Quasi one dimensional charge transfer salts

Charge transfer salts consist of donor and acceptor molecules. These can either alternate in a single stack (mixed-stack arrangement: for example in TTF-CA ) or be arranged in alternating stacks of donors and acceptors (segregated stack arrangement: for example in TTF-TCNQ . Since along the stacks the distance is smaller than the van-der Waals radius, the p-orbitals of the molecules overlap, forming electronic bands. In the case of TMTTF and TMTSF salts, the system crystallizes in a A2B stoichiometry, i.e. the organic molecules donate half an electron each to the monovalent anions.

 

TMTXF1

The molecule arrangement in the TMTXF-salts which is an example of the alternating stacking of the donor, TMTXF, and anion molecules.

TMTXF2

Skeleton of the TMTXF molecule in which the yellow inked atoms can be selenium in the case TMTSF or sulfur for TMTTF, respectively.

Fig 1: Molecular structure of the TMTXF-salts.

Based on electron counting arguments, the TMTSF-salts are metals with a formally 3/4 filled conduction band. The weak dimerization along the chains, however, splits the band and the systems are actual half-filled; further modifications may be caused by electronic correlation. While (TMTSF)2ClO4 is the only compound which at ambient pressure stays metallic down to 1 K where it becomes superconducting, most of the other Bechgaard salts undergo a metal-to-insulator transition (at temperatures around 10 K) which in some cases like (TMTSF)2PF6 can be suppressed by external pressure (dimensional crossover). Due to the larger anisotropy, stronger dimerization, and larger on-site Coulomb repulsion the Fabre TMTTF salts are closer to the Mott-Hubbard insulating state. (TMTTF)2SbF6 is known to be the most correlated compound of the sulfur series. In the phase diagram (TMTTF)2Br lies between (TMTSF)2PF6 and (TMTTF)2PF6 since superconductivity has been observed only under very high pressure.

Fig 2: Phase diagram of (TMTSF)2X and (TMTTF)2X. loc denotes charge localization, CO charge order, SP spin-Peierls, AFM antiferromagnetic, SDW spin-density wave, and SC superconducting.

 

Bechgaard salts (TMTSF)2X

 

 

 

Prof. Dr. Dr. h.c. Denis Jerome (right) discussion Prof. Dr. Martin Dressel (center) and Prof. Dr. Dieter Schweitzer (left) on occasion of the celebration of the honorary doctorate of the Universität Stuttgart bestowed upon Prof. Jerome in November 2005.

In 1979 D. Jerome found superconductivity in (TMTSF)2PF6 at temperatures of about 1 K and external pressure; however a first step was done. The Bechgaard salts (TMTSF)2X, where TMTSF stand for tetramethyltetraselenafulvalene, and X is one of the monovalent anions like PF6, AsF6, ClO4, ReO4etc., are also interesting for other reasons:

  • Many of the systems are good metals down to low temperature before they become superconducting.
  • Although they are basically one-dimensional, the interchain coupling may be changed by applying pressure or replacing the anions, thus allowing to tune the dimensionality.
  • some of the salts show transition to a spin-density-wave (SDW) ground state or a charge-density wave ground state.
  • Anion ordering may cause structural changes.
  • Charge ordering represents an entirely electronic ferroelectricity, albeit small effects on the anions may occur and the magnetic symmetry is changed.

 

Fig 3: (a) represents (TMTSF)2PF6-Structure: The planar organic molecules are stacked along the a-axis; in the c-direction they are separated by the PF6 anions; (b) illustrates the view along the stack of (TMTSF)2PF6: the TMTSF molecules are oriented along the c-axis; in the b-direction the selenium atoms develop interstack contacts and thus form sheets in the ab-plane with the tendency toward two-dimensionality (indicated by the red dashed lines).

Due to the one-dimensional nature of the Bechgaard salts, the low-energy excitations cannot simply be described by Landau's theory of a Fermi-liquid, instead the Tomonaga-Luttinger model (one-dimensional metals ) has to be applied. Of high importance is the influence of the interchain interaction on the physical properties since it has to lead to modification of the theoretical description.

