Upper critical field divergence induced by mesoscopic phase separation in the organic superconductor (TMTSF)2ReO4

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by  C. V. Colin

Upper critical field divergence induced by mesoscopic phase separation in the organic
superconductor (TMTSF) ReO
2 4
C.V.Colin,∗ B.Salameh,† and C.R.Pasquier
Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay, France
7
0 K.Bechgaard
0 Department of Chemistry, H.C.Oersted Institute,
2 Universitetsparken 5, DK2100, Copenhagen, Denmark

n
Duetothecompetitionoftwoanionorders,(TMTSF)2ReO4 presentsaphasecoexistencebetween
a
semiconducting and metallic (superconducting) regions (filaments or droplets) in a wide range of
J
pressure. Inthisregime,thesuperconductinguppercriticalfieldforHparalleltobothc* andb’ axes
6
present a linear part at low fields followed by a divergence above a cross-over field. This cross-over
2
correspondstothe3D-2Ddecouplingtransitionexpectedinfilamentaryorgranularsuperconductors.

The sharpness of the transition also demonstrates that all filaments are of similar sizes and self
]
n organize in a very ordered way. The distance between the filaments and their cross-section are
o estimated.
c
- PACSnumbers: 74.70.Kn,74.25.Dw,74.25.Fy,74.25.Op
r
p
u
Superconductivity in anisotropic and inhomogeneous in lamellar superconductors10 when the magnetic field is
s
. materialsremains animportantopen questionespecially perfectly aligned parallel to the superconducting layers
t
a the influence of the microstructureon the superconduct- and was shown to adjust the data in Nb/Cu multilay-
m ing properties. In organic superconductors, there are ers for instance11. Such a dimensional cross-over exists
- essentially two types of inhomogeneities. On the one also for superconducting droplets embedded in an insu-
d hand, a small substitution of ClO−anions by ReO−in lating matrix and the finite size of the droplets leads to
n 4 4
(TMTSF) ClO leads to a fast decrease of the critical a parabolic evolution of the upper critical field at low
o 2 4
c temperature1 and a phase repulsion with the compet- temperatures12.
[ ing spin density wave (SDW) state2. On the other In this communication, we report, for the first time

hand, large SDW domains may be introduced by a high in an organic compound, a precise estimate of the mi-
1
v cooling rate in pristine (TMTSF)2ClO43,4 or by ad- crostructureofthesampleinitsphaseseparationregime.
0 justing the pressure in (TMTSF)2PF65,6. The criti- Indeed,in(TMTSF)2ReO4,wewillshowthatduetothe
5 cal temperature is nearly independent of the SDW do- self-organization of charges and the quality of the sam-
6 main density while the upper critical field5 or the criti- ples, the dimensional cross-over appears clearly on the
1 cal current6 are strongly affected. The formation of al- uppercriticalfieldlinewhichestablishesalowdispersion
0
ternating slabs from the two different ground states has in the distances between the superconducting filaments.
7
0 thereforebeensuggestedin(TMTSF)2PF6toexplainthe Then, from the evolution of the upper critical field at
/ data. Recently, in (TMTSF)2ReO4, we have reported a lower temperatures, we will extract an estimate of the
at self-organization of charge in a wide range of pressure7 cross-sectionof the filaments in the (b-c) plane.
m due to the competition between the two anion orders Theexperimentswereperformedinthepressurerange
- q2 = (1/2,1/2,1/2) and q3 = (0,1/2,1/2)8. It has been 10-11.8kbar where both q2 and q3 orders coexist. The
d demonstrated that metallic (superconducting) droplets metallicparts,associatedtotheq order,presentasuper-
3
n or filaments associated with q3 order, elongated along conducting transition (Tc =1.52K) which is nearly pres-
o the a-axis are embedded in the semiconducting matrix sure independent13. The results are presented on two
:c where q2 order prevails7. The existence of a possible different samples: on the first one, the current and the
v structural ordering of the filaments can be checked from magnetic field are applied along the c*-axis, so that ρ
c
Xi the superconductingstate when the magneticfield is ap- is measured. On the second one, we performed ρa resis-
plied perpendicular to the filaments. Indeed, the influ- tivity measurements with the magnetic field, H, applied
r
a ence of a regular arrangement of filaments on the up- nearly along the b’-axis. The alignment was made by
per critical field has been already estimated a long time eye and was performed before the application of the hy-
ago by Turkevich et al.9. A 3D-2D dimensional cross- drostatic pressure. The dimensions of the samples are
overoccursatacharacteristictemperatureT*whichde- typically 2.5 0.2 0.05 mm3.
