ECRYS-2011, August, 15-27, 2011 at the Institute of Scientific Studies in Cargese, Corse Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular

ECRYS-2011, August, 15-27, 2011 at the Institute of Scientific Studies in Cargese, Corse Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors Toshihiro Takahashi Department of Physics, Gakushuin University, Mejiro 1-5-1, Toshima-ku, Tokyo 171-8588, Japan

Charge Fluctuation Charge 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:

Outline Introduction to NMR technique to probe charge degree of freedom Charge fluctuation and charge ordering in -phase BEDT-TTF salts Charge disproportionation in the zero-gap state of -BEDT-TTF 2 I 3 Coupling with the permanent electric dipolar moment of anion in TMTSF 2 FSO 3 Charge disproportionation in -type BETS salts Summary & Remarks

Simple Picture of Charge Ordering (CO) 1/4-filled system, D 2 A or DA 2, without large dymerization One 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 spindensity 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 -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 A 2 D Q-1D system DI-DCNQI 2 Ag (K. Hiraki, 1998) TMTTF 2 X (PF 6, AsF 6, ) (D.S. Chow, 2000) 2D ET salts -ET 2 I 3, (Y. Takano, 2001) -ET 2 RbZn(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 -phase BEDT-TTF salts Charge disproportionation in the zero-gap state of -BEDT-TTF 2 I 3 Coupling with the permanent electric dipolar moment of anion in TMTSF 2 FSO 3 Charge disproportionation in type BETS salts Summary

-(ET) 2 MZn(SCN) 4 (M=Rb,Cs) H. Mori et al., Phys. Rev. B57, 12 023(1998)

Electric and Magnetic property electric resistivityspin susceptibility RbZn salt CsZn salt

Charge ordered transition in - (ET) 2 RbZn(SCN) 4 K. Miyagawa et al., 2000 Charge Order T

p a =2kbar electron hole Ambient Pressure YM X Fermi Surface CP (p a =4kbar) Contact Point & Zero Gap State (ZGS) Dirac cone p a > 3kbar CP (contact point) 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) / SC Further 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 T MI CO of CD aboveT MI Because of site-dependence? Precursor effect of CO? Pattern of CO C > B cf. -ray Relation to the ZGS under pressure H S. Moroto 2003 Y. Takano 1999 C C

Measurements under pressure P = 0.1 ~ 1.1 GPa H 0 = 7 T (75 MHz) in the ab-plane Pressure cell by Prof. W. Kang, Ewha Womans Univ., Seoul H0H0 -ET 2 I 3

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 Point Dirac 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, V p =0.05, V c =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 -I 3 salt?

Outline Introduction to NMR technique to probe charge degree of freedom Charge fluctuation and charge ordering in -phase BEDT-TTF salts Charge disproportionation in the zero-gap state of -BEDT-TTF 2 I 3 Coupling with the permanent electric dipolar moment of anion in TMTSF 2 FSO 3 Charge disproportionation in type BETS salts Summary

Bechgaard Salt with asymmetric anion, FSO 3 Crystal Structure of (TMTSF) 2 FSO 3 a- axis FSO 3 - TMTSF molecule

(TMTSF) 2 FSO 3 under Pressure Y. J. Jo et al., 2003 Thermoelectric power Phase diagram Resistivity

77 Se-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 s with long delay ~ 600 s

77 Se-NMR T 1 -1 No anomaly at 90 K. Double comp. of T 1 -1 below 40 K. Broader line has shorter T 1 Sharper line has longer T 1

Angular dependence of 77 Se-NMR Lineshape

Inhomogeneous width assuming CD of 0.6~0.4 Angular dependence of 77 Se-NMR Lineshape

Enhancement of 77 Se-NMR T 2 -1 Anomalous T 2 -1 enhancement was not observed at ambient pressure. Double Peaks of T 2 - 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 19 F-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 19 F-NMR 3D-rotated signal Anion-ordered signal

