1 Ferroelectricity in organic low- dimensional systems Pierre Monceau * Institut Neel, CNRS and University Joseph Fourier, Grenoble, France * in collaboration with Felix Nad, Institut Kotel’nikov of Radioengineering and Electronics, RAS, Moscow, Russia

Ferroelectricity is defined by the appearance of a macroscopic electric polarization and its reversibility by applying an external field For some ferroelectric materials, electron degrees of freedom and/or electronic interactions directly give rise to a macroscopic electric polarization and a ferroelectric transition  electronic ferroelectricity 2

Electronic ferroelectricity 3 for a review: S. Ishihara, J. Phys. Soc. Jpn 79, , 2010

Ferroelectricity induced by charge ordering 4 J.Van der Brick and D. I. Khomskii J. Phys.: Condens. Matter 20, , 2008 S. Ishihara J. Phys. Soc. Jpn 79, , 2010

5 Ground state phase diagram of the 1D extended Hubbard model at 1/4 filling on the plane of U/t and V/t S. Ejima et al. Europhys. Lett. 70, , 2006 The mean field approximation of the 1D Hubbard model show that when V exceeds a critical value, V c,, charge disproportionation occurs among sites with alternating « charge rich » and « charge poor » sites (Seo and Fukuyama 1997). With  D ≠ 0 numerical calculations on the plane U and V for a fixed  D where the metallic phase at  D = 0 is replaced by the Mott insulating phase, and a phase with Wigner crystal-type CD is still present in the large U and V region Shibata et al. Tsuchiizu et al /4 filled band

6 Acknowledgements for samples J. M. Fabre Laboratoire de Chimie Organique, Montpellier, France MT. Nakamura and K. Furukawa Institute for Molecular Science, Okazaki, Japan H. Müeller ESRF, Grenoble, France H. M. Yamamoto Riken, Saitama, Japan K. Yamamoto Institute for Molecular Science, Okazaki, Japan

7 Temperature dependence of the real part of the dielectric permittivity  ' measured at 1MHz for (TMTTF) 2 Br and (TMTTF) 2 PF 6 F. Nad, PM and J-M. Fabre J. Phys. IV 9, Pr10, 1999 ECRYS 2008

8 Charge disproportionation D.S. Chow et al. Phys. Rev. Lett. 85 (2000) 1698 C 13 NMR spectra for (TMTTF) 2 AsF 6 Spectral splitting (~charge disproportionation order parameter)versus temperature NMR measurements in an external field of 9T (fre 96.4 MHz) Below T CO, doubling of the spectral line due to two inequivalent molecules with unequal electron densities Charge disproportionation : 3:1 from T 1 -1 measurements At high temperatures the unit cell consists of two equivalent TMTTF molecules related by inversion about the counterion. The breaking of the inversion symmetry within the unit cell below T CO, and the spontaneous dipole moment associated with the charge imbalance on the two molecules yield the ferroelectric behaviour.

9 AC conductivity of (TMTTF) 2 AsF 6 T dependence of the conductance T dependence of the real part of the dielectric permittivity,  ’ at 100 et 300kHz, 1,3 and 10MHz 100kHz Nad et al.: J. Phys.:Cond. Matter, 12(2000)L435

10 Real part of dielectric constant of (TMTTF) 2 X salts  ’ = ImG/  ReO 4 SbF 6 AsF 6 PF 6 1- For all anions: at T≈ T , there is no anomaly 2- for CSA and ReO 4 anions,  ’ diverges at T CO. Huge magnitudes of  ’ : for AsF 6, for ReO 4

Anion ordering 11 F. Nad and P.M. J.Phys. Soc. Jpn. 75, , 2006

12 Imaginary part of the permittivity of(TMTTF) 2 AsF 6 T > T CO = 101 KT <T CO

13 Frequency of the maximum in  ’’ the same at T=97 K and T=105 K (T CO = 101K) The slow relaxation processes involved in the shoulder of  ’’ may correspond to the motion of the domain wall structure developped in the ferroelectric state Freezing of the ferroelectric domain structure below 90K = T CO - 10K Motion of domain walls

14 Ferroelectric character The ferroelectric state is triggered by the uniform shift of anions yielding a macroscopic ferroelectric polarization which is gigantically amplified by the charge disproportionation on the molecular stacks ( S. Brazovski and T. Nattermann, Adv. In Phys. 53, 177, 2004) CSA and ReO 4 salts show at T CO a second order phase transition described by the Curie law A  ’ =  T- T CO  1/  ’ (T) is close to be linear Ratio A L / A H (A L at T  T CO A H at T>T CO ) in CSA: A L / A H ≈ 2 in ReO 4 A L / A H ≈ 1.5 ReO 4 SbF 6 AsF 6 PF 6 Phys. Rev. Lett. 86 (2001) 4081