Fig 4: Temperature dependence of the electrical resistivity of (TMTSF)2PF6 along all three directions. Below TSDW = 12 K (displayed in part (1) of (a)), the material undergoes a spin-density wave transition that leads to an opening of a gap in all directions of the Fermi surface. In the intermediate temperature range (part (2) of (a)), the system is metallic in all three directions with a strong anisotropy; it can be described by a Fermi-liquid. At temperature higher than the interstack coupling (represented by part (3) of (a) zoomed and illustrated in (b)) , the system behaves like a Luttinger liquid with the corresponding power-law dependences in the a- and c- directions.

The optical conductivity of (TMTSF)2PF6 shows a strong anisotropy. At low temperatures strong deviations from a simple Drude behavior is seen in the chain direction. There is a finite-energy excitation around 200 cm-1 (corresponding to excitations across the Mott gap) which develops for temperatures below 200 K and thus is not related to the SDW gap. And a zero-energy mode builds up as the temperature is lowered with an extremely small relaxation rate. Perpendicular to the stacks the conductivity is lower, but still shows a Drude-like behavior at low temperatures

 

Fig 5: Reflectivity spectra of (TMTSF)2PF6 measured at different temperatures along the stacking axis a (solid black line) and perpendicular to it (solid green line). The filled symbols are obtained by a coherent THz source , the open symbols are calculated from microwave experiments. The dashed lines represent a Drude fit, respectively. The inset of panel (b) shows the schematic phase diagram of the deconfinement transition for a system of weakly coupled conducting chains as suggested by Giamarchi and collaborators. The transition from a Mott insulator to a two- or three-dimensional metallic state occurs at T=0 K when t reaches a critical value t*. At high enough temperature, the increase in t leads to a transition from a Mott insulating to a one-dimensional Luttinger liquid and further to a dimensional crossover into a metallic state. The development of the SDW gap at 70 cm-1 is seen from the low-temperature conductivity E a plotted in the inset of panel (c).

Fig 6: Optical conductivity of (TMTSF)2PF6 for two different directions parallel and perpendicular to the stacks. In the longitudinal direction two contributions can be observed at low temperatures: a rather broad peak (green) centered around 200 cm-1that can be assigned to excitations across the Mott-Hubbard gap. The narrow zero-frequency mode corresponds to coherent transport along the chain due to self-doping of the Mott-insulator by a finite coupling between the chains.

At around 12 K (TMTSF)2PF6 undergoes a transition to a spin-density-wave ground state, i.e. a periodic modulation of the electronic spins which is not accompanied by a charge modulation or a lattice distortion. However, a gap in the density of states opens at the Fermi-surface and causes a drastic change in most of the physical properties. Due to spin-phonon coupling there is also a significant change in the acoustic properties, like sound velocity and attenuation. The susceptibility vanishes rapidly and the dc resistivity increases many orders of magnitude. The optical properties, however, still show appreciable contributions in the low-energy range below the single-particle gap. Some can be identified as collective excitations of the SDW as a whole. Most of the transport measurements have been performed along the chain direction where nonlinear conductivity was observed due to collective transport of the SDW. Much less is known about the properties in the perpendicular direction.

The nature of the superconductivity is not fully understood yet. Slowly cooled (TMTSF)2ClO4 becomes superconducting at 1.2 K; for (TMTSF)2PF6 on the other hand an external pressure of 6.5 kbar is needed to induce superconductivity. Early NMR experiments show no Hebel-Slichter maximum and may indicate the influence of antiferromagnetic fluctuations and p-wave pairing. Recently this idea was supported by measurements of the c-axis resistance in an external field of 10 Tesla and more. However, alternative explanations by Fulde-Ferrell-Larkin-Ovchinnikov phase have been suggested. Experiments on the thermal transport rule out the existence of nodes in the gap. Investigations of the electrodynamic properties might clear this controversy since the optical conductivity is sensitive to low-energy excitations.


