Journal of Physics and Chemistry of Solids 62 (2001) 105±108
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Charge ordering in organic conductors T. Takahashi* Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588, Japan
Abstract Recent developments in the ®eld of organic conductors are reviewed from the experimental point of view. The existence of charge ordering has been established in various materials. New experimental evidence of charge ordering in two different BEDT-TTF salts with two-dimensional quarter-®lled band and TTM-TTP with one-dimensional (1D) half-®lled band is presented. These observations are compatible with the recent prediction of the Hartree±Fock calculation, taking into account the on-site and inter-site Coulomb interactions. q 2000 Published by Elsevier Science Ltd. Keywords: A. Organic compounds; B. Electronic structure; D. Nuclear magnetic resonance; D. Spin-density waves
1. Introduction The most striking feature of organic conductors is the large variety of electronic properties, from magnetic insulators to superconductors. Most of the organic conductors investigated extensively so far are 2:1 cation radical salts, such as (TMTCF)2X (TMTCF TMTTF, TMTSF) and (BEDT-TTF)2X. In these compounds, the anion X`s are monovalent, X 2, so that the averaged valence of the organic molecule becomes 11/2. Thus the conducting properties are attributed to the p-band with quarter-®lling. It is surprising to ®nd that even compounds with the same constituent molecules behave quite differently. The difference in the electronic properties should have originated from the different molecular arrangements. Thus, the most fundamental question is: what is the relation between the molecular structure and the conduction properties? Band structure calculations, based on the extended HuÈckel model for molecular orbitals and rather simple tight-binding approximation, have been veri®ed very well by various experimental techniques to determine the Fermi surface. It is another important feature of the organic conductors that the band structure is very well de®ned. Owing to the recent extensive studies from experimental and theoretical points of view, our understanding of this family has progressed considerably. Theoretically, trials to understand the diversity of the ground state of the organic * Corresponding author. Tel.: 1 81-3-5992-1023. E-mail address:
[email protected] (T. Takahashi).
conductors from uni®ed viewpoints have been proposed by Kino and Fukuyama, and recently also by Seo. They have considered the Coulomb interaction and the full anisotropy of transfer integrals between molecules, within the framework of the Hartree±Fock approximation [1,2]. They have found the possibility of various types of charge ordering in a wide parameter region. Experimentally, 13C NMR using single crystals based on organic molecules selectively enriched by 13C isotope has been applied as a standard technique. This is a very sensitive method of investigating the electronic properties from the microscopic point of view. In this review, I will talk about the recent topics in the ®eld of organic conductors, including some direct experimental evidence of charge ordering in various systems.
2. Coulomb correlation in organic conductors The importance of on-site Coulomb interaction U has been recognized at an early stage of the research on organic conductors, since many salts have shown various magnetic ground states, incommensurate SDW, long range antiferromagnetic (AF) order, and spin-Peierls state. Organic conductors have been revealed as strongly correlated systems. Generally speaking, the on-site Coulomb interaction, U, should be relatively small in the organic system because of the large size of the constituent organic molecules. On the other hand, the transfer integrals, t, between the neighboring molecules are much more
0022-3697/00/$ - see front matter q 2000 Published by Elsevier Science Ltd. PII: S 0022-369 7(00)00109-8
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Fig. 1. Charge ordering in 1D chain. (a) The large and small circles represent the charge-rich and the charge-poor sites, respectively. (b) Magnetic order in the charge-ordered state.
reduced, so that the ratio of U/t can be as large as in the transition metal oxides. In a half-®lled system, it is well known that the on-site Coulomb interaction stabilizes a Mott±Hubbard type insulating state, where each carrier is localized at each molecular site. There is no charge ordering in any sense. Even in a quarter-®lled system, a Mott±Hubbard insulator is realized when strong dimerization is present; there exists one carrier per dimer, which leads to an effective half-®lled band. This is the case of the k -(BEDT-TTF)2X salts. When the inter-site Coulomb interaction V is important, another type of charge ordering is expected even in the quarter-®lled band: Wigner crystallization. The ®rst observation of charge ordering of this type has been done on another family of organic conductor, (DI-DCNQI)2Ag [3]. The planer organic molecule, DI-DCNQI, forms a 1D pband with quarter-®lling. There is no dimerization along the chain. The temperature dependence of resistivity is nonmetallic below room temperature. From 13C NMR measurements, it was observed that the resonance line splits into two below 220 K; the author identi®ed these lines as the ones corresponding to electron-rich and electron-poor sites (Fig. 1(a)). It is believed that this is due to the long range part of the Coulomb interaction; the carriers are localized with equal spacing along the chain. This is the ®rst observation of Wigner crystal in an organic system. A similar situation has been suggested in (TMTTF)2Br. This salt is also quasi-1D with little dimerization. Resistivity is metallic at high temperatures and shows a broad minimum around 100 K. Various experiments have revealed an antiferromagnetic long-range order below 14 K. We have carried out the 1H NMR analysis of the magnetic ordering in the AF state and found the wave number is commensurate, (1/2, 1/4, ,0), and the amplitude ,0.15 mB/molecule [4]. In addition, we have found that the observed lineshape is well reproduced only when the phase of SDW with respect to the lattice periodicity is assumed as " ±0± # ±0,¼, schematically (Fig. 1(b)). This type of con®guration is easily understood if the