× ×
pends only on the distance, d⊥, between the filaments Figure 1 presents typical interlayer resistivity versus
in the plane perpendicular to the magnetic field. Above temperature curves obtained at 10kbar when the mag-
T*, the normal core of the vortices penetrates the fil- netic field is applied along the c*-axis. We first notice
aments whereas below T*, they stack between the fila- thataboveT andfornearlyallmagneticfields,theresis-
c
ments. This model is in fact an extension of the model tivitypresentsametalliccharactercontrarytotheSDW-
applied to determine the upper critical field evolution metal phase separation in (TMTSF) PF . Above 2T,
2 6
2
the transition is so broad that it is nearly impossible to the image of a filamentary superconductor already sug-
extracta criticaltemperature. Then, above3T,the field gested using resistivity anisotropy data is valid7. Since
induced spin density wave state manifests at ultra low (TMTSF) ReO is strongly one dimensional, we will de-
2 4
temperature by a rapid increase of the resistance14. At noteξ ,ξ andξ ,thecoherencelengthsalongtheaxesa,
a b c
eachmagneticfield,thecriticaltemperatureisdefinedby b’ andc* axesrespectively. Inaregularstackofdroplets,
theonsettemperatureinasimilarwaytopreviousdeter- filaments or slabs,a dimensional cross-overin the super-
mination in (TMTSF) PF 5. This criterion is justified conducting state is expected at a fixed temperature T*
2 6
since this definition also corresponds to the temperature defined by :
where non linearities in the voltage-current characteris-
ticsdisappear. Themagneticfield-temperaturephasedi- ξ (T∗)= ξ⊥(0) = d⊥ (1)
⊥
agram deduced from these data is shown in Fig.2. The 1 T∗ √2
same data can be extracted for various pressures and q − Tc
the phase diagram obtained for P=11kbar is also shown
where ξ (T) is the temperature dependent coherence
on this figure. At high temperatures, for all pressures, ⊥
length perpendicular to the field, H, and d is the
theuppercriticalfieldvariessmoothlyandquasi-linearly ⊥
distance between the superconducting objects in the
with the magnetic field. However, at low temperatures,
plane perpendicular to H. Above this temperature T*,
a drastic upward curvature in the H curve is clearly
c2
the superconductor is 3D and the upper critical field
visiblewhichistranslatedtolowertemperaturesaspres-
varies linearly with temperature like a standard homo-
sure is increased. Finally, at P=12kbar, H is quasi-
c2
geneous superconductor. Below T*, vortices remain
linear with magnetic field, no more divergence from this
between the filaments and are of Josephson nature15
linear behavior is observed in the explored temperature
and a Lawrence-Doniach model may be applied16. In
range. Figure 3 presents the magnetic field-temperature
phasediagramforH//b’,atP=10kbar,deducedfromthe this two-dimensional regime, a divergence of the up-
per critical field is expected and is limited by finite-
ρ resistivitycurvesobtained atdifferentmagnetic fields
a
size effects, the paramagnetic limit or eventually spin-
which are shown in the inset. Here again, just above
orbit coupling. The latter possibility is not pertinent
T ,theresistivityremainsmetallicinthewholeexplored
c
range of magnetic fields. Similarly to H//c* data, a lin- in organic conductors made of light elements. However,
in strongly one-dimensional systems, a Fulde-Ferrell-
ear variation of H is observed at low fields which is
c2 Larkin-Ovchinikov (FFLO) superconducting state17,18
replaced by a strong upturn of the upper critical field
mayalsobe considered19. However,FFLO superconduc-
below a characteristic temperature.