Literature:

  1. M. Dressel et al., Phys. Rev. Lett. 77, 398 (1996).
  2. L. Degiorgi et al., Phys. Rev. Lett. 76, 3838 (1996).
  3. A. Schwartz et al., Phys. Rev. B 58, 1261 (1998).
  4. J. Moser et al., Eur. Phys. J. D 1, 39 (1998).
  5. M. Dressel
    Spin-charge separation in quasi one-dimensional organic conductors
    Naturwissenschaften 90, 337 - 344 (2003).
  6. M. Dressel, K. Petukhov, B. Salameh, P. Zornoza und T. Giamarchi
    Scaling behavior of the longitudinal and transverse transport in quasi-one-dimensional organic conductors
    Phys. Rev. B 71, 075104 (2005).
  7. M. Dressel
    Ordering Phenomena in Quasi One-Dimensional Organic Conductors
    Naturwissenschaften 94, 527 (2007).
  8. B. Köhler, E. Rose, M. Dumm, G. Untereiner und M. Dressel
    Comprehensive transport study of anisotropy and ordering phenomena in quasi-one-dimensional (TMTTF)2X salts (X = PF6,AsF6,SbF6,BF4,ClO4,ReO4)
    Phys. Rev. B 84, 035124 (2011).
  9. M. Dressel
    Quantum criticality in organic conductors? Fermi-liquid versus non-Fermi-liquid behavior
    J. Phys.: Condens. Matter 23, 293201 (2011).
  10. M. Dressel
    Electrodynamics of Bechgaards Salts: Optical Properties of One-Dimensional Metals
    International Scholarly Research Network (ISRN)
    Condensed Matter Physics 732973 (2012).
Fabre salts (TMTTF)2X

The TMTTF-salts where TMTTF denotes tetramethyltetrathiafulvalene are even more one-dimensional compared to their TMTSF analogs because the selenium atoms are replaced by smaller sulfur atoms which reduces the overlap within the stack and more important between the stacks. Therefore the ratio of Coulomb repulsion U and bandwidth W (transfer integral t) is larger and the systems become at low temperatures a Mott insulators.

Fig 7: Temperature dependence of the dc resistivity of several Fabre and Bechgaard salts. As the temperature is reduced, the charges become increasingly localized in (TMTTF)2AsF6 and (TMTTF)2PF6, before the charge-ordered state is entered below 100 K. (TMTTF)2SbF6 shows a transition from a metal-like state directly into the charge-ordered state at TCO = 157 K. (TMTSF)2PF6 undergoes a SDW transition at TSDW = 12 K. Only (TMTSF)2ClO4 remains metallic all the way down to approximately Tc = 1.2 K.

Only at elevated temperatures the charges are delocalized and rather poor metallic conductivity is observed. Detailed studies of the temperature and pressure dependence of the crystal structure and band structure help to understand the transition from the rather one-dimensional behavior to the more two-dimensional properties exhibit at low temperatures and high pressure. Optical experiments can identify the crossover in the electronic properties by looking at the coherent transport.

Fig 8: The coherence parameters of the interstack charge transport k = wp/2Γ as a function of temperature and pressure for (TMTTF)2PF6 and (TMTSF)2PF6 . The solid blue lines corresponds to kb = 0.85.

Upon cooling a charge order transition occurs with a sharp increase in resistivity. Due to electronic interaction, the charge per molecule is varied from a homogeneous distribution of half an electron per molecule to an alternation of charge rich and charge poor molecules.
Structural considerations are of superior importance for the understanding of the differences between the various TMTSF and TMTTF salts. The organic molecules are stacked along zig-zag chains in the a-direction, separated in the c-direction by the anions. The dimerization decreases by going from the selenium compound to the sulfur counterparts. In contrast to the selenium analogs which in general are metallic down to low temperatures, the TMTTF salts discussed here are Mott-Hubbard insulators due to the small transfer integrals. Consequently they show a broad, but distinct resistivity minimum at high temperatures attributed to the continuous opening of a charge gap which is closely connected to the increased Coulomb interaction and dimerization.
By applying pressure on (TMTTF)2PF6 the temperature resistivity minimum decreases and at 13 kbar the salt is fully metallic and undergoes a SDW phase transition similar to (TMTSF)2PF6. Applying pressure also enhances the interchain coupling, in agreement with the fact that it is more one-dimensional than the selenium analog. (TMTTF)2Br is close to the borderline between itinerant and localized carriers: only below 100 K the resistivity increases due to charge localization. As a consequence, the transition to an antiferromagnetic ground state at 13 K does not lead to a SDW, as observed in (TMTSF)2PF6 which stays metallic down to 13 K, but to a localized antiferromagnet (AFM).