carriers have already been localized as shown in Fig. 1(a). In fact, the stability of this spin con®guration has been con®rmed theoretically by taking account of the inter-site Coulomb interaction. In such a 1D salt, the effects of Coulomb correlation are rather easy to understand. However, what happens in a 2D system is a delicate question. A theoretical approach to this question has been carried out by Kino and Fukuyama [1]. They have investigated the effect of the on-site Coulomb interaction on the tight-binding 2D band by using the Hartree±Fock approximation. They found that the ground state of the 2D band changes drastically depending on the band parameters and the strength of the on-site Coulomb interaction, U. They proposed two parameters to explain the variety of the BEDT-TTF salts; the band overlap and the dimerization. When the band overlap is small, a large U leads to a band insulator with a magnetic ordering. It explains fairly well the difference between the a-I3 salt and the a-MHg(SCN)4 (M NH4, K, Rb, Tl) salts. When the dimerization is large, the system can be understood as a half-®lled metal where the large U limit results in a Mott±Hubbard insulator. This picture explains well the competition between the magnetic insulating state and the superconducting state in a series of the k -phase salts. Thus the BEDT-TTF salts should be considered as a highly correlated system, where the interplay with the molecular arrangement realizes a large variety of electronic properties.
3. a-(ET)2X a-(BEDT-TTF)2I3 is rather old well-known salt, which is metallic around room temperature and exhibits a M±I transition at 135 K
TMI at ambient pressure. It is con®rmed that the insulating state is nonmagnetic with a large spin gap. By applying pressure of 1.4 GPa, the insulating state is suppressed and a new type extremely narrow-gap semiconducting state appears [5]. This salt contains four BEDT-TTF molecules (A, A 0 , B and C) per unit cell. A schematic view of the molecular arrangement is shown in Fig. 2(a). A and A 0 constitute stack I, and stack II consists of B and C. According to the band calculation, there are four slightly overlapped bands, three of which are almost occupied. The band structure is semimetallic very near a band insulator. Although many experimental and theoretical studies have been made, the origin of this M±I transition is not understood yet. A structural anomaly was observed at the transition, but it was not large enough to lead to any real gapopening. In order to clarify the mechanism of this M±I transition, we have made 13C NMR measurements. Single crystals were synthesized with the BEDT-TTF molecule, of which the central double-bonded carbon sites were selectively
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4. u-(ET)2RbZn(SCN)4
Fig. 2. Schematic view of the molecular arrangement of: (a) a(BEDT-TTF)2I3; and (b) u-(ET)2RbZn(SCN)4.
enriched with 13C isotopes. Details of the measurements are presented elsewhere in this workshop. We have observed that the 13C NMR lineshape is split into two components with almost equal intensity below the transition temperature TMI. Relaxation rate, 1/T1, is quite different between the two components. The shift of the component with longer T1 is almost temperature independent, while that of the other component with shorter T1 has a large temperature dependence; the latter moves towards the zero shift position as temperature decreases. These results clearly indicate that there exist two kinds of BEDT-TTF molecules with a different microscopic environment in the insulating state. It is reasonable to assume that half of BEDT-TTF molecules become nearly neutral, resulting in the longer T1 and the smaller temperature dependence of the spectrum, and the other half have a large charge density with the shorter T1 and the larger temperature dependence of the shift. Since it is believed that the charge is equally populated on the molecules in the higher temperature region, this M±I transition should be accompanied by charge re-distribution among the molecules. Taking account of the actual anisotropy of the transfer integrals and the on-site Coulomb interaction, Kino and Fukuyama have predicted this kind of charge ordering in this salt [1]. According to their calculation, the charge-rich sites should form a stripe structure along the a-axis and a 1D antiferromagnetic state should be the ground state. They claimed that this was the prediction of the Hartree±Fock approximation and a spin-Peierls type ordering should take place in reality. Recently, Seo has extended his treatment by considering the inter-site Coulomb interaction and found that the stripe should go along the b-axis (`vertical' stripe) [2]. In order to determine the charge distribution in the molecular layer, measurements of the precise angular dependence of 13C NMR lineshape are in progress. Preliminary results seem to favor the vertical stripe model.