tivity leads to an inhomogeneous superconducting state
in the reciprocal space whereas we are dealing here with
phase separation in the real space. Moreover,FFLO su-
perconductivityisexpectedtoappearatT 0.56T
FFLO c
≈
40 incontradictionwithourdataat11kbar. Finally,inthis
3.50T 2D regime, a square-root variation of the upper critical
3.00
2.50 field line is expected below T* including the finite size
30 1.84 of the superconducting objects10,12. Assuming spherical
1.66
) 1.49 metallic grains, Deutscher et al. estimated the upper
(R 20 1.32 critical field at zero temperature to be given by :
1.11
1.00
0.80
10 0.70 5Φ 1 ξ2(0)
0.32 Hc2(0)=r32π0ξ (0)Rr1−2 ⊥t2 (2)
0.09 0.04 0.02 0T ⊥
0
0.0 0.5 1.0 1.5 whereRistheradiusofthegrainsandtisacharacteristic
Temperature (K) length which measures the Josephson coupling between
them. In the ultra-weak coupling limit, t is infinite and
Eq.2 reduces to the standard upper critical field of an
FIG. 1: Resistance along the c*-axis versus temperature in
(TMTSF)2ReO4atP=10kbarandH//c*. Thecurvesareper- individual spherical object20. Here, the cross-section of
formedwithanappliedmagneticfieldof0to3.50Tfrombot- the filaments is not a circle but an ellipse. In a first
tom to top. approximation,thepreviousformulaappliesiftheradius
Risreplacedbythehalf-axisoftheellipseperpendicular
These evolutions of the upper critical field with tem- to the field, R .
⊥
perature for both field directions are in strong contrast In order to determine the precise texture, the coher-
with the reported observations in (TMTSF) PF where ence lengths have to be determined first. The zero
2 6
the upturn of the upper critical field is observed start- field linear extrapolation of the upper critical field for
ing from the lowest fields5. The data may then be ana- H//c*, H 0.2T is similar to the value obtained
c2,c
lyzed using a different model and it appears clearly that for homogeneo≈us superconductivity in (TMTSF) PF 21
2 6
3
misalignment is not crucial and in the following and we
will correct the measurements from this angle. For clar-

2.0 ity, we will denote b” our direction of measurement.
) From Hc2,b = 4T24, we get ξ⊥,b′ = √ξaξc 9nm.
d (T1.5 Using ξa = 100nm as in (TMTSF)2ClO422, w≈e obtain
Fiel 10kbar ξlabtt≈ice4.p1anrmamaentedrξcc. ≈In0t.h9insmsenwseh,icthheisesstmimalalteerdthvaalnuethoef
c 1.0
ti ξc is compatible with the observation of Josephson vor-
e
n ticesin(TMTSF)2ClO4forHperfectlyalignedalongthe
ag0.5 11kbar b’-axis25. The misalignment of the field with respect to
M the b’-axis avoids then to have a mixing of two different
0.0 physical phenomena. Indeed, the possibility of Joseph-
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 son vortices between the individual layers, separated by
Temperature (K) the lattice parameter c, can be ruled out to analyze our
data.