15 (ET) 2 X compounds Mott insulator in the case of half-filled band, due to strong interactions between electrons with strong U between neighoring sites If U is large, it is more favourable to localize the particules on the lattice sites to minimize the repulsion and the system is an insulator In presence of strong dimerization as in  -(ET) 2 X compounds, a single electron occupy the bonding state of each dimer half-filled band and to the insulating state due to the effect of U [ called a dimer-Mott state - Hotta et al.: Chem. Rev. 114 (2004)]

Structures of and  - (BEDT-TTF) 2 RbZn(SCN) 4 and  - (BEDT-TTF) 2 I 3 16 Y. Tanaka and K. Yonemitsu J. Phys. Soc. Jpn 79, , 2010

17 Stripe phases Different spatial patterns of stripe phases are stabilizeddepending on the anisotropy of the transfer integrals tc and tp and of the values of intersite Coulomb energies along the stacking direction Vc and along the bonds in the transverse direction Vp Seo: J. Phys. Soc. Japan 69 (2000) 805

18 Metal-insulating phase transition in  -(BEDT-TTF) 2 I 3 Abrupt phase transition at T=135.1K of first order Transition slightly hysteretic in specific heat with latent heat[ Fortune et al. Solid St. Comm 77 (1991) 265] Change of intensity of Bragg peak (for reflections only with an odd index with the a-component) (Nogami et al. Synth. Metals 16 (1986) 367 And T. Kakiuchi et al. J. Phys. Soc. Jpn. 76, , 2007)  Relative change of the sample length along a, b and c * Measured by capacitive dilatometry et x-ray diffraction from Heidmann etal.: Solid St. Comm. 84 (1992) 711 Dimerization of stacks I along the a axis of Peierls type

19 Charge ordering from NMR in  -(BEDT-TTF) 2 I 3 from Takano et al. J. Phys. Chem. Solids 62 (2001) C-NMR spectra at different temperatures below the M-I transition, the spectra consist of two Pake doublets. The positions of the two doublets have differentT dependences. That indicates two differently charged BEDT-TTF molecules below the transition: Also from Raman spectroscopy Wojciechowski etal. Phys. Rev. B67 (2003)

Charge disproportionation 20 T. Kakiuchi et al. J. Phys. Soc. Jpn 76, , 2997 Horizontal stripe structure CD already above CO transition From infrared spectroscopy, NMR, and x-ray At room temperature: A=A’= 0.60 B=0.68 C=0.44 In the CO state: A=0.81 A’= 0.26 B=0.74 C=0. 23

21 ac conductivity in  -(BEDT-TTF) 2 I 3 Conductivity Dielectric constant at 2MHz (sample 1) Dielectric constant (sample 2) Drop of  ’ below T MI  Structural transition (dimerization)

22 The  ’ growth above T MI may indicate the polarizability of the charge disproportionation seen in NMR. The jump below T MI is associated with the 2c superstructure and the large charge gap  Role essential of the structural transition in the metal-insulating transition (posssibly alter the symmetry and the magnitude of the transfer integrals relative to V) -3 orders of magnitude jump of conductivity at T MI with hysteresis T cooling =199K, T heating =204.5K -charge gap below T MI = 1900K much larger than in (TMTTF) 2 AsF 6 with  =350K -  ’(T) shows a smooth monotonic increase from room temperature, more sharp, closed to divergence near T MI -  ’(T) jumps down to a small magnitude sharply below T MI -the same jump up of  ’ in heating  First order transition

Low temperature dielectric response in  -(BEDT-TTF) 2 I 3 23 Frequency dependence of the real (ε') and imaginary (ε'') part of the dielectric function in α-(BEDT-TTF)2I3 for E // [1¯10]. Below 75 K, two dielectric relaxation modes are observed T. Ivek et al. Phys. Rev. B83, , 2011

Optical second harmonic generation 24 K. Yamamoto et al. J. Phys. Soc. Jpn, 77, , 2008 Activation of the even-order nonlinear optical phenomenom signifies the lack of inversion symmetry

Observation of ferroelectric domains by SHG interferometry 25 K. Yamamoto et al. Appl. Phys. Lett. 96, , 2010 a)Transmission image SH images at 140K (b) and 50K (c). d) SH image after annealing above Tco and slow cooling at T=50K e) SH intensity versus T

Photoexcitation in  -(BEDT-TTF) 2 I 3 26 For ordinary feroelectrics, polarization is induced by lattice modulation. In  -(BEDT-TTF) 2 I 3, the crystal shows a monotonic lattice shrinkage without substantial displacement of molecules (structural modulation makes a minor contribution to the polarization) The polarization is mainly due to the modulation of the electron distribution caused by CO. The large value of SHGsignal indicates the growth of large polar domains. Then, if polarization originates from electron phenomena, fast response to external perturbations is expected. Pump-probe measurement of the SHG : stimulation of the CO by strong pumping pulse and recorded the induced variation of the SHG with a weaker probing pulse Melting of the CO See also the suppression of the SHG femtosecond signal in TTF-CA

