The Spin Density Wave phases induced by the magnetic field (FISDW) have been observed in three among the "Bechgaard salts". They appear under atmospheric pressure in (TMTSF)₂ClO₄, but under about 10 kilobars in the PF₆ and ReO₄ compounds [1]. These phases are characterised by all a series of quantum oscillations: not only magnetoresistance oscillations, but particularly Quantum Hall Effect plateaus, the first ones ever observed in massive samples:

FIG. 1. Quantum Hall effect in (TMTSF)2ClO4. The open circles, open triangles, filled circles and filled triangles correspond to cooling rates dT/dt of 310, 6.5, 2.6 and 0.37 K/h, respectively. The magnetic field H is applied parallel to c* direction. Note the appearance of a negative plateau below 2.6 K/h: the so-called "Ribault anomaly" [2].

This is an orbital effect of the magnetic field, and not a Zeeman effect due to the electron spin. In effect the observed phenomena depend on the field orientation, and they are maximum as the field is applied perpendicularly to the c* direction (the least conducting one) of the single crystal sample. The field-induced effect corresponds to a second order phase transition, passing from a normal metal to a semi-metallic state [3]. Magnetic resonance measurements allowed to identify the high field state as itinerant antiferromagnetic like, that is to say, a spin density wave [4].

[1] For an experimental revue, see: M. Ribault, in "Low Dimensional Conductors and Superconductors", edited by D. Jérome and L.G. Caron (NATO ASI, Plenum Press) 155, 199 (1986).
[2] M. Ribault, Electronic states below 5 K in (TMTSF)₂ClO₄, Mol. Cryst. Liq. Cryst. 119, 91 (1985).
[3] see publi. n°1.
[4] T. Takahashi, D. Jérome and K. Bechgaard, J. Phys. (Paris) Lett. 43, L-565 (1982)

Our calorimetric studies as a function of the magnetic field have demonstrated for the first time that an order parameter is well associated with each Hall effect plateau (this is a notable difference with the Quantum Hall Effect observed in semi-conductor heterojunctions). Our measurements have enabled to establish the thermodynamic phase diagram of the FISDW phases:

FIG. 2. Phase diagram deduced from the specific heat anomalies, for two kinds of sweeps: at fixed temperature and at fixed magnetic field [publi 7].

According to available theoretical models, the SDW phases induced by the magnetic field would arise from the quantisation of the electronic orbits in the field, associated with an interference effect between three periodicities of the system, i.e., the cyclotron period, the SDW wavelength, and the lattice periodicity. For example, Fig. 3 displays the principle of the "quantised nesting" [5] of the open Fermi surface, in such quasi-one-dimensional conductors.

FIG. 3. The Fermi surface of a quasi-1D conductor consists of two distinct parts at +kF and -kF (here in a cut view). The Q wave vector allows to nest one part to another , by translation [5].

The wave density instabilities result from a topological property of the Fermi surface, which makes the electronic system extremely sensitive to any perturbation with a Q wave vector coupling a large number of electronic states from one Fermi surface side to the another one. This sensitivity is related to the electronic susceptibility divergence of the non interacting one dimensional electron gas. The wave density may be viewed as resulting from the Fermi level states condensation into electron-hole pairs. Since the nesting is imperfect, pockets of unpaired holders subsist (hatching in Fig. 3).

Quantisation in a magnetic field arises from the existence of closed electron trajectories within the pockets, which are thus quantisable into Landau levels. So as to always maintain completely filled an integer number of these levels, the Q(H) wave vector permanently adjusts itself to the magnetic field [5]. This explains why the Hall plateaus are constant (they are associated with order parameters). When the energetic cost becomes too large, the nesting vector exhibits a jump, which yields the phase transitions we have revealed [publis 7, 8, 9].

