Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors

ECRYS-2011, August, 15-27, 2011at the Institute of Scientific Studies in Cargese, Corse

Charge Fluctuation, Charge Ordering and Zero-Gap State

in Molecular Conductors

Toshihiro TakahashiDepartment of Physics, Gakushuin University,

Mejiro 1-5-1, Toshima-ku, Tokyo 171-8588, Japan

Charge FluctuationCharge Ordering

Zero-Gap State

“San-dai-banashi”

A style of Japanese traditional comic story, “rakugo”.

Three keywords are given independently by the audience.

The storyteller, “rakugo-ka”, makes ad lib a consistent comic

story using all the keywords.

3 keywords:

三題噺

Outline Introduction to NMR technique to probe

charge degree of freedom Charge fluctuation and charge ordering in θ-

phase BEDT-TTF salts Charge disproportionation in the zero-gap

state of α-BEDT-TTF2I3 Coupling with the permanent electric dipolar

moment of anion in TMTSF2FSO3 Charge disproportionation in λ-type BETS

salts Summary & Remarks

Simple Picture of Charge Ordering (CO)

1/4-filled system, D2A or DA2, without large dymerizationOne carrier per two molecules

Coulomb interaction, U & V, … finding a charge arrangement to minimize Coulomb energy

As including transfer =>rich variety of phenomena

Charge Ordering vs. Charge

Disproportionation Long-range Charge Ordering (CO) vs. Charge Disproportionation (CD)

Charge Frustration Melting of CO Charge Fluctuation/Charge Dynamics Various Optical/Dielectric responses

How can NMR detect CO/CD?

Not detecting “charge” but “spin”density Not detecting Long Range CO but just the distribution

of local charge (spin) What we observed in CO/CD systems in common

were anomalous broadening of NMR spectrum. How can CO/CD affect NMR spectrum and other NMR parameters?

Note that;

Brief introduction to NMR(Nuclear Magnetic Resonance)

Nuclear spin carries angular momentum, and magnetic moment, .

Zeeman splitting in strong magnetic field: Resonance condition:

Magnetic moment; Angular momentum; Zeeman splitting for I=1/2 Resonance Condition;

NMR can detect CO/CD Nuclei in material see local fields given by the

environments in addition to the external field. What we detect with NMR are the information of the

local field;

Central shift

Local field distribution

Local field at each nuclear site

Interaction with electrons Orbital motion and Chemical shift Spin interaction and Knight shift

Orbital motion

Spin

Local fields are produced by surrounding electrons!


Shielding current

Magnetic shielding current gives local field. Chemists concerns the isotropic part of the chemical shift tensor. It is usually small compared with the spin contribution.


Spin magnetization


Spin magnetization

Lone-pair spin contribution is also anisotropic and much larger than orbital contribution in the present systems.

Hyperfine interaction Hyperfine interaction

Hyperfine interaction tensor

Knight shift

~ proportional to electron spin susceptibility~ anisotropic due to the hyperfine tensor

for a pure p-electron with uniaxial symmetry

Hyperfine interaction Inhomogeneity of Knight shift

causes inhomogeneous broadening.

Inhomogeneous width should be proportional to the Knight shift.

~ proportional to electron spin susceptibility~ anisotropic due to the hyperfine tensor

Typical Materials, exhibiting CO

1/4-filled Organic molecular conductors, of the chemical form of A2D

Q-1D systemDI-DCNQI2Ag (K. Hiraki, 1998)TMTTF2X (PF6, AsF6, …) (D.S. Chow,

2000) 2D ET salts

-ET2I3, (Y. Takano, 2001)-ET2RbZn(SCN)4 (K. Miyagawa, 2000, R.

Chiba, 2001)

X-ray, Raman & IR spectroscopy also confirmed CO in various materials





moment of anion in TMTSF2FSO3 Charge disproportionation in λ type BETS

salts Summary

-(ET)2MZn(SCN)4 (M=Rb,Cs)

H. Mori et al., Phys. Rev. B57, 12 023(1998)

Electric and Magnetic property

electric resistivity spin susceptibility

RbZn salt

CsZn salt

Charge ordered transition in -(ET)2RbZn(SCN)4

K. Miyagawa et al., 2000

Charge Order T<190KSpin-singlet T<30K

Unusual broadening above TMI

Mechanism of the broadening above TMI ?at 204K

TMI

Observed excess width is anisotropic!~proportional to the central shift

Angular dependence of the 2nd moment is proportional to K2

Inhomogeneous broadening due to the distribution of K

Inhomogeneous and homogeneous 13C-NMR

lineshape in -RbZnMetal state

T2 measurementDouble peak about 90 K & 70 K

Below 30 KTMI

LR-CO

Inhomogeneous broadening due to CD

T2-1

enhancement due to slow dynamics of CD

(Chiba, 2004)

