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 .
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:
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" .
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 .
Magnetic resonance measurements allowed to identify the high field state
as itinerant antiferromagnetic like, that is to say, a spin density wave
 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,
 M. Ribault, Electronic states
below 5 K in (TMTSF)2ClO4,
Mol. Cryst. Liq. Cryst. 119, 91 (1985).
 see publi.
 T. Takahashi, D. JÚrome 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:
Phase diagram deduced from the specific heat anomalies, for two kinds
of sweeps: at fixed temperature and at fixed magnetic field [publi
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" 
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 .
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.
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 .
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,
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 TMO=24 K .
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
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 . 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
 and (TMTSF)2PF6
. 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).
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)
 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,
Piveteau, L. Brossard, F. Creuzet, D. Jérome, R.C. Lacoe, A.
Moradpour and M. Ribault, Hall
effect study of the field-induced instabilities in
under pressure, J. Phys.
C19, 4483 (1986).
Cooper, W. Kang, P. Auban, G. Montambaux, and D. Jérome, Quantized
Hall effect and a new field-induced phase transition in the organic
Rev. Lett. 63, 1984 (1989).
 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
-2- A phase transition is indeed associated with each
step between two quantised Hall plateaus (Fig. 2)
-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
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
-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
Tc, 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
Tc 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
-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
-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