In the Bechgaard salts, the (TMTSF)₂X compounds, the X^- anions are located at the centres of the cavities that are delimited by the zigzag patterns of the conducting TMTSF chains. The inversion symmetry element is present in these compounds, which implies a static disorder for the non centrosymmetric anions such as ClO₄, with at least two inverse configurations, equally occupied (each orientation favouring a close contact with one of the TMTSF molecules Selenium atoms).

FIG. 4. The two non equivalent positions for the tetrahedral ions.

The low-temperature fundamental state of these molecular compounds is strongly modified by order-disorder transitions. In the perchlorate case, the anion ordering transition of the ClO₄ anions occurs around T_MO=24 K [6].

This transition exhibits kinetics effects: anion ordering is partial as the cooling rate through the transition exceeds about 10 kelvins per hour, while new quantised phases appear as the cooling rate decreases below about the degree per hour [publi 3].

Negative Hall effect plateaus have been observed, in the slowly cooled perchlorate compound (Fig. 1) as well as in the hexafluorophosphate compound under pressure (typically around 10 kbars). However, the plateaus have not as beautiful shapes in the latter compound [7]. By adjusting the (TMTSF)₂ClO₄ cooling rate, i.e., by controlling the amount of anion disorder, both "normal" and negative Hall effect can be observed (Fig. 1). On the contrary, not all the (TMTSF)₂PF₆ sample exhibit negative Hall effect [8,9]. Besides, a ternary periodicity (two positive plateaus followed by one negative plateau) has been reported concerning the Hall voltage evolution of both the well ordered (TMTSF)₂ClO₄ [2] and (TMTSF)₂PF₆ [7]. These new periodicities have motivated our magnetocalorimetry measurements, which enabled us in particular to reveal the arborescent structure of the transition lines separating the SDW sub-phases induced by the magnetic field (see the following).

[5] M. Héritier, G. Montambaux and P. Lederer, Stability of the spin density wave phases in (TMTSF)₂ClO₄: quantized nesting effect, J. Phys. (Paris) Lett. 45, L943 (1984), and: Phase diagram of quasi-one-dimensional conductors in strong magnetic field, ibid 46, L-831 (1985)
[6] For an experimental review, see : J.-P. Pouget, in "Low Dimensional Conductors and Superconductors", edited by D. Jérome and L.G. Caron (NATO-ASI, Plenum Press) 155, 17 (1986).
[7] B. Piveteau, L. Brossard, F. Creuzet, D. Jérome, R.C. Lacoe, A. Moradpour and M. Ribault, Hall effect study of the field-induced instabilities in (TMTSF)₂ClO₄ under pressure, J. Phys. C19, 4483 (1986).
[8] J.R. Cooper, W. Kang, P. Auban, G. Montambaux, and D. Jérome, Quantized Hall effect and a new field-induced phase transition in the organic superconductor (TMTSF)₂PF₆, Phys. Rev. Lett. 63, 1984 (1989).
[9] S.T. Hannahs, J.S. Brooks, W. Kang, L.Y. Chiang, and P.M. Chaikin, Quantum Hall effect in a bulk crystal, Phys. Rev. Lett. 63, 1988 (1989).

Usually, calorimetric measurements are performed to precise the thermodynamic properties of a phase transition, to check the order of the transition, the strength of the coupling that originated it, its possible mean field character, or the importance of critical fluctuations. For example, the (TMTSF)₂ClO₄ metal-to-superconductor transition is characterised by its specific heat anomaly, which indicates a volume phase transition coherent with the Bardeen-Cooper-Schrieffer (BCS) theory. Our calorimetry measurements in the FISDW region have provided important information:

-1- A phase transition toward a non metallic state is induced by a moderate magnetic field (a few teslas), in the same temperature range (around the kelvin degree) as the metal-to-superconductor transition at very low field [publi 1].

-2- A phase transition is indeed associated with each step between two quantised Hall plateaus (Fig. 2) [publi 7].

-3- Our specific heat measurements in the vicinity of the ClO₄ anions ordering transition (between 10 and 30 K) have shown that the transition character is in the same time second order like (the specific heat anomaly looks like a jump), and first order like (there is a super-cooling effect) (section 3: Anion ordering and low-dimensional phonons).