Inhomogeneous and homogeneous linewidth

Dynamics of Inhomogeneous local fieldT2

-1 life time of Zeeman Leveltc

-1 correlation frequency 2nd moment for the

inhomogeneous field

Inhomogeneous and homogeneous

13C-NMR lineshape in -CsZn

Inhomogeneous broadening due to large CD

Motional narrowing

Slow dynamics ~kHz

Crossover into different broadening

Explained by expanded exponential correlation;

(t) = <2>exp(-(t/tc)) with tc~exp(-/kBT)

Salt Rb Cs /kB 7600 K 5100 K<2>1/2 3.3 kHz 1.4 kHz

T dependence of 1/T2 in -RbZn & -CsZn

Angular dependence of NMR lineshape of -CsZn

295 K 101 K 5 Kspin vanishes!Nonmagnetic ground state

Comparison of -CsZn and -RbZn salts at 5K

charge ordered statecharge : ~ +0.5

charge rich

charge poor

-phase Salts

Spin-singlet without CD !

Domains with finite coexist!Chiba, PRB 2007

What is the origin of slow dynamics of CD in -phase

salts?Competition between different types of CO may be responsible. -RbZn salt with LR-CO of (0, 0, 1/2) below 190K

Diffuse X-ray scattering with q=(1/4, k, 1/3) is observed above TMI.

Spin-singlet ground state with LR-CO.-CsZn salt without LR-CO

Diffuse X-ray scatterings with q1=(2/3, k, 1/3) and q2=(0, k, 1/2) are observed below 120K.

Coexistence of spin-singlet domain and paramagnetic domain without any sign of CO.


charge degree of freedom Charge fluctuations and charge ordering in θ-




salts Summary

Various ground states in -(BEDT-TTF)2I3

NGS

Metal

along b-axis

SC

CO

along a-axis

Ambient Pressure　 Metal-Insulator Transition with COUnder hydrostatic pressure　 Anomalous NGS state with high mobilityUnder Uniaxial strain　 SC within CO-state

Tajima et al. (2003)

pa=2kbar

electron

hole

AmbientPressure

G

Y M

X

Fermi Surface

CP

(pa=4kbar)

Contact Point & Zero Gap State (ZGS)

Dirac conepa >

3kbar CP (contact point)

Γ

M

Zero Gap State under pressure

Kobayashi et al., JPSJ (2005)

The first ZGS in a bulk system was confirmed!

All peculiar ground states are explained on the basis of unified band parameters! CO / ZGS (NGS) / SCFurther questions: How does CO behave under pressure?What is the relation between CO and the ZGS?How about in other isostructural salts?

Development of CD above TMI

CO of CD aboveTMIBecause of site-dependence?Precursor effect of CO?

Pattern of CO ： C > B cf. Ｘ -ray Relation to the ZGS under pressure

H

S. Moroto 2003Y. Takano 1999

C C

Measurements under pressure

P = 0.1 ~ 1.1 GPaH0 = 7 T (75 MHz)

in the ab-plane

Pressure cellby Prof. W. Kang, Ewha Womans Univ., Seoul

H0

-ET2I3

T-dependence of Local Susceptibilities under

pressure

Local susceptibility is the smallest on ‘B’ molecule.B molecule is a charge-poor site!

Title: Charge Ordering in $\alpha$-(BEDT-TTF)$_2$I$_3$ by Synchrotron X-ray DiffractionAuthors: by Toru Kakiuchi, Yusuke Wakabayashi, Hiroshi Sawa, Toshihiro Takahashi, Toshikazu NakamuraPublished: October 25, 2007J. Phys. Soc. Jpn., Vol.76, No.11, p.113702

Charge Ordering determined by Synchrotron X-ray

Diffraction

CD in the metallic state at ambient pressure:‘B’ molecule is charge-rich!~ inconsistent to the NMR results?

Kakiuchi et al., JPSJ (2007)

Contact PointDirac cone

Theory explains this difficulty

Transfer energies evaluated from first principle calculation by Kino

A,A' = +0.54

B = +0.64

C = +0.29

Katayama et al., JPSJ (2008)

B molecule is charge-rich!

Contact Point & Zero Gap State (ZGS)


Katayama et al., Eur.Phys. (2009)

Local susceptibility is proportional to the density of state around the contact point, and not to the local charge!