The reduced dimensionality leads to instabilities (one-dimensional metals) of the electronic system and has a distinct influence on the transport as well as on the magnetic properties. By applying external pressure or magnetic field, changing the anions or substituting sulfur for selenium, these compounds can be varied from itinerant to localized electrons and spins. It is very interesting to compare the charge and the spin dynamics by changing the anions in these systems in order to vary the dimensionality and to change the on-site Coulomb repulsion. In this way we can tune the system from a one-dimensional Tomonaga-Luttinger liquid (one-dimensional metals) to a more two-dimensional Fermi liquid. Similar impacts are expected for the application of external pressure.
Charge order affects most of the electronic properties, but for many years no change in the spin arrangement could be observed: the magnetic susceptibility remains unchanged. Only recently electron-spin-resonance experiments on quasi-one-dimensional (TMTTF)2X salts (X = PF6, AsF6, and SbF6) could reveal that the magnetic properties are modified below TCO when electronic ferroelectricity sets in. The coupling of anions and organic molecules rotates the g-tensor out of the molecular plane creating magnetically nonequivalent sites on neighboring chains at the domain walls. Due to anisotropic Zeeman interaction a novel magnetic interaction mechanism in the charge-ordered state is observed as a doubling of the rotational periodicity of ΔH.


Literature:

  1. M. Dumm et al., Phys. Rev. B 62, 6512 (2000).
  2. B. Salameh, S. Yasin, M. Dumm, G. Untereiner, L.K. Montgomery und M. Dressel
    Spin dynamics of the organic linear chain compounds (TMTTF)2X (X = SbF6, AsF6, BF4, ReO4, and SCN)
    Phys. Rev. B 83, 205126 (2011).
  3. S. Yasin, B. Salameh, E. Rose, M. Dumm, H.-A. Krug von Nidda, A. Loidl, M. Ozerov, G. Untereiner, L.K. Montgomery und M. Dressel
    Broken magnetic symmetry due to charge-order ferroelectricity discovered in (TMTTF)2X salts by multifrequency ESR
    Phys. Rev. B 85, 144428 (2012).
  4. M. Dressel, M. Dumm, T. Knoblauch und M. Masino
    Comprehensive Optical Investigations of Charge Order in Organic Chain Compounds (TMTTF)2X
    Crystals 2, 528 - 578 (2012).
  5. M. Dressel, M. Dumm, T. Knoblauch, B. Köhler, B. Salameh, S. Yasin Charge Order Breaks Magnetic Symmetry in Molecular Quantum Spin Chains Advances in Condensed Matter Physics 2012, 398721 (2012).
Neutral-Ionic Transition in TTF-CA

While in the previous example of TMTTF and TMTSF salts the crystals consist of separate cation and anion chains between which the electron transfer occurs, mixed-stack organic charge-transfer compounds have only one type of chain composed of alternating p-electron donor and acceptor molecules (... ADADAD...).

TTF-CA1

The TTF and chloranil QCl4 are planar molecules. In the mixed-stack compound TTF-CA the two distinct molecules alternate.

TTF-CA3

 

Naturally grown single crystal of TTF-CA in the neutral phase (green phase) synthesized according to the plate sublimation technique.