-4- These calorimetric studies have also shown the low dimensionality of the vibration modes, which exhibit a crossover 3D to 2D above a lower Debye temperature - about 7 kelvins- (section 3-b).

These results, of fundamental character, did not shed as surprising a light as did our later calorimetric investigations. Indeed, the latter have led to a series of discoveries that initiated many theoretical works:

-5- Our zero-field specific heat studies in the superconducting state have characterised a pair-breaking effect induced by the anion disorder, which is quite similar to the similar effect induced by magnetic impurities in a conventional superconductor. This behaviour gives evidences of the exotic character of the superconducting state in this quasi-one-dimensional compound (section 7: Effect of disorder: superconductor and FISDW depairing).

-6- The simultaneous specific heat and thermal conductivity measurements, performed in the vicinity of the transition line separating the normal metal phase from the quantised FISDW phases, have evidenced several kinds of critical behaviours. Below 8 teslas, the metal-FISDW transition exhibits a weak coupling character, demonstrated by the value of the specific heat jump at the transition, DC/g T_c, close to the BCS value (section 4: A singular critical behaviour).

-7- We have demonstrated for the first time that some transitions are partially reentrant [publis 7 and 14, and section 6: Evidence of a tetracritical point).

-8- However, the jump -that is to say, the coupling strength!- oscillates as a function of the magnetic field, moreover its value exhibits discontinuities at the limits between the quantised SDW phases. This behaviour qualitatively changes above 8 teslas: the DC/g T_c jumps reaches up to four times the BCS value around 10 teslas, as the system enters a strong (possibly very strong) coupling region. The behaviour appears to evolve from 3D to 2D when crossing the border (section 4: A singular critical behaviour).

-9- Thermal conductivity too presents a critical behaviour evolution. Surprisingly enough, thermal conductivity seems to be dominated by lattice vibrations, but the critical behaviour is associated with the electronic transition (section 4-b: A singular critical behaviour). It appears that phonons play a singular role in the pairing mechanism, for superconductivity as well as for the spin density wave.

-10- Close to the end of the cascade of phase transitions, where the coupling becomes strong, the transition becomes exothermic whatever the direction of the field variation across the last transition line, the signature of a highly irreversible behaviour [publi 8].

-11- Our simultaneous specific heat and magnetocaloric effect measurements have revealed a fine structure for the transition lines between quantised SDW phases. In the case of a sample being cooled slowly enough through the anion ordering transition, these transition lines split in an iterative process, yielding the observation of an arborescent phase diagram (section 5: An arborescent phase diagram).

-12- Within the framework of François Tsobnang's thesis (held in December 1991), our specific heat and magnetocaloric investigations have revealed a multicritical behaviour for the metal-FISDW transition in a particular region of the phase diagram: we have evidenced the existence of a tetracritical point, which corresponds to the meeting of four transition lines in a single point (section 6: Evidence of a tetracritical point).

-13- His thesis work also demonstrated that anion disorder produces dramatic effects on the FISDW sub-phases. First, the tetracritical behaviour evolves toward a bicritical behaviour as the cooling rate is increased. Second, the transition lines arborescence disappears. Third, we have observed a pair-breaking effect similar to the one exhibited by the superconducting phase of the same compound, but with a much greater magnitude (section 7: Effect of disorder: superconductor and FISDW depairing). These behaviours seem to indicate that the electron mean free path plays a key role in this physical system: disorder does not produce a mere renormalisation effect of the interactions, as in conventional systems. On the contrary, in this quasi-one-dimensional system, it appears to govern the very criticality of the phase transitions. The mean free path variations would alter the quantisation condition that is responsible for the formation of the spin density wave phases induced by the magnetic field in (TMTSF)₂ClO₄.

-14- Finally, we have described the role of defects on the magnetic properties of organic conductors (see section 8).