Local susceptibility is determined by the density of states around the contact point.

U=0.4, Vp=0.05, Vc=0.17

ZG

1. Non-stripe CO develops at low temperatures and under pressure. It does not break the lattice symmetry.2. Charge-rich ‘B’ molecule has the smallest local susceptibility. It is consistent with X-ray and theoretical analysis.3. Non-stripe CO may be relevant to the stabilization of the ZGS.

Conclusions

ZGS

T

ZG

Non-stripe CO should come from a band nature together with Coulomb interaction. Characteristic time of charge dynamics, if any, should be much shorter than the NMR time scale. The mechanism of CD is quite different from the case of the -salt.

ZGS

T

What is the origin of CO in the metallic state of -I3

salt?






salts Summary

Bechgaard Salt with asymmetric anion, FSO3

Crystal Structure of (TMTSF)2FSO3

a- axis

FSO3-TMTSF

molecule

(TMTSF)2FSO3 under Pressure

Y. J. Jo et al., 2003

Thermoelectric power

Phase diagramResistivity

77Se-NMR Lineshape

Coexistence of sharp & broad components

4 sharp peaks~4 Se-sites in a unit cell

Line broadening

Sharp component appears

with short delay ~ 3 swith long delay ~ 600 s

77Se-NMR T1-1

No anomaly at 90 K.Double comp. of T1

-1 below 40 K.Broader linehas shorter T1

Sharper linehas longer T1

Angular dependence of 77Se-NMR Lineshape

Inhomogeneous width assuming CD of 0.6~0.4

Angular dependence of 77Se-NMR Lineshape

Enhancement of 77Se-NMR T2-

1

Anomalous T2-1 enhancement

was not observed at ambient pressure.

Double Peaks of T2

-1 around 90 K & 70 K.90 K: the phase boundary (I).70 K: inside the intermediate phase.

0.65 GPa

Possibility of slow Charge fluctuations as in the q-ET salt.

0.4 GPa

Anion dynamics seen by 19F-NMR

Coexistence of 3D-rotated signal and Anion-ordered signal in the region between boundary I & II.

3D-rotated signal

Anion-ordered signal

0.4 GPa

Anion dynamics seen by 19F-NMR

3D-rotated signal

Anion-ordered signal

0.4 GPa

T-dependence of 19F-NMR T1-1

BBP relaxation suggesting 3D-rotation

Coupling with methyl-group rotation in AO state?

Conclusions■ Metallic phase above I and

Nonmagnetic Insulating phase below II were confirmed.

■ Large charge disproportionation was found in the anomalous metallic phase with below I.

■ Coexistence of the metallic and insulating phase suggests the boundary II is of first order.

■ 19F-NMR & X-ray analysis strongly suggest that; Boundary I associates with the ordering of tetrahedrons; Boundary II with the ordering of elec. dipoles.

Metal

Anomalous metal with CD

Nonmag. Insulator

CD was observed in the region where partial ordering of FSO3 appears. Magnitude of CD is moderate compared with the other CD systems.CD may be due to the intramolecular charge imbalance and the first indication of the coupling between the electric dipoles and the carriers.

Metal

Nonmag. Insulator

What is the origin of CD in FSO3 salt?

+ - -+





moment of anion in TMTSF2FSO3 Charge disproportionation in λ-type BETS

salts Summary

p-d interaction on -(BETS)2FeCl4: 77Se NMR

K. Hiraki16, H. Mayaffre1, M. Horvatic2, C. Berthier12, H. Tanaka3, A. Kobayashi4, H. Kobayashi5 and T. Takahashi6

1. Laboratoire de Spectrometrie Physique, Université Joseph Fourier2. Grenoble High Magnetic Field Laboratory3. Nanotechnology Research Institute, AIST4. Department of Chemistry, University of Tokyo5. Institute for Molecular Science6. Department of Physics, Gakushuin University

AcknowledgementWe would like to thank prof. K. Takimiya (Hiroshima University)

Structure and electronic properties

Hext

H. Kobayashi et al., J. A. C. S. 118, 368 (1996)H. Tanaka et al., J. A. C. S. 121, 760 (1999)H. Akutsu et al., PRB58, 9294 (1998)

Brossard et al. EPJ B1, 439(1998) AFI

Balicas et al.PRL87, 067002(2001)SC

Balicas et al. PRL87, 067002(2001)

pHext

Fe 5/2 spin

Mechanism of Field-Induced SC

Orbital decoupling effect is suppressed by applying external filed strictly parallel to the conducting 2D layer (a*c plane).