0.4 GPa T-dependence of 19 F-NMR T 1 -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. 19 F-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 FSO 3 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 FSO 3 salt? + - - +

Outline Introduction to NMR technique to probe charge degree of freedom Charge fluctuations and charge ordering in - phase BEDT-TTF salts Charge disproportionation in the zero-gap state of -BEDT-TTF 2 I 3 Coupling with the permanent electric dipolar moment of anion in TMTSF 2 FSO 3 Charge disproportionation in -type BETS salts Summary

-d interaction on -(BETS) 2 FeCl 4 : 77 Se NMR K. Hiraki 16, H. Mayaffre 1, M. Horvatic 2, C. Berthier 12, H. Tanaka 3, A. Kobayashi 4, H. Kobayashi 5 and T. Takahashi 6 1. Laboratoire de Spectrometrie Physique, Universit Joseph Fourier 2. Grenoble High Magnetic Field Laboratory 3. Nanotechnology Research Institute, AIST 4. Department of Chemistry, University of Tokyo 5. Institute for Molecular Science 6. Department of Physics, Gakushuin University Acknowledgement We would like to thank prof. K. Takimiya (Hiroshima University)

Structure and electronic properties H ext 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) H ext 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 (Fe 2+ : S=5/2) compensates the external field; SC appears when, H 0 + H exch H c2, where H exch = J /g B Our aims is to confirm the exchange field seen by -electrons through 77 Se-NMR AFI SC

H 0 dependence of NMR shift at 1.5K M10 magnet GHMFL oct2005/apr2006 7/16 5 B J=322 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 2003 1 H NMR/Endo JPSJ 2002 X ray/Komiyama JPSJ 2004 I-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, , 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 - phase BEDT-TTF salt Charge disproportionation in the zero-gap state of -BEDT-TTF 2 I 3 Coupling with the permanent electric dipolar moment of anion in TMTSF 2 FSO 3 Charge disproportionation in type BETS salts Summary & Remarks

Summary-1 Anomalous NMR line broadening was observed in metallic states of various molecular conductors; -(ET) 2 MZn(SCN) 4, (M=Rb, Cs) -(ET) 2 I 3 (TMTSF) 2 FSO 3 -(BEST) 2 MCl 4, (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) 2 MZn(SCN) 4, (M=Rb, Cs) Long-range CO in the Rb-salt CD due to the competition of different COs -(ET) 2 I 3 Long-range CO; Non-stripe CO in the ZGS CD due to band formation, enhanced by Coulomb correlation. (TMTSF) 2 FSO 3 CD in the metallic state under pressure. Coupling with electric dipoles on FSO 3 anion may be relevant. -(BEST) 2 MCl 4, (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) 2 I 3 under uniaxial strain (Tajima, 2003) -(DODHT) 2 PF 6 T c = 3.1 K at 16.5 kbar: Nishikawa, 2003) -(meso-DMBEDT-TTF) 2 PF 6 T c = 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. !

Comparison with the other isostructural -phase I 3 salts BETS BEDT-STF Single crystal 1 peace with double bond carbons enriched with 13 C Ensemble of small single crystals with all Se sites enriched with 77 Se isotope Large amount of small single crystals containing natural 77 Se (7.5%) ET C C Se Single crystal 1 peace with double bond carbons enriched with 13 C Small single crystal containing natural 77 Se (7.5%) C C

-(BETS) 2 I 3 v.s. -(ET) 2 I 3 M. Inokuchi et al, BCSJ 68 (1995) 547 N. Tajima et al, EPL 80 (2007) 47002 -BETS 2 I 3 may correspond to -ET 2 I 3 under pressure of ~1.1 GPa

Angular dependence of resonance shift for the 3 peaks Sinusoidal dependences Relative phase Red-Green58 Black-Green78 Black-Red20 Amplitude ratio Green : Red : Black = 2.8 1 3.0 ~ 0.6 0.2 0.6

Documents

ECRYS-2011, August, 15-27, 2011 at the Institute of Scientific Studies in Cargese, Corse Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular