As shown in Figure 1, Bechgaard and Fabre salts are made of a zig-zag stacking of TMTSF and TMTTF molecules arranged nearly perpendicularly to the 1D direction, a. In the short direction of the molecule, stacks, shifted from each other along b, form (a, b) donor layers. In the long direction of the molecule, out of phase first neighboring zig-zag stacks delimit methyl group cavities which are filled by the anions X. This packing leads to an alternation of layers of well coupled donors with anions along c. Two aspects of the structure at ambient conditions are noticeable: (i) the slight dimerization of the zig-zag stack; and (ii) the presence of a sizeable thermal motion of the anion X in its cavity [9]. These salts crystallize in the triclinic space group P-1 with the inversion centers located in between the molecules and in the center of the methyl group cavities. If one ignores the slight stack dimerization and the location of the anions close to the shortest zig-zag bond, the structure has an underlying monoclinic C2/m symmetry (a: binary axis, b’ = 2b-a, c) tending to promote a 2₁ screw axis symmetry in the stack direction [8]. In this respect it is interesting to remark that both Bechgaard and Fabre salts, with X = PF₆, undergo, at 5.5GPa and 8.5GPa respectively, a first order phase transition to a monoclinic (a: binary axis, b’, c) structure [10]. In the (a, b) donor layer, this discontinuous structural change could be achieved by the relative shift, along a, of first neighboring stacks.

In a 1D description of the quarter filled interacting electron gas, the dimerization of the zig-zag stack activates an umklapp 4k_F = a* electron–electron scattering term which, in presence of sizeable Coulomb repulsions, facilitates the charge localization (k_F is the Fermi wave vector of the quarter filled 1D electron gas) [12]. The strength of this umklapp process depends of the amplitude of the dimerization gap 2Δ_D which opens at ±a*/2 in the band structure well below the Fermi level. Δ_D amounts to the difference of transfer integrals (in presence of the Hartree anion potential) on the two inequivalent bonds of the zig-zag. Δ_D calculated by the DFT differs from Δ_D calculated by the Extended Hűckel Theory (EHT) which does not take into account the anion potential. For example in (TMTSF)₂ClO₄ at room temperature (RT) DFT gives Δ_D = 26 meV [13], while EHT gives Δ_D = 37–54 meV (see Table 4.3 in [2]). Another complication arises if one considers the interstack coupling: the inter-chain transfer integrals lead to a significant variation of Δ_D along b*. In (TMTSF)₂ClO₄Δ_D varies from ~50meV in (a*/2, 0) to ~0meV in (a*/2, b*/2) [13] at RT. Δ_D decreases upon cooling and under pressure, while Δ_D increases from the TMTSF’salts to the TMTTF’salts. Δ_D is controlled by the shape and volume of the anion which deforms the donor packing via its interaction with the terminal methyl groups.

Structural effects associated to anions require a special attention because the anions are located in soft cavities delimited by the methyl groups of the TMTSF or the TMTTF molecules. The anions fit these cavities in a more or less compact manner depending upon the volume and shape of the anion [14,15,16]. The anions were considered in earlier studies as spacers acting on the inter-layer distance as does the pressure [17]. In fact recent works summarized in this review show that their role is more subtle than it was previously believed. First, the anions are located in centro-symmetric cavities. This location causes no problem for centro-symmetric anions such as octahedron MF₆ (M = P, As, Sb) or sphere (Br), but it implies at RT the existence of an orientation disorder for tetrahedral (ReO₄, ClO₄, BF₄), triangular (NO₃) or asymmetric linear (SCN) anions. Second, each anion experiences quite a symmetric environment from its six first neighbor donors [18] due to the six closest methyl groups. Among them, four groups are located in the (b’, c*) plane perpendicular to the stacking axis, while the two remaining groups, located in the (a, c*) plane, are significantly tilted with respect to a. These six methyl groups delimit three sets of three-fold symmetry axis close to the symmetry axis of the octahedral anions. The four planar methyl groups delimit two sets of two-fold symmetry axis close to the symmetry axis of the tetrahedral anions [18]. Third, the F or O outer atoms of the anion form weak H-bonds with the closest methyl groups, especially at low temperatures when thermal disorder is reduced [19]. The 4K neutron scattering structural refinement [11], which allows precisely locating the H of the methyl groups of (TMTSF)₂PF₆, shows the formation of 6 H-bonds with F(1) and F(3) of the PF₆ (red dotted lines in Figure 1). All these H-bonds are located in the plane perpendicular to the stacking axis a. In addition, the anion develops short contact distances with the Se of the closest donors. Figure 1 shows (blue dotted lines) the two short Se…F(1) contacts established in (TMTSF)₂PF₆. The anion and thermal dependences of the geometry of the S...F interactions have been analyzed in (TMTTF)₂PF₆, AsF₆ and SbF₆ [20]. Note that F(2), which presents the strongest disorder [11], is not involved in any interactions. Any change of the shape of the methyl group cavity, caused by an elastic deformation of the donor stack for example, should react on the location of the anions and vice versa.

These two kinds of short contacts provide respectively indirect (via the polarization of the H-bond network and of the intra-molecular σ bonds) [21] and direct (via the Se or S atoms) attractive interactions between the anion and the π holes cloud located in the inner part of the donor. In this respect infrared measurements provided evidence of a considerable electron-molecular-vibration coupling of the methyl groups of both TMTSF and TMTTF with the charges on the molecules [22]. These interactions are involved in the inter-chain coupling mechanism (see Section 3.1.2) and for this reason play a key role in the stabilization of various ground states exhibited by Bechgaard and Fabre salts such as the AO transition involving non centro-symmetric anions (see Section 7), the CO transition breaking the inversion symmetry (see Section 5) and the SP transition subject to an important magneto-elastic coupling (see Section 6).

The location of anions in methyl group cavities provide flexibility in the structure due to the soft interface provided by the methyl groups between the anions and the core of the donors and the incomplete fit of the anion in the volume delimited by these methyl groups [14,15,16]. This soft environment tolerates the presence of disordered anions in the structure even for centro-symmetrical anions [9]. At ambient conditions, the non centro-symmetrical tetrahedral anions are disordered in Bechgaard and Fabre salts while they are ordered in others structurally related 2:1 salts, such as (BEDT-TTF)₂ReO₄, (t-TTF)₂X with X = ClO₄ and BF₄ and (DMtTTF)₂ClO₄, built with donors which do not provide a methyl group environment at the anion.

The lattice softness is revealed by thermal expansion measurements. First, linear expansion coefficients, α_i, are one order of magnitude larger in the PF₆ salt than in the Br salt where the anion better fits the volume of its methyl group cavity [23]. Second, in salts incorporating PF₆ or AsF₆ anions, the rate of variation of α_i upon heating becomes negative at high temperature [24]. This finding points out peculiar lattice dynamics, possibly due to “free” rotation and/or translation of the anions in their cavities. This effect, which is observed both for TMTTF and TMTSF salts, is mostly pronounced along the c* direction where layers of donors and anions alternate [23,24,25].

The enhanced values of Debye Waller factors obtained in structural refinements show the presence of an atomic disorder for both the methyl groups and the outer atoms of the anions. An orientation disorder is expected for non centro-symmetrical anions located in a centro-symmetric cavity. This disorder is removed at a well defined AO transition which will be the object of Section 7. Below we shall consider the case of centro-symmetrical octahedral anions such as PF₆. At RT, F atoms exhibit a sizeable thermal motion but the finding of well defined maxima in electron-density map, obtained in the structural refinement of (TMTSF)₂PF₆ [9], show that there is no free rotation of the centro-symmetrical anion. At 20K, the anion disorder is almost completely suppressed especially for F(1) and F(3) atoms forming H bonds and a linkage with the Se (see Figure 1) [11]. However neutron refinements show that methyl groups sustain a certain disorder even at 4K [11], probably due to quantum-mechanical tunneling. NMR studies show that PF₆ disorder is established upon heating above ~70K in (TMTSF)₂PF₆ [26]. More recent NMR studies performed in (TMTTF)₂SbF₆ [27,28] show, by the measurement of different activation energies in the molecular motion, that in fact anion disorder is progressively set upon heating. A detailed analysis [29] of the Debye Waller factor of (TMTSF)₂AsF₆ at 125K suggests that the disorder could take place between two well defined orientations of the AsF₆ anion in its cavity. Several activation energies also govern the motion of the methyl groups in TMTSF salts [30,31,32,33].

Thermal variation of the principal directions of the dilatation tensor of (TMTSF)₂PF₆ [11] suggests a lattice modification around 60–50K which could be related to the “freezing out” of the PF₆ disorder previously considered. More precisely, the thermal variation of the lattice expansion in the direction i divided by T, α_i/T, or more likely the volume expansion divided by T, (Σ_iα_i)/T, is proportional to the entropy derivative ∂S/∂T [34]. α_┴/T taken from the data of [24] exhibits broad maxima around 30–40 K in (TMTSF)₂PF₆ before dropping to zero at lower temperature [34]. This finding implies that below these maxima a net decrease of the “lattice” entropy, probably due to the vanishing of the structural disorder, should occur. The best way to reduce simultaneously the PF₆ and methyl group disorders is to link these two entities, as suggested from methyl protons NMR [32]. These findings have important consequences on the density wave instabilities which will be considered in Section 3.

The PF₆ anion disorder could be even more significantly reduced by a well defined thermodynamic transformation recalling the AO transition (see Section 7). This could be achieved by an orientation ordering transition achieving a well defined orientation at the anion which oscillates between several positions in its methyl group cavity at high temperature [29]. Such a transition has been observed in (EDO-TTF)₂PF₆ [35] where the orientation ordering of PF₆, accompanied by its shift, stabilizes a 3D pattern of CO and BOW distortions of the EDO-TTF stack. All these effects lead to a unit cell doubling which causes the 2k_F MI transition of (EDO-TTF)₂PF₆. In P-1 triclinic (TMTSF)₂PF₆, where there is no cell doubling (above T_SDW), the only possible symmetry breaking operation while keeping the translation symmetry will be the loss of inversion centers as for the CO transition of the (TMTTF)₂X’s (see Section 5). However neutron scattering structural refinements of (TMTSF)₂PF₆ performed at 4K and 20K [11] do not provide any evidence of the loss of the inversion centers (Note that this also implies that PF₆ does not shift from the centre of its methyl group cavity).

The 1D 2k_F BOW instability of (TMTSF)₂ClO₄ [40] behaves as the one of (TMTSF)₂PF₆ and AsF₆. Figure 4 reports the thermal dependence of the 2k_F peak intensity, I(2k_F) given by expression (1), of the X-ray diffuse scattering from (TMTSF)₂ClO₄. In this salt the low temperature vanishing of I(2k_F) has to be associated with the 3D critical growth below ~40 K of the (0, 1/2, 0) AO structural instability promoting the uniform ClO₄ ordering and anion shift in stack direction (see Section 7.3) [61]. Figure 4 shows surprisingly that the thermal dependence of the 2k_F BOW fluctuations of (TMTSF)₂ClO₄ is strongly modified upon substitution by the TMTTF [62].

A low temperature divergence of I(2k_F) appears for very small amount of TMTTF substituent. For x = 0.5% this additional divergence pushes down at lower temperatures the drop of I(2k_F) which remains due to the competing AO instability as in pure (TMTSF)₂ClO₄. The thermal behavior of I(2k_F) in the x = 0.5% salt resembles the one observed (see Figure 2 in [63]) in the (TMDTDSF)₂PF₆ iso-structural salt built on a donor hybrid between the TMTSF and TMTTF molecules. However in (TMDTDSF)₂PF₆ the drop of I(2k_F) below 20 K is not due to an AO transition but, as for (TMTSF)₂PF₆, to the stabilization of a SDW ground state below 7 K. Note that because of the orientation disorder of the TMDTDSF molecule in the structure [64], I(2k_F) does not vanish completely at low temperature in (TMDTDSF)₂PF₆ so that a 1D SP short range order (on ξ_a~25 Å) still coexists with the 2k_F SDW modulation.

Only the low temperature divergence of I(2k_F) remains in the x = 30% salt below 100K. This low temperature divergence of the 2k_F diffuse scattering intensity recalls the divergence of the SP fluctuations observed in (TMTTF)₂Br and PF₆ below 80 K and 60 K respectively [65].

In TMTTF salts the occurrence of a low temperature divergence of I(2k_F) coincides with the presence of a high temperature charge localization [51,52] which leaves the spin degrees of freedom available for a low temperature SP or AF instability. This charge localization manifests below a temperature, T_ρ [66], higher than the onset temperature of the critical growth of the SP fluctuations. In the x = 30% salt the 2k_F fluctuations detected below the spin-charge separation temperature T_ρ [67] are thus the structural fingerprint of an incipient SP instability which fully diverges in (TMTTF)₂PF₆ .

In conclusion the [(TMTSF)_1−x(TMTTF)_x]₂ClO₄ solid solution illustrates quite well when x increases that the evolution from a 2k_F BOW instability, which vanishes at low temperature, to a divergent SP instability follows the growth of the 4k_F charge localization

(TMTTF)₂PF₆ develops 2k_F SP critical fluctuations below about 60 K (taken as the mean field transition temperature of the SP transition, T_SP^MF). The critical nature of the SP fluctuations is assessed by the divergent growth of the SP susceptibility, χ(2k_F) [7,8,65], and of the intra-chain correlation length, ξ_SP; both quantities being defined by expression (3). The divergence is achieved at T_SP ~ 17 K, temperature at which a long range (1/2, 1/2, 1/2) SP stack tetramerization occurs [68].

Figure 5 compares the thermal dependence of ξ_SP⁻¹ of (TMTTF)₂PF₆ and of (TMTTF)₂Br. It clearly shows that the SP fluctuations of (TMTTF)₂Br do not diverge. Thus Figure 5 resembles for the SP fluctuations of (TMTTF)₂Br at Figure 2b for the 2k_F BOW fluctuations of (TMTSF)₂PF₆. We shall consider at the end of this section this aspect of the SP fluctuations of (TMTTF)₂Br.

The thermal dependence of ξ_SP⁻¹ of (TMTTF)₂PF₆ can be well accounted for by the calculation of the fluctuations of the weakly localized SP chain [69]. From this calculation one deduces that the SP coherence length ξ₀ amounts to 12 Å. This value is very close to ξ₀ ~ 10 Å found for the SP instability of (BCPTTF)₂PF₆ [7]. From the relationship linking ξ₀ to T_SP^MF:

ξ₀= ħv_σ/πk_BT_SP^MF (6)

one gets a “spin velocity” ħv_σ ~ 0.2 eVÅ in (TMTTF)₂PF₆. A similar value ħv_σ = 0.27 eVÅ is obtained in (BCPTTF)₂PF₆ where T_SP^MF ~ 100 K. For this last compound which can be described by the Heisenberg Hamiltonian coupling well localized spins one gets, with ħv_σ = πJa/2, an AF exchange coupling J = 280K which is close to J = 330 K deduced from the fit of the thermal dependence of the spin susceptibility of (BCPTTF)₂PF₆ [70]. If the same analysis is performed for (TMTTF)₂PF₆, where the holes are less localized than in (BCPTTF)₂PF₆, one gets, using the above quoted ħv_σ value, J = 210 K, which is twice smaller than J = 420K obtained from the fit of the thermal dependence of the spin susceptibility [71]. A similar discrepancy is obtained for (TMTTF)₂Br where expression (6) leads, with ξ₀ ~ 10 Å and T_SP^MF ~ 80 K, to a J value of 230 K twice smaller than J = 500 K obtained from the fit of the thermal dependence of the spin susceptibility [71]. It thus appears that the analysis using the Heisenberg Hamiltonian, strictly valid for localized spins, does not hold for the TMTTF salts where the holes bearing the spins are too delocalized.

Let us remark that in the TMTTF salts k_BT_SP^MF amounts to the energy of the transverse acoustic phonon mode, ħΩ~5meV, which controls the dynamics of the SP instability. With k_BT_SP^MF ~ ħΩ, the SP transition should occur in the adiabatic limit with however a strongly damped soft mode (see Figure 4b in [72]). This is consistent with the adiabatic limit used in [69] for the calculation of ξ_SP^-1 shown in Figure 5. However with k_BT_SP^MF ~ ħΩ, (TMTTF)₂PF₆ should not be too far from the adiabatic-antiadiabatic crossover. As T_SP^MF decreases when the size of the anion increases, the AsF₆ salts could be located in the anti-adiabatic regime and the SbF₆ salt in the gapless regime where the SP ground state cannot be stabilized (see Section 6.2 and the analysis performed in [73]). The location of the SbF₆ salt in the gapless regime agrees with the non detection of SP X-ray diffuse scattering fluctuations in this salt. Due to the absence of a SP instability the SbF₆ salt undergoes an AF transition. The SCN salt behaves similarly. However the mutual exclusion between AF and SP instabilities is not general among the TMTTF salts because the Br salt exhibits below 80 K quasi-1D SP fluctuations which coexist with AF fluctuations whose divergence [74] stabilizes below T_N = 13 K the AF ground state.

As previously mentioned, the thermal dependence of the SP fluctuations of (TMTTF)₂Br resembles those of the 2k_F BOW fluctuations of (TMTSF)₂PF₆. Figure 5 shows that ξ_SP reaches ~13 Å before the vanishing of the SP fluctuations, a similar value of ξ_BOW (14 Å) was found in (TMTSF)₂PF₆ (Figure 2b). The vanishing of the SP fluctuations in the Br salt could have the same origin as for the BOW fluctuations of (TMTSF)₂PF₆. However there is no low temperature structural refinement in the Br salt allowing sustaining this assertion. Such a structure would be all the more desirable than thermal expansion measurements [23] show that the lattice (as well as electronic properties, see Section 4.1) exhibits unusual features just above T_N. Upon cooling below 18 K α_c* abruptly drops, exhibits a negative maximum around 17 K, then gently increases towards zero. These low temperature thermal expansion anomalies, which recall glassy phenomena involving ethylene groups in (BEDT-TTF)₂X [3], could be also associated to the freezing of the disorder of methyl groups of the TMTTF.

AF order which develops below a 2nd order phase transition in (TMTTF)₂Br stabilizes a q_AF = (1/2, 1/4, ?) commensurate magnetic modulation [75]. The magnetic order is accompanied by a structural modulation at the q_S = (1, 1/2, ?) reduced wave vector (the component 1a*, corresponding to the 4k_F wave vector, means that the superstructure reflections are detected in H odd layers of Bragg reflections [65]). As q_S = 2q_AF the structural modulation should result from a “magneto-elastic” coupling which will be considered below.

The coupling between the structural and AF order parameters is analyzed in Annex A.1 using the simplest Landau development of the free energy. Its minimization gives two solutions shown in Figure 6.

Solution (a) corresponds to an AF order with one site out of two bearing the magnetization, while solution (b) gives an AF order where all the sites bear the magnetization. In the Landau theory of Annex A.1 only solution (a) gains energy by setting a 4k_F structural modulation. NMR lineshape analysis [75] better agrees with the spin configuration shown in (a). In the schematic representation of Figure 5a the presence of a spin on one site out of two is accompanied by an excess of hole on the magnetic site and a defect of hole on the non magnetic site. This leads to the formation of a 4k_F CDW or CO [76]. CO should be accompanied by a 4k_F internal deformation wave of the TMTTF molecules in phase with the charge density per molecule. The CO pattern could be also stabilized by a displacement wave of the Br towards the molecule bearing the excess of hole (if there is no H-bonds blocking the anion shift), recalling the one found in the structural refinement of δ-(EDT-TTF-CONMe₂)₂Br in its CO ground state [77]. As previously mentioned in Section 3.3, (TMTTF)₂Br exhibits unusual features few degrees above T_N. In addition to the lattice thermal expansion anomaly previously reported, (TMTTF)₂Br exhibits below T* ~ 18–22 K anomalous electronic properties:

(TMTTF)₂Br bears some resemblance with (TMTTF)₂SCN which also stabilizes the same modulations. (TMTTF)₂SCN (see Section 7.4) sets at T_CO = 160K an anti-ferroelectric (1, 1/2, 1/2) CO superstructure followed at T_N = 7 K by a q_AF = (1/2, 1/4, ?) magnetic order while in (TMTTF)₂Br both modulations are established at the same 13K transition. This analogy is better revealed by dielectric permittivity measurements showing in both salts upon cooling an increase of dielectric constant, probably due to the growth of CO ferroelectric segments on individual stacks, followed by an abrupt drop of the dielectric constant ~20K above T_CO in (TMTTF)₂SCN [81] and below ~T* in (TMTTF)₂Br [82], probably when the inter-chain anti-ferroelectric coupling develops. 3D CO local order should induce the charge non homogeneities revealed by NMR [80] below T* in (TMTTF)₂Br. These charge non homogeneities could trigger local random Br displacements, possibly inducing methyl group disorder, which could cause the lattice expansion anomaly observed along the c* direction [23].

(TMTSF)₂PF₆ stabilizes below T_SDW = 12 K an incommensurate q_SDW = (1/2, ~1/4, ?) magnetic modulation [54,55] stabilized by the nesting of its FS [56] and where the exchange field due to the intra-site coulomb repulsion U opens a full gap at the Fermi energy. However the phase transition of (TMTSF)₂PF₆ exhibits additional features. First, the 2k_F SDW order is stabilized by a first order transition [83], while the Peierls or Slater transition caused by the simple divergence of CDW/BOW or SDW electron-hole response functions is of second order [1,2]. It follows that the order parameter, the magnetization [71] or the square root of the 2k_F satellite intensity [65] (see below), does not continuously vanish to zero at T_SDW. There is also a jump of electrical conductivity at the MI transition. Second, a “specific heat” anomaly is observed at T_SDW in thermal expansion measurements [25]; a feature not expected for a pure electronic SDW transition. Third, very weak X-ray satellite reflections (but too intense to be due to magnetic scattering) are observed below T_SDW at the reduced q_SDW (2k_F CDW reflections) and 2q_SDW (4k_F CDW reflections) wave vectors [7,65,84].

Thus the ground state of (TMTSF)₂PF₆ must be described with 3 order parameters related to the 2k_F SDW, 2k_F CDW and 4k_F CDW modulations. A simplified analysis of the phase transition is given Annex A.2 in the frame work of the Landau development of the free energy. This simple analysis shows, in agreement with experimental observations, that for an attractive enough coupling between the 2k_F SDW and 2k_F CDW order parameters a mixed SDW-CDW modulated ground state can be directly obtained through a first order transition.

The stabilization of a first order phase transition particularly requires that the Landau coefficients:

These conditions together with additional requirements given in Annex A.2, lead to phase diagrams shown in Figure 7.

The phase diagrams shown in Figure 7 leave the possibility (interrupted lines) of an additional transition at lower temperature towards a pure 2k_F SDW phase. This transition could occur in (TMTSF)₂PF₆ at ~3.5 K, temperature at which earlier NMR measurements [86,87] exhibit anomalies. Consistently with the occurrence of a pure SDW sub-phase, a vanishing of the 2k_F CDW satellite reflection intensity is observed below ~3.5 K [84].

The finding of a mixed 2k_F SDW/CDW ground state implies that both 2k_F SDW and 2k_F CDW response functions should be strong. Let us first consider the electronic phase diagram. Recent calculation [88,89] shows that, in addition to the FS nesting process tending to promote, in presence of sizeable intra-chain coulomb repulsions, the 2k_F SDW ground state, the inter-chain backward repulsive coulomb interaction g_1┴ previously considered in Section 3.1.2 can in parallel stabilize a 2k_F CDW ground state for strong enough g_1┴. These calculations show that with both kinds of inter-chain coupling there is a proximity between the 2k_F SDW and 2k_F CDW phases, and that, even if the SDW ground state is stabilized, sizeable 2k_F CDW electronic correlations remain above the transition temperature. Interestingly when the FS nesting breaking effects destabilize the insulating density wave ground state, strong g_1┴ tends to stabilize triplet f superconductivity instead of the singlet d superconductivity occurring for small g_1┴ (for a recent review of the interplay between superconductivity and 2k_F density waves see [90]).

However in the present case, already discussed in Section 3.1.2, g_1┴ stabilizes a different periodicity as does the FS nesting, a feature not considered in the theory performed in [88,89]. This competition together with the lock-in of the anion destabilizes the 2k_F BOW as seen in Section 3.1. However the CDW counterpart of 2k_F instability could remain active and contribute to the ground state modulation if the 3D ordering of CDW is achieved by the same FS nesting mechanism as for the 2k_F SDW. As g_1┴ is not activated below 30K, the structural modulation observed below T_SDW must not be of the BOW type (The absence of BOW structural features explains why the 2k_F satellite reflections are of very weak intensity). For this reason it was proposed in [7] and [65] that the weak satellite reflections detected below T_SDW could correspond to the X-ray scattering by the electronic 2k_F CDW. Eventually a molecular distortion could follow the setting of the 2k_F CDW (see below).

The separation between pure 2k_F SDW and 2k_F CDW ground states implies that there is a natural repulsion between the associated density waves, which means that the bare coupling term ν introduced in the Landau free energy of Annex A.2 is repulsive. However if these two density waves are simultaneously stabilized in the same phase, the free energy is minimized if the 2k_F SDW and 2k_F CDW are in phase quadrature (ω = π/2 phase shift). This corresponds also to a π/2 phase shift between the spin ↑ and spin ↓ components of the SDW and of the electronic CDW [8,65].

The “specific heat” anomaly observed at T_SDW in thermal expansion measurements [25] shows that the electronic CDW should have a structural counterpart. This counterpart is not a BOW modulation (see Section 3.1). However if the CDW consists primarily in a modulation of the hole occupancy on the molecules, one expects that molecular deformations should follow the electronic density wave by elongating the TMTSF hole rich molecules and contracting the TMTSF electron rich molecules. This should lead to a modification of intra-molecular vibration modes in Raman and/or infrared spectra of (TMTSF)₂PF₆ below T_SDW. The electronic CDW could also trigger “phase phonons” which should be observable in reflectance measurements. These latter effects apparently have been detected below T_SDW in the parent (TMTSF)₂SbF₆ compound [91]. However there are very few optical studies performed below T_SDW in (TMTSF)₂X’s to assess this statement.

The coupling between the 2k_F SDW and the 4k_F CDW could be achieved by a “magneto-elastic” effect similar to the one considered in (TMTTF)₂Br. By analogy with the findings of Annex A.1, this coupling should lead to an increase of hole concentration on the site having the larger magnetization. However as the intensity of the 4k_F CDW reflections of (TMTSF)₂PF₆ is much weaker than the one of (TMTTF)₂Br, the lattice distortion which eventually accompanies the 4k_F CDW of (TMTSF)₂PF₆ must be much smaller than the 4k_F distortion of (TMTTF)₂Br. This difference could be explained by the incommensurate nature of the modulation (leading to the loss of umklapp effects) and the smaller amplitude of modulation [a reduction of the magnetization by a factor 1.75 (0.08μ_B for (TMTSF)₂PF₆ versus 0.14μ_B for (TMTTF)₂Br [71]) reduces, according to (A.2), the amplitude of the distortion by a factor 3 and the 4k_F reflection intensity by a factor 9]. Whatever its microscopic origin, the coupling between the 2k_F SDW and the lattice remains appreciable in the density wave ground state because optical studies [92] show that the SDW condensate presents a large dynamical mass enhancement, which is however several times smaller than the mass enhancement of a CDW condensate.

The first indication of the now well established symmetry breaking CO phase transition was revealed by anomalies in conductivity measurements performed in the (TMTTF)₂X salts with X = PF₆, AsF₆ and SbF₆ and their solid solutions [93]. The most striking finding was the observation of a MI transition at T_CO = 154 K in the SbF₆ salt, recalling the one previously observed at 160 K in the SCN salt [66]. Although this transition was correctly interpreted as due to a 4k_F electronic localization phenomenon, no lattice symmetry breaking could be detected at T_CO in this preliminary study, in the difference of the SCN salt [94]. For this reason this transition was labeled “structureless” in later studies [95] which also revealed an anomaly at T_CO in the thermal dependence of the thermo-power (possibly due to a gap opening) of these salts and similar anomalies in the ReO₄ salt well above its AO transition. During the following year two important, but often ignored studies, revealed a dielectric divergence [81] and a few percent Young modulus softening [96] at T_CO. The symmetry breaking consisting of a loss of all the inversion centers at T_CO was only revealed 15 years later by the NMR observation of a charge differentiation between the two TMTTF molecules of the unit cell [97] providing the first evidence of the occurrence of a charge disproportion below T_CO. Charge disproportion between molecules was soon confirmed by the observation of split intra-molecular vibration modes below T_CO [98,99]. This charge disproportion together with the incipient stack dimerization leads to a stack dielectric polarization and, as there is no cell doubling (at the difference of the SCN salt), to the establishment of electronic ferroelectricity. This was sustained by accurate measurements of the dielectric divergence at T_CO [100].

Although it was suspected in these first works that the anions should control the CO transition [93] or even should be displaced with respect to donors at T_CO[38], several attempts to find a structural modification at T_CO were unsuccessful [7,101,102,103]. The reason, found recently [104], is that minute irradiation defects created by X-ray beams in laboratory diffraction conditions kill the CO. It was only recently that the finding [24] of a lattice thermal expansion anomaly at T_CO provides convincing evidences of a structural counterpart at the electronic ferroelectricity. Then evidence of a tiny structural modification was found from the detection of weak (<15%) variations at T_CO of the intensity of several main Bragg reflections using neutron diffraction on (TMTTF)₂PF₆ deuterated powders [21,105]. These quite small structural modifications explain why earlier attempts to solve the (TMTTF)₂PF₆ and AsF₆ structures on hydrogenated crystals in the P1 space group from conventional neutron scattering data collection at 4K were unsuccessful [106]. Recently the low temperature non centro-symmetric P1 structure of (TMTTF)₂PF₆ has been assessed using high energy X-ray beam from synchrotron radiation [107]. The main result of this study was the finding of intra-molecular deformations associated to charge disproportion. However no sizeable change of the F-S contact distance could be detected at T_CO.

From a general point of view, three main structural features are expected at the CO transition of the Fabre salts [108]:

The first feature, expected from the splitting of intra-molecular mode frequencies at T_CO [98,99,109], has been recently detected [107]. Although the differentiation of the two molecules of the unit cell already suppresses the inversions centers, a deformation of the methyl group cavities and/or a shift of the anions should also contribute to stabilize the non centro-symmetric structure. In this case both the polarization of the methyl groups and/or the shift of the anions provide the efficient couplings with the π cloud [21,110] necessary to stabilize the CO ground state [111].

The influence of the anions in the CO process is assessed by the observation that:

Figure 9 shows two different processes where the shift of the anion could lead to a disproportion of charge on the TMTTF. In Process 2 of Figure 9, the anion moves towards the S of a TMTTF where the shortening of the anion –S contact distance below T_CO enhances directly the π hole density of the TMTTF in the vicinity of the anion. In Process 1 of Figure 9, the anion moves inside its methyl group cavity and deforms it. This deformation polarizes the H-bond network. The H-bond polarization induces a displacement of charge in the σ bonds connected to the H-bonds. This shift of σ electrons towards the center of the TMTTF stabilizes the excess of π holes [21].

Both direct process 2 and indirect process1 stabilize an excess of π hole on the TMTTF towards which the anion moves. However the excess of hole is not localized on the same molecule because the direction of displacement of the anion is different in the two processes. However as the recent structural refinement [107] does not provide evidence of a sizeable change of the anion -S short contact distance below T_CO in the PF₆ salt, the stabilization of the CO pattern probably occurs via the deformation of the methyl group cavity in Process 1. Such an assertion is sustained by the following observations:

Interactions via the methyl groups could also explain why strong T_CO lattice parameter anomalies are observed in the (b', c*) plane containing the H-bond network (see Figure 1); the strongest anomaly being along c* [24]. In addition the easy squeezing of the soft methyl group cavity under pressure explains simply, via the blockade of the anion in its cavity, the rapid decrease of T_CO under pressure [116]. Until now there is no direct evidence of the deformation of the methyl group cavity at the CO transition. This deformation should be better revealed by neutron diffraction more sensitive to H or D positions.

An eventual shift of the anion in the CO phase does not mean that the anion orientation disorder is completely removed at T_CO in the TMTTF salts. ¹⁹F NMR studies of (TMTTF)₂SbF₆ show the contrary [27,28]. Evidence of the decoupling between CO and orientation order of the anion is provided by the observation of successive CO and AO transitions in the ReO₄ (T_CO = 230 K and T_AO = 154 K) and BF₄ (T_CO = 83 K and T_AO = 40 K) salts [117].

Process 1 in Figure 9 which achieves an anion shift inside the methyl group cavity is structurally different from Process 2 which achieves an anion shift towards the S of the donor as found at the (1/2, 1/2, 1/2) AO transition (see Section 7.2). It is thus possible that these two types of nearly perpendicular anion displacements could be successively active in the CO and (1/2, 1/2, 1/2) AO transitions of the TMTTF salts with the ReO₄ and BF₄ tetrahedral anions. This decoupling allows to simply understand that the (1/2, 1/2, 1/2) AO transition, which does not substantially activate the H-bond network, is less sensitive to deuteration [114] and irradiation defects [118].

In this picture TMTTF salts incorporating small anions, such as ClO₄ and NO₃ which do not establish important interactions with the methyl groups [14,110] should not exhibit the CO transition. This seems to be the case for the ClO₄ salt [113]. In the opposite situation where an anion perfectly fits the methyl group cavity there is no room for an anion shift inside this cavity and thus no CO transition is expected. This could be the case of the Br salt. This better fit, which also occurs under pressure with the squeezing of the methyl group cavities, can be taken as responsible of the rapid drop of T_CO, as observed for example in pressurized AsF₆ salt [116].

In this framework the (0, 1/2, 1/2) anti-ferroelectric CO transition of (TMTTF)₂SCN, which coincides with the AO transition of the SCN [94], is singular. In this salt the small SCN anion, which has no real linkage with the methyl groups [110], can only strengthen its contacts with one donor out of two via the AO shift [103]. In this respect the wave vector of the AO superstructure of (TMTTF)₂SCN, which simultaneously stabilizes the CO, is different from the wave vectors stabilized at the others AO and CO transitions (see Section 7). The AO/CO transition of the SCN salt which does not directly involve the methyl groups is consistently weakly sensitive to X-ray irradiation damage.

Because of the involvement of the fragile methyl groups in the stabilization of the CO pattern, the ferroelectric ground state is subject to defects. Defects break the long range ferroelectric order into domains forming local clusters of polarization. This leads to a frequency dependant dielectric permittivity which does not really diverge at a well defined T_CO. Such features, recalling those of dielectric relaxors, are found in (TMTTF)₂PF₆ at ambient pressure and in (TMTTF)₂SbF₆ under pressure near its transformation to a (local) SP ground state [117]. The domain walls nucleated by these defects are described by charge soliton excitations of the CO ground state [119].

Electronic ferroelectricity [100,119] occurs in others organic systems [120]. Among them let us mention the 2D organic salt α–(BEDT-TTF)₂I₃ where ferroelectricity appears at the 135 K MI transition [121]. The interesting aspect of this phase transition is that, analogously to TMTTF salts, the charge rearrangement on type A BEDT-TTF molecules (called CO for this reason) is triggered by the deformation of the I₃ sublattice which thus modifies of the H-bond network between I₃ and the ethylene groups of the BEDT-TTF [122]. This mechanism, similarly to Process 1 in Figure 9, modulates the density of π holes on the BEDT-TTF.

The CO transition observed in the Fabre salts is just a manifestation of the general tendency of organic conductors to form a Wigner lattice of localized charges because of the presence of long range intermolecular Coulomb repulsions (for a recent review see [73]). As the lattice is soft such an electronic instability is coupled to the lattice where it drives a 4k_F CDW which also, in presence of an electron-phonon coupling with the acoustic modes, leads to the formation of a 4k_F BOW [123,36]. However in quarter filled band systems, one has to distinguish between two different types of charge localization phenomena [73,76]:

For uniform quarter filled band systems, these two ground states have different inversion symmetry. However the TMTTF salts are more complex because with a stack being already dimerized (see Section 2.2) the divergence of the 4k_F BOW instability is killed (the static dimerization itself gives rise to a charge localization [12] “visualized” by the development of an activated conductivity below Tρ ~ 200K higher than T_CO). Thus the only symmetry breaking instability remaining in the dimerized salts is the CO if the stacks are not too strongly dimerized [73,119].

Ferroelectric CO is not announced by easily detectable pre-transitional structural fluctuations (the pretransitional structural fluctuations at the anti-ferroelectic CO transition of (TMTTF)₂SCN are also barely detectable). Also the ferroelectric instability associated to CO appears to be mean-field because the dielectric susceptibility divergence follows a Curie Weiss behavior on a large (~30 K) temperature range above T_CO [100,117]. This means that CO in the TMTTF’s is mostly announced by a regime of 3D fluctuations which isotropy reflects the importance of the inter-chain Coulomb coupling. In contrast, regular (i.e., non dimerized) quarter filled systems such as (DIDCNQI)₂Ag [124] or (o-DMTTF)₂X [125] exhibit a sizeable regime of 1D 4k_F BOW fluctuations above the “CO” transition which in fact presents a mixed CO/DM character.

The SP transition of (TMTTF)₂PF₆ is characterized by the appearance below T_SP ~ 17 K of superlattice reflections of very weak intensity at the (1/2, 1/2, ?) reduced reciprocal position according to earlier X-ray investigations [40] (see Figure 10). The third component 1/2c* has been determined by a recent neutron scattering investigation [68].

At ambient pressure the SP transition of the TMTTF’s occurs in the CO phase. The SP order is rapidly destroyed by X-ray irradiation as for the CO transition. This irradiation sensitivity explains that recent structural studies of the SP order have been performed with neutron scattering. The structure of the SP ground state has not yet been determined, but it should present some analogies with the (1/2, 1/2, 1/2) AO superstructure [58,59]. Thus it is expected that the stack tetramerization, corresponding to a dimerization of stack of dimers, each dimer bearing a spin ½, will be accompanied by synchronized shift of the anions towards donors [68]. The involvement of the anions in the SP instability is assessed by the observation of a T_SP critical divergence of the ⁷⁵As NMR T₁⁻¹ in (TMTTF)₂AsF₆ [126,127]. In this process the anion shift should tune the interchain coupling between the individual stack tetramerization, as discussed in Section 3.1.2. The 3D inter-chain coupling regime should occur in the near vicinity of T_SP because the observation of precursor X-ray diffuse scattering lines on a large temperature range above T_SP shows that the SP instability is basically 1D (see Section 3.3).

The temperature T_SP at which the (1/2, 1/2, 1/2) superlattice reflections are observed coincides with the temperature at which a singlet gap develops in the spin susceptibility [112]. At T_SP lattice expansion measurements exhibit a lambda type anomaly which coincides with the specific heat anomaly [128]. The value of the singlet-triplet gap in controversial in the literature which mixes calculated values, using approximate theories [129,130], and measured quantities [74,112]. These last measurements have been confirmed by a direct determination, using inelastic neutron scattering, of the SP gap in the spin excitation spectrum [131]. The SP wave vector is the same in the TMTTF salts and in the isostructural BCPTTF salts [7,70]. BCPTTF)₂PF₆ and AsF₆, which does not undergo a CO transition, have a twice higher T_SP than (TMTTF)₂PF₆ and AsF₆.

The SP transition is very sensitive to the magnetic field, H, as in others SP compounds such as MEM-(TCNQ)₂ and CuGeO₃. In (TMTTF)₂PF₆T_SP decreases as H² [132] and above 19T this salt undergoes a phase transition to an incommensurate soliton-like structure [133,134].

NMR measurements show that there is coexistence between CO and SP pairing in (TMTTF)₂PF₆ and AsF₆. However the observation of an opposite variation of T_CO and T_SP under pressure shows that there is repulsion between the order parameters associated at the CO and SP transitions [116]. In this context, the real part of the microwave dielectric function, ε', which increases by ~10% in the SP phase, shows that the gap of charge (i.e., CO order parameter) decreases at the SP transition [132]. This competition is analyzed in Annex A.3 in the framework of the Landau theory. In particular Landau development predicts the behavior of T_SP in function of T_CO. This dependence, obtained with the restrictions outlined in Annex A3 and shown in Figure 11, accounts for the experimental results.

Figure 11 shows that T_SP of (BCPTTF)₂PF₆ and AsF₆ is consistent with the absence of CO (in that case the SP transition occurs at T_SP⁰ defined Annex A3). Figure 11 shows also that the SP transition vanishes for T_CO ~ 190 K or more likely for ~ 150 K if one assumes that for T_SP < 5 K the spin-liquid phase is stabilized (see below). 150 K is close to T_CO of (TMTTF)₂SbF₆ and SCN which do not exhibit a SP ground state.

To describe completely the SP phase diagram of the TMTTF salts, one has to consider explicitly the non-adiabatic effect of the phonon field (see Section 3.3). These effects have already been discussed in [73] with the main conclusions being:

The microscopic origin of the competition between CO and SP instabilities relies on the fact that CO, which localizes the holes every second neighbor molecules, establishes also a reduced AF exchange integral, J, between the spin of the holes. With a spin-phonon coupling following the decrease of J, T_SP^MF (i.e. the SP instability) decreases [73].

The weakening of the SP instability by the CO is just the manifestation of the repulsion existing between 4k_F CDW (or CO) and 2k_F BOW (or SP) instabilities in quarter filled band systems: the next neighbour Coulomb repulsion V₁ which promotes CO in quarter filled band systems kills in the same time the divergence of the 2k_F BOW response function [135,136]. In other words CO induces hetero-polar charge configurations which destabilize the modulation of bond distances in the 2k_F Peierls mechanism. This was clearly shown in the study of the [(TMTSF)₁₋x (TMTTF)x]₂ReO₄ solid solution [137,138]. For x = 0.5 the alternate stacking of TMTSF and TMTTF induces a chemical CO. In its presence it is observed a sizeable decrease of T_AO of the (1/2, 1/2, 1/2) AO transition which involves the formation of 2k_F BOW on the organic stacks (see Section 7.2).

T_SP increases when T_CO decreases under pressure [116]. At higher pressure when the CO vanishes instead of reaching T_SP⁰ at a value comparable to T_SP measured in the BCPTTF’s, T_SP further decreases. In the PF₆ salts T_SP even exhibits a singular depression around Pc ~ 9 kbar before entering the AF phase [139]. This behavior suggests the existence of a quantum critical point where the normal phase is further stabilized around Pc.

A possible explanation could be, that with TMTTF salts being close to the crossover boundary between the adiabatic and anti-adiabatic regime, the hardening of the phonon mode under pressure will shift the SP instability to the anti-adiabatic regime followed by the spin-liquid regime around Pc. In the anti-adiabatic SP regime the enhancement of quantum fluctuations should strongly reduce the amplitude of 1D SP gap. In this scenario the suppression of the SP phase should occur through a critical point due to the enhancement of spin-liquid fluctuations. Then above P_c the 3D AF ground state will be stabilized by the inter-chain exchange coupling. If the succession of ground states is described by the generic phase diagram [52], AF pressurized (TMTTF)₂PF₆ should be identical to AF ambient pressure (TMTTF)₂Br.

In order to assess the development of a pressure induced non-adiabaticity one must prove that the amplitude of the 1D SP gap decreases under pressure as a result of the enhanced quantum fluctuations. However, as it is observed that T_SP^MF (linearly related to the mean field 1D SP gap when the phonon fluctuations are neglected) slightly increases from (TMTTF)₂PF₆ to (TMTTF)₂Br (see Figure 5), the opposite situation seems to occur. In addition in order to sustain the non-adiabatic scenario one should have a considerable phonon frequency hardening (by a factor ~4) to stabilize the spin-liquid phase in pressurized (TMTTF)₂PF₆. This requires a phonon frequency as high as Ω > 4T_SP^MF, which seems unrealistic for an acoustic mode. The difficulty with this scenario is that SP fluctuations are still detected in AF (TMTTF)₂Br, at the difference of (TMTTF)₂SbF₆ where it was stated in Section 6.2 that the AF ground state is caused by the enhanced non-adiabaticity of the phonon field which in the same time kills the SP fluctuations.

Another scenario could be that the squeezing of the methyl group cavities under pressure blocks the shift of the PF₆, the necessary ingredient setting the interchain coupling between the individual SP stack tetramerization. This is corroborated by a recent determination of the structure of pressurized (TMTTF)₂PF₆ [140] showing a sizeable contraction of the methyl group cavity. The mechanism of blockade of the anion in its methyl group cavity explains also that only a short range SP order is stabilized in pressurized (TMTTF)₂SbF₆ [27] when both the CO and AF phases are suppressed above 0.5 GPa.

In Fabre and Bechgaard salts incorporating non-centrosymmetric anions, the anion orientation is disordered at RT. However for entropy reasons, the anions order upon cooling. The ordering is achieved at a well defined phase transition showing that the AO leads to a symmetry breaking. The AO transition stabilizes a superstructure which generally doubles the RT lattice periodicity in one or several directions [7]. The AO transition can be of 2^nd [(0, 1/2, 0), (1/2, 0, 0) and (0, 1/2, 1/2) AO] or 1st order [(1/2, 1/2, 1/2) AO] depending on the strength of the coupling of the AO process at the elastic lattice degrees of freedom The transition not only consists of an orientation ordering of the anion inside its methyl group cavity, which in itself breaks its inversion symmetry, but also of a concomitant deformation of this cavity associated with an anion shift. This shift can be either towards selected methyl groups as in the (0, 1/2, 0) AO transition of (TMTSF)₂ClO₄ (direction 1 in Figure 9) [141] or towards the S or Se atom of a given donor as in the (1/2, 1/2, 1/2) AO transition of (TMTSF)₂ReO₄ (direction 2 in Figure 9) [58,59]. The deformation of the methyl group cavities can be achieved by a cooperative PLD of the organic stacks. In the case of the (1/2, 1/2, 1/2) AO transition this corresponds to a 2k_F BOW distortion of the stacks. In (TMTSF)₂ReO₄ the 2k_F PLD leads to a MI transition [142]. Even if the coupling of the PLD with the 1D electron gas provides the necessary energy gain to open a gap at the Fermi level, the (1/2, 1/2, 1/2) AO transition is not achieved by a standard Peierls instability because the associated pretransitional fluctuations are 3D and not 1D [143]. This means that the anions located in between the stacks trigger by their ordering the 2k_F stack deformation while providing the necessary inter-chain coupling to stabilize the AO insulating ground state. This differs of a conventional Peierls transition where the driving force is due to the individual stack instability towards the formation of a 2k_F PLD. Indeed the electron-anion coupling displayed in Figure 9 plays in the AO transition the role played by the intra-stack electron-phonon coupling in the Peierls transition.

These few examples, as well as the case of (TMTTF)₂SCN already considered Section 5.2, show that important changes of the electronic properties generally accompany the AO transition. AO transitions lead to substantial modifications of the electronic structure [144,145] and of the electronic ground states [146,147] of the Bechgaard and Fabre salts. These structural-electronic coupled properties will be revisited below in light of the most recent findings.

Among salts undergoing an (1/2, 1/2, 1/2) AO transition, several cases must be distinguished:

The early discovery [94] of the 2nd order AO transition of (TMTTF)₂SCN was a very important step to assess the importance of electron-electron repulsions in organic conductors. Indeed the stabilization of the (0, 1/2, 1/2) superstructure below T_AO = 160 K was the first realization of a MI transition [66] not accompanied by the opening of a gap in the spin degrees of freedom. In other words the AO of (TMTTF)₂SCN achieved the spin-charge decoupling expected from the stabilization of a 4k_F periodicity. Recently the structural refinement of the AO structure [103] was able to prove from the variation of the intra-molecular distances that the AO transition is accompanied by a 4k_F CDW of an amplitude of 0.15 electrons, with an excess of hole on the TMTTF towards which the SCN points and an excess of electron in the opposite situation. This transition is also accompanied by a reduction of the amplitude of the stack dimerization. This result is expected by the repulsive coupling between the 4k_F CDW and 4k_F BOW order parameters (this is exactly the opposite of the effect described in Section 6.2 and Annex A.3 where the establishment of the SP tetramerization reduced the amplitude of the CO). At low temperature (TMTTF)₂SCN undergoes at T_N = 7 K [94] an AF transition which stabilizes the q_AF = (1/2, 1/4, ?) commensurate magnetic order [177].

(TMTSF)₂SCN also undergoes a MI transition at ~90K which does not affect the spin degrees of freedom and which is also associated to a structural modulation [178]. Thus a “4k_F” charge localization should accompany this MI transition as in (TMTTF)₂SCN. However the structural modulation surprisingly corresponds to the establishment of a triply incommensurate short range order. The wave vector of this modulation (0.48 ± 0.015, 0.65 ± 0.01, 0.1 ± 0.02) is quite different to the one, (0, 1/2, 1/2), stabilized at the CO/AO transition of (TMTTF)₂SCN. It is however interesting to remark that the wave vector components of the incommensurate modulation of (TMTTF)₂SCN approximately verify the relationship qd₁ = 0, i.e., q_a− q_b + q_c = 0 (mod. 1) derived in [60], for the setting of CO via direct interactions (S…NCS) between anions and donors. As the SCN anion can only take two orientations, the incommensurability of the modulation is certainly related to the probability of occupancy of one of the two orientations of the anion. For such a wave the incommensurability observed in diffraction experiments results from a statistical average because locally the modulation must be commensurate. The perfection of such a wave is altered (i.e., the harmonic content of the modulation is reduced) if there is a broad distribution of commensurate domain sizes. In addition, if visualizing the modulation from the origin of the lattice there are increasing fluctuations on the position of successive domain walls, or equivalently cumulative fluctuations of domain size, the long range order is lost. The Fourier transform of such a modulation pattern leads to broadened satellite reflections. Similar features are observed for the incommensurate CO modulation of (DMtTTF)₂ClO₄ [102].

Both (TMTSF)₂NO₃ and (TMTTF)₂NO₃ undergo an AO transition at T_AO = 41 K [143] and 50 K [157] respectively and which stabilizes the same (1/2, 0, 0) superstructure. Even if this superstructure establishes the 2k_F periodicity in stack direction, the AO transition has a weak influence on the electronic properties of the donor stack.

The (1/2, 0, 0) superstructure of (TMTSF)₂NO₃ has been refined [165]. No substantial stack tetramerization and differentiation between the individual TMTSF are observed below T_AO (the doubling of stack periodicity should, in principle, differentiate two molecules per unit cell). This means that the NO₃ anion orders without significantly perturbing its methyl group cavity. Such a result is expected because of the small size of the NO₃ anion. As the organic array is not perturbed by the AO process the electronic structure remains basically unchanged below T_AO and (TMTSF)₂NO₃ does not become semi-metallic as previously predicted [144,145]. Its FS remains quasi-1D below T_AO [179] and available for a nesting instability. Indeed (TMTSF)₂NO₃ stabilizes a SDW ground state at T_SDW = 9 K whose modulation wave vector, determined by NMR [180], is close to the wave vector of the SDW phase of (TMTSF)₂PF₆ [54,55].

(TMTTF)₂NO₃ undergoes a (1/2, 0, 0) AO transition below which the TMTTF stack is probably weakly tetramerized because a weak spin gap, less than k_BT_AO [66,118], opens, resulting in the ground state of (TMTTF)₂NO₃ being non-magnetic at the difference of the magnetic SDW ground state of (TMTSF)₂NO₃.