Jaccarino-Peter mechanism: Exchange field from magnetic ions (Fe2+: S=5/2) compensates the external field; SC appears when,

H0 + Hexch Hc2,where Hexch = J<S>/gB

Our aims is to confirm the exchange field seen by p-electrons through 77Se-NMR

AFI SC

H0 dependence of NMR shift at 1.5K M10 magnet GHMFL

oct2005/apr2006

7/16

5B J=32±2 T

Linewidth vs. magnetization

Excess broadening below 30K is very likely due to CD!

Angular dependence of linewidth in the Fe-salt

Angular dependence of spectral width is proportional to that of the central shift, suggesting CD.

Angular dependence of linewidth in the Fe- and the Ga-salt

Fe ions are not relevant to CD! Organic BETS layers should be responsible for CD!

Which mechanism gives the CD?

Charge imbalance was already suggested in the Fe-salt by;

microwave/Matsui PRB 20031H NMR/Endo JPSJ 2002

X ray/Komiyama JPSJ 2004I-V characteristics./ Toyota PRB 2002

15/16

Magnetic Fe ions are not relevant to the line broadening. It should be attributed to the inhomogeneity of the local susceptibility, p, in the BETS layer, suggesting large CD, while their dynamics have not yet been examined.

Mechanism of CO is not clarified yet.

Dielectric Anomaly

H. Matsui, 2003



phase BEDT-TTF salt Charge disproportionation in the zero-gap



salts Summary & Remarks

Summary-1

Anomalous NMR line broadening was observed in metallic states of various molecular conductors; -(ET)2MZn(SCN)4, (M=Rb, Cs) -(ET)2I3 (TMTSF)2FSO3 -(BEST)2MCl4, (M=Fe, Ga)

Angular dependence of the width is proportional very well to that of the central shift of the spectrum, which suggests the appearance of CO/CD.

Details of the nature of CO/CD are found quite different among them.

Summary-2

-(ET)2MZn(SCN)4, (M=Rb, Cs)Long-range CO in the Rb-saltCD due to the competition of different CO’s

-(ET)2I3 Long-range CO; Non-stripe CO in the ZGSCD due to band formation, enhanced by Coulomb correlation.

(TMTSF)2FSO3 CD in the metallic state under pressure.Coupling with electric dipoles on FSO3 anion may be relevant.

-(BEST)2MCl4, (M=Fe, Ga) BETS layers are responsible for CD in the metallic state.

Mechanisms responsible for CO/CD are full of variety!

Concluding remarks

Increasing numbers of molecular conductors are found to exhibit CO/CD.

CO/CD are found to interplay with various types of ground states.

Even Superconductivity is found in the vicinity of CO’ed state. -(ET)2I3 under uniaxial strain (Tajima, 2003) -(DODHT)2PF6 （ Tc = 3.1 K at 16.5 kbar: Nishikawa, 2003)-(meso-DMBEDT-TTF)2PF6 （ Tc = 4.3 K at 4.0 kbar: Kimiura,

2004 ）CO/CD will open new possibility of molecular conductors

and other correlated systems!

Collabrators:

Ko-ichi Hiraki, Yoshiki Takano, Ken-ichi Arai, Shiro Harada,Hidetaka Satsukawa Dept. Physics, Gakushuin Univ.

N. Tajima, H.M. Yamamoto, R. Kato RIKEN, JST-CREST, and T. Naito,Ehime Univ.

ご静聴ありがとうございました !

おしまい

ご静聴ありがとうございました

Comparison with the other isostructural -phase I3 salts

BETS

BEDT-STF

Single crystal 1 peacewith double bond carbons enriched with 13C

Ensemble of small single crystals with all Se sites enriched with 77Se isotope

Large amount of small single crystalscontaining natural 77Se (7.5%)

ET

C C

Se Se

SeSe

Se

Se

Single crystal 1 peacewith double bond carbons enriched with 13C

Small single crystalcontaining natural 77Se (7.5%)

C C

-(BETS)2I3 v.s. -(ET)2I3

M. Inokuchi et al, BCSJ 68 (1995) 547 N. Tajima et al, EPL 80 (2007) 47002

-BETS2I3 may correspond to -ET2I3 under pressure of ~1.1 GPa

Angular dependence of resonance shift for the 3

peaksSinusoidal dependencesRelative phaseRed-Green 58°Black-Green 78°Black-Red 20°

Amplitude ratioGreen : Red : Black= 2.8 ： 1 ： 3.0~ 0.6 ： 0.2 ： 0.6

Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors

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