

squa

re la

ttic

e

triangle

(U/W)critical

PG

DMFT of Hubbard model at high temperatures

Quantum Critical Transport Near the Mott Transition H. Terletska et al., PRL 107 (2011)

Resistivities (T,δ) are scaled with the one parameter, T/T0

Characteristic energy, T0∝δzv

quantum criticality

T

δ=(t/U)-(t/U)c

T - t/U phase diagram

t/U

T

vs T calc.

vs T/T0 　 calc.

Mott Ins. Fermi Iiq.

Zv=0.57

T0∝ δ zv

High-T scaling of resistivity for -(ET)2Cu2(CN)3

cf. zv =0.57 (DMFT)

T/T0

(T, )=c(T)f(T/T0)

f(T/T0)= exp[(T/T0)1/zv]

-(ET)2Cu2(CN)3

QSL FLSC

Critical endpoint

P (MPa)

T(K

)

QSL FLSC

Critical endpoint

P (MPa)

T(K

)

Zv=0.60±0.05T0=c zv

35K, 40K, 45K, 50K, 55K, 60K, 65K, 70K, 75K, 80K, 90K, 100K, 110K

P<Pc

Nearly perfect !

0.33

>10

1

R/Rc

0.33

>10

1

R/Rc

P>Pc

P>Pc

T/T0

~T 2

35K, 40K, 45K, 50K, 55K, 60K, 65K, 70K, 75K, 80K, 90K, 100K, 110K

T0 ∝ δ zv

High-T scaling of resistivity for -(ET)2Cu[N(CN)2]Cl

cf. zv =0.57 (DMFT)

T/T0

(T, )=c(T)f(T/T0)

f(T/T0)= exp[(T/T0)1/zv]

-(ET)2Cu2(CN)3

Zv=0.50±0.05T0=c zv

P<Pc

P (MPa)T (K

)

AFI

Critical endpoint

FLSC

P (MPa)T (K

)

AFI

Critical endpoint

FLSC

P<Pc

P>Pc

0.33

>10

1

R/Rc

0.33

>10

1

R/Rc

Quantum phase transitionT

(K

)

DoniachQ

CP

AF Fermi Liq.

Heavy electrons

RKKY vs Kondo

Mott

Kinetic energ vs Coulomb

T (

K) U

W

Mott transition

~5000 K

20 Kt

Fermi liq.Mott ins.

Doped triangular lattice

U/t t’/t

1/2-filled systems>-(ET)2Cu2(CN)3 8.20 1.06-(ET)2Cu[N(CN)2]Cl 7.58 0.74-(ET)2Cu[N(CN)2]Br 7.20 0.68-(ET)2Cu(NCS)2 6.98 0.86-(ET)2I3 6.48 0.58

(U/t)critical

Metal/SC

Mott insulator

Mot

t in

sula

tor

-(ET)4Hg2.89Br8　　---11% hole doped/ET2

Hg3-X8 (X=Br, Cl)

(ET)2+1+ Hole dopingET layer

X layer

-(ET)4Hg2.89Br8 10.01 1.02 Metal/SC

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0 50 100 150 200 250 300

T(K)

⊥

∥

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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

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0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 50 100 150 200 250 300Temperature (K)

E a�C pade[6,6]J=150K

Ñ pade[6,6]J=160K

D pade[7,7]J=150K

A pade[7,7]J=160K

Triangular LatticeHeisenberg model

J =160 K

J =150 K

Spi

n(e

mu/

mol

e of

ET

dim

er)

Taniguchi et al.

Spin susceptibility

Well fitted to triangular-lattice HeisenbergJ=150 K

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0 50 100 150 200 250 300

T(K)

⊥

∥

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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

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0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 50 100 150 200 250 300Temperature (K)

E a�C pade[6,6]J=150K

Ñ pade[6,6]J=160K

D pade[7,7]J=150K

A pade[7,7]J=160K

Triangular LatticeHeisenberg model

J =160 K

J =150 K

Spi

n(e

mu/

mol

e of

ET

dim

er)

Taniguchi et al.

Spin susceptibility

Well fitted to triangular-lattice HeisenbergJ=150 K

Hall coefficient

Lyubovslaya (1986)

P (GPa)

d(1/

R H)/

dP (C

/cm

3/G

Pa) 10K

Compressibility of 1/RH

Conductivity of -(ET)4Hg2.89Br8 measured by contactless method under pressure

Non-Fermi liq. Fermi liq. by pressure

Non-Fermi liq.

Fermi liq.

//∝T

//∝T 2

Temperature (K)

//

(

m

cm)

sample#3

Tem

pera

ture

(K)

Pressure(GPa)

sample#3

Tem

pera

ture

(K)

Pressure(GPa)

R = r0 + aT

Possible quantum phase transition

U>W U<WDouble occupancy

forbiddenSmall FS ?

(Doped Mott; t-J)

Double occupancy allowed

Large FS ? (Hubbard metal)

-(ET)4Hg2.89Br8

high-Tc cuprate

Conclusion

1) variation at low temperatures (gapless) SL vs AFM weak Mott strong Mott pseudo-gap no pseudo-gap higher Tc lower Tc

2) universality at high temperatures Mott criticality ---- quantum

½-filled systems with variable frustration

Even under doped systemsA QPT or sharp crossover at (U/W)critical