Femtosecond photoresponse 27 Photoinduced variation of reflectivity and second harmonic generation (SHG) as the function of the delay time between pump and probe pulses. T=100K. K. Yamamoto et al. J. Phys. Soc. Jpn, 77, , 2008 See also:Y. Kawakami et al. Phys. Rev. Lett. 105, , 2010 Y. Tanaka and K. Yonemitsu, J. Pjys. Soc. Jpn. 79, , 2010 H. Nakaya et al. Phys. Rev. B81, , 2010 The time required for CO melting and generation of the metallic state is 15fs. at 20K. The early stage photo-induced dynamics is driven by the electron response. Additional slower (300fs) growth indicates interplay between electron oscillations and vibrations

28 Charge ordering from NMR in  - (ET) 2 RbZn(SCN) 4 from Miyagawa et al. Phys. Rev. B62 (2000) R C-NMR with H=8T normal to the conducting layers With T decrease, the spectra become broadened indicating a continuous molecule to molecule distribution of Knight shift. Below 195K, the spectrum consits of a broad line (A) (with a much larger relaxation rate)and a paket doublet (line B).  Separation of the BEDT-TTF into two inequivalent molecules Also from vibrational spectroscopy K. Yamamoto et al. Phys. Rev. B65 (2002)

29 AC conductivity in  - (BEDT-TTF) 2 RbZn(SCN) 4

30 The  ’ growth above T MI may indicate the polarizability of the charge disproportionation seen in NMR The jump below T MI is associated with the 2c superstructure and the large charge gap  Role essential of the structural transition in the metal-insulating transition (posssibly alter the symmetry and the magnitude of the transfer integrals relative to V) -3 orders of magnitude jump of conductivity at T MI with hysteresis T cooling =199K, T heating =204.5K -charge gap below T MI = 1900K much larger than in (TMTTF) 2 AsF 6 with  =350K -  ’(T) shows a smooth monotonic increase from room temperature, more sharp, closed to divergence near T MI -  ’(T) jumps down to a small magnitude sharply below T MI -the same jump up of  ’ in heating

Effect of cooling rate on the CO in  - (ET) 2 RbZn(SCN) 4 31 F. Nad, PM and H.M. Yamamoto Phys. Rev. B76, , ) conductivity

Effect of cooling rate on the CO in  - (ET) 2 RbZn(SCN) ) Dielectric permittivity F. Nad, PM and H.M. Yamamoto Phys. Rev. B76, , 2007

Glass-like state in  - (BEDT-TTF) 2 CsZn(SCN) 4 33 F. Nad, PM and H.M. Yamamoto J. Phys.: Conden. Matter 20, , 2008

Neutral-ionic transition 34 The neutral-ionic transition is caused by the energy gain of the long range Coulomb interaction overcoming the effective ionization energy of DA pairs. There is a finite transfer energy between the D and A molecules in the mixe-stack CT compounds, the degree of CT (  ) between D and A is not equal to 0 and 1.  is 0.3 and 0.7 between the N and I phases, respectively. In the I phase, each molecule has spin S=1/2, constituting 1D spin chains, which are dimerized due to the spin-Peierls mechanism. Neutral chains Ionic chains

Dielectric response TTF-p-cloranil (TTF-CA) 35 H. Okamoto et al. Phys. Rev. B43, 8224, 1991

Ferroelectric domains 36 H. Kishida et al. Phys. Rev. B80, , 2009 The domain wall (DW) is located between the rightward polarized domain (IA) and the leftward one (IB) The direction of spontaneous polarizations, P s, in IA and IB are opposite while the electric-field-induced polarizations,  P, in IA and IB are parallel These changes in polarization are accounted for the change in the charge transfer,  Electroreflectance microscopy

SHG in TTF-CA 37 Luty et al. Europhys. Lett. 59, 619, 2002 Generation dynamics of metastable N phase fraction converted from the stable ferroelectric I phase at 77K. The second harmonic generation (SHG) disappears within 100ps. The amount of converted N phase starts to increase around 100ps after the excitation light pulse - flash illumination 1230fs - (60% at around 500ps delay time)

TTF-p-bromanil TTF-BA 38 F. Kagawa et al. Nature Phys. 6, 169, 2010 TTF and BA molecules are almost ionic. The D + A - stacks can be regarded as a 1D Heisenberg chain with spin 1/2.

Magnetoelectric coupling in TTF-BA 39 F. Kagawa et al. Nature Phys. 6, 169, 2010