Spin frustration and Mott criticality in triangular-lattice orga nics 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 f rom SL/AFM 3. Quantum criticality at high te mperatures H. Oike, T. Furukawa, Y. Shimizu (Nagoya Un iv.), 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
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Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness
2013 Hangzhou Workshop on Quantum Matter, April 22, 2013. Spin frustration and Mott criticality in triangular-lattice organics under controlled Mottness. K. Kanoda, Applied Physics, Univ. of Tokyo. - PowerPoint PPT Presentation
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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
BBBBBBBBBBBB
BBBBBBBB
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