Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors
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Transcript of 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
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!
Interaction with electrons Orbital motion and Chemical shift Spin interaction and Knight shift
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.
Interaction with electrons Orbital motion and Chemical shift Spin interaction and Knight shift
Spin magnetization
Interaction with electrons Orbital motion and Chemical shift Spin interaction and Knight shift
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
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
-(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.
Outline Introduction to NMR technique to probe
charge degree of freedom Charge fluctuations 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
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)
Theory explains this difficulty
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!
Theory explains this difficulty
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?
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
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?
+ - -+
Outline Introduction to NMR technique to probe
charge degree of freedom Charge fluctuations 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
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
Outline Introduction to NMR technique to probe
charge degree of freedom Charge fluctuations and charge ordering in θ-
phase BEDT-TTF salt 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
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.
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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