The u-type salts have a highly symmetric molecular arrangement with two molecules per unit cell (Fig. 2(b)) [6]. Because of inversion symmetry, all BEDT-TTF molecules are crystallographically equivalent, as far as the roomtemperature structure is concerned. Two p-bands are well degenerated and result in a 3/4®lling with a 2D closed Fermi surface. However, u-(ET)2RbZn(SCN)4 exhibits a sharp M±I transition at 190 K [6]. A structural distortion with the doubling of the lattice periodicity along the c-axis is observed at the transition. Spin susceptibility, j , has no anomaly at the M±I transition temperature. The low temperature electronic properties depend strongly on the cooling rate around the transition [7,8]. In the slowly cooled state, the susceptibility shows a Bonner±Fisher-like behavior in the higher temperature region and starts to decrease rapidly below 30 K, indicating a spin-singlet ground state. On the other hand, in the rapidly cooled state, the susceptibility is enhanced below 100 K. EPR measurements suggest that the rapidly cooled state is a metastable state where the higher temperature phase is frozen down. We have focused on the behavior of the slowly cooled state, and tried to clarify the origin of the curious magnetic property and the mechanism of the metal± insulator transition, by analyzing the angular dependence of the 13C NMR lineshape for a single crystal. Details are presented separately in this workshop. The results are summarized as follows: 1. At 286 K, all BEDT-TTF molecule are crystallographically equivalent. 2. At 5 K, where the electronic state is nonmagnetic, the 13C NMR signal splits into two sets of Pake doublet, indicating the existence of two kinds of nonequivalent BEDTTTF molecules with different chemical shifts. 3. Angular dependence of half of the NMR peaks agrees with that of the chemical shift of neutral BEDT-TTF. 4. From the temperature dependence of the Knight shift, the charge separation between the two sites is estimated as 0.2:0.8. To determine the charge distribution in the organic layer, we measured the angular dependence of NMR lineshape when the ®eld is applied in the ab- and the ac-plane. We found that the electric charge in the insulating phase orders so as to form a stripe structure along the a-axis and the charge-rich and charge-poor site alternate along the c-axis (Fig. 3). The spin-singlet phase below 30 K is recognized as being due to a spin-Peierls transition of the 1D spin system. We conclude that the M±I transition in the title compounds is of a novel type accompanied with a charge re-distribution in the organic layer. The situation is quite similar to that in a-(BEDT-TTF)2I3 and very well theoretically discussed by Seo [2].
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molecules are crystallographically equivalent at high temperatures. This is a strong evidence of charge disproportionation in the insulating phase. We propose a charge order of 2±0±2±0 along the c-axis. 6. Concluding remarks Fig. 3. Schematic view of the proposed charge order in the insulating state of u-(ET)2RbZn(SCN)4.
5. (TTM-TTP)I3 (TTM-TTP)I3 is a salt with the donor to acceptor ratio of 1:1. The TTM-TTP molecules form highly 1D stacks along the crystallographic c-axis [9]. Therefore, it is expected that (TTM-TTP)I3 has a 1D half-®lled band. Generally, 1D half®lled band systems are expected to become Mott insulators due to the on-site Coulomb repulsion. However, this compound exhibits a metallic conductivity in a wide temperature range down to 160 K. This is believed to re¯ect the fact that the on-site Coulomb repulsion is small since the TTM-TTP molecule contains two TTF skeletons and has relatively large size compared with that of the other organic donors, such as TMTSF and BEDT-TTF. This compound exhibits a M±I transition at 160 K (TMI) and at ambient pressure. To clarify the mechanism of the M±I transition and the nature of the ground state, we have carried out 13C NMR measurements. The experiments have been performed on two different powder samples, where 6 or 1 carbon-site(s) of TTM-TTP molecule are selectively substituted with 13C isotope. In the 6-site substituted sample, we found that relaxation rate, 1=T 1 , suddenly decreases below TMI. This suggests that the insulating phase is nonmagnetic. In the measurement of the 1-site substituted sample, lineshape was found to split into two peaks with equal signal intensity below about 80 K. This clearly indicates that there exist two different kinds of TTM-TTP molecules in this temperature region, while all TTM-TTP
We have presented experimental evidence of the charge ordering in various organic conductors with the use of 13C NMR measurements on selectively 13C enriched samples. It is evident that precise analysis of single crystal measurements is a powerful method. The agreement between the theory and experiments are satisfactory, considering the limitation of the Hartree±Fock or the Hartree approximation. Acknowledgements The author would like to thank H. Fukuyama, H. Seo, H. Kino and K. Kanoda for valuable discussion. The original works have been carried out in collaboration with K. Hiraki, K. Yamamoto, T. Nakamura and other members of Takahashi lab of Gakushuin University. These are carried out as part of ªResearch for the Futureº Project, no. JSPSREFTF97P00105, of Japan Society for Promotion of Science. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
H. Kino, H. Fukuyama, J. Phys. Soc. Jpn 65 (1996) 2158. H. Seo, J. Phys. Soc. Jpn 69 (2000) 805. K. Hiraki, K. Kanoda, Phys. Rev. Lett. 80 (1998) 4739. T. Nakamura, et al., Synth. Met. 70 (1995) 1293. N. Tajima, et al., Synth. Met. 103 (1999) 1958. H. Mori, et al., Phys. Rev. B 57 (1998) 12 023. T. Nakamura, et al., Mol. Cryst. Liq. Cryst. 285 (1996) 57. T. Nakamura, et al., Synth. Met. 96 (1997) 1991. T. Mori, et al., Bull. Chem. Soc. Jpn. 67 (1994) 661.