These materials are either neutral or ionic, but under the influence of pressure or temperature certain neutral compounds become ionic. There is a competition between the energy required for the formation of a D+A- pair and the Madelung energy. Neutral-ionic (NI) phase transitions are collective, one-dimensional charge-transfer phenomena occurring in mixed-stack charge-transfer crystals, and they are associated to many intriguing phenomena, as the dramatic increase in conductivity and dielectric constant at the transition.
In the simplest case, the charge per molecule changes from completely neutral ρ=0 to fully ionized ρ=1. Ideally this redistribution of charge is decoupled from the lattice, and therefore should not change the inter-molecular spacing. In most real cases, however, the NI transition is characterized by the complex interplay between the average ionicity ρ on the molecular sites and the stack dimerization δ. The ionicity may act as an order parameter only in the case of discontinuous, first order phase transitions. While the inter-site Coulomb interaction V favors a discontinuous jump of ionicity, the intra-chain charge-transfer integral t mixes the fully neutral and fully ionic quantum states and favors continuous changes in ρ. The coupling of t to lattice phonons induces the dimerization of the stack, basically a Peierls-like transition to a ferroelectric state, which is a second order phase transition. Intramolecular (Holstein) phonons, on the other hand, modulate the on-site energy U and favor a discontinuous jump in ρ.

The temperature induced NI transition of tetrathiafulvalene-tetrachloro-p-benzoquinone (TTF-CA) at TNI = 81 K is the prime example of a first-order transition with a discontinuous jump in ρ. This can be seen be an abrupt change in the optical properties; below the NI transition the coupled bands shift to higher frequencies. In terms of a modified, one-dimensional Hubbard model the NI transition can be viewed as a transition from a band insulator to a Mott insulator due to the competition between the energy difference between donor and acceptor sites, and the on-site Coulomb repulsion U. Peierls and Holstein phonons are both coupled to charge transfer electrons, albeit before the NI transition the former are only infrared active, and the latter only Raman active. This makes polarized Raman and reflection measurements a suitable tool to explore the NI transition.

The optical experiments identify practically all the totally symmetric modes of both neutral and ionic phases of TTF-CA. The vibronic bands present inthe infrared spectra for T > TNI are due to sum and difference combinations involving the lattice mode, which gives rise tothe Peierls distortion at the transition. Three lattice modes which couple to electrons and become stronger as the transition is approached; they behave as soft modes of the ferroelectric transition at TNI= 81 K. The lowest mode softens most and is seen strongly overdamped around 20 cm-1. The temperature evolution of this Peierls mode, which shows a clear softening before the first-order transition to the ionic ferroelectric state takes place. In the ordered phase a clear identification and theoretical modelling of the Goldstone mode is still an open problem because the system has several degrees of freedom coupled to each other.The cooperative charge transfer among the constructive molecules of TTF-CA can also be induced by irradiation of a short laser pulse. A photoinduced local charge-transfer excitation triggers the phase change and cause the transition in both directions. When Cl is replaced by Br in the tetrachloro-p-benzoquinones the lattice is expanded, (like a negative pressure) and the ionic phase vanishes completely. Hydrostatic pressure or Br-Cl substitution is utilized as a control parameter to more or less continuously tune the NI transition at T → 0.
In the simplest case, the charge per molecule changes from completely neutral ρ=0 to fully ionized ρ=1. Ideally this redistribution of charge is decoupled from the lattice, and therefore should not change the inter-molecular spacing. In most real cases, however, the NI transition is characterized by the complex interplay between the average ionicity ρ on the molecular sites and the stack dimerization δ. The ionicity may act as an order parameter only in the case of discontinuous, first order phase transitions. While the inter-site Coulomb interaction V favors a discontinuous jump of ionicity, the intra-chain charge-transfer integral t mixes the fully neutral and fully ionic quantum states and favors continuous changes in ρ. The coupling of t to lattice phonons induces the dimerization of the stack, basically a Peierls-like transition to a ferroelectric state, which is a second order phase transition. Intramolecular (Holstein) phonons, on the other hand, modulate the on-site energy U and favor a discontinuous jump in ρ.