FIG. 2: Temperature-magnetic field phase diagram of We now turn to the determination of the texture at
(TMTSF)2ReO4for P=10 kbar (open circles) and 11 kbar P=10kbar. For simplicity, in absence of any X-ray data,
(open squares) and H//c*. The straight line represents the we will assume that filaments elongated along the a-axis
uppercriticalfieldinthehomogeneousstatewhilethedotted form a rectangular lattice in the b’-c plane following the
lines represent fitsof theHc2 lines with a parabolic law. Deutscheret al. model12. Thisassumptionisjustifiedby
boththelinearvariationatlowfieldsandthesquareroot
variation of the upper critical field and its observations
along both directions. As a result, the distance between
the filaments and the cross-section of each filament are
2.0 H=2T
0.04 nearly constant over the crystal. We will denote B and
1.5
d (T) 1.5 R()0.030.85 rCe,spthecetidviesltya.nTcehsesbeetqwueaenntittihees cfialanmbeentesxtarlaocntgedb’froamndthc*e
Fiel 00..00120.4 Hc2 lines and using Eq.1 with d⊥=B or C. To define T*,
c 1.0 0.2 we use the intersection of the temperature axis with the
ti 0.00 0.1 0.05 0
ne 0.5 1.0 1.5 parabolic fit of the Hc2 line at low temperatures which
g Temperature (K) gives a more precise determination than any cross-over
a 0.5
M at a finite field. At P=10kbar, we get T*=0.75K and
T*=0.85Kalongc* andb”-axisrespectivelywhichleads
0.0 toB 80nmandC 50nmusingonlyonesignificantdigit.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
≈ ≈
Temperature (K) Finally, we can estimate the cross-section of the fila-
mentsatP=10kbar. Inafirststep,thecouplingbetween
thefilamentscanbe assumedtobe verysmall. Fromthe
FIG. 3: Temperature-magnetic field phase diagram of
(TMTSF)2ReO4for P=10 kbar and H nearly parallel to b’. fits of the low-temperature Hc2 lines, we can estimate
The straight line represents the extrapolation of the linear Hc2,c(0) 2.5T andHc2,b′′(0) 2.9T soHc2,b′(0) 17T
≈ ≈ ≈
part of the upper critical field while the dotted lines repre- from which we extract R 9nm which is about 2
⊥,c
sents the fit of the Hc2 line with a parabolic law. Inset : times ξb and R⊥,b′ 6nm w≈hich is about 6 times ξc
resistance versustemperature for H nearly parallel to b’. with a large uncertai≈nty in this case. Indeed, we believe
thatforsymmetryreasons,theratioR /ξ andR /ξ
⊥,c b ⊥,b c
shouldbe identical. The discrepancyis attributedto the
or (TMTSF) ClO 22 and leads to the determination of uncertainties in the determinations of both T* and H .
2 4 c2
ξ = √ξ ξ 41nm. However, our zero field ex- The texture proposed at P=10kbar is depicted on Fig.4
⊥,c a b
trapolation of t≈he upper critical field for H//b’ which assuming a rectangular lattice. As R /B 1/9 and
⊥,c
≈
is obtained by extrapolating linearly the upper crit- R /C 1/8,the hypothesis of a low coupling between
⊥,b
≈
ical field line from its value at low fields, H the filaments is justified a posteriori. The metallic frac-
c2,b
≈
0.9T is much smaller than measurements reported in tion obtained is about 0.8% in excellent agreement with
(TMTSF) ClO or(TMTSF) PF performedwithaper- the resistivity data7 considering the crude assumptions
2 4 2 6
fect alignment of the magnetic field21,22,23,24. This is made here. We notice that the cross-sections of the fil-
due to our experimental set-up which do not allow a aments are of the same order of magnitude as the co-
perfect alignment of our sample with respect to the herence lengths justifying the term of ’mesoscopic phase
b’-axis under pressure. We can deduce a rough esti- separation’. In order to confirm our image, the evolu-
mate of the misalignment of our sample to be about tion of the phenomena with increasing pressure has to
10◦ assuming that the upper critical field is identical beclarified. Thebasicinfluenceofpressureistoincrease
for(TMTSF) ClO and(TMTSF) ReO forH//b’. This theamountofmetallicpartwhichmeanslargerfilaments
2 4 2 4
4
with a smaller distance between them. Smaller B and FIG. 4: Texture of (TMTSF)2ReO4at P=10kbar deduced
C parameters manifest by a decreasing temperature T*. from theuppercritical fielddataandassumingarectangular
This is effectively observed experimentally. As shown in lattice. SC denotes thesuperconducting filaments.
Fig.2, from 10 to 11 kbar, T* varies from 0.75K to 0.2K
leading to a decrease of the distance between the fila-
ments from80 to 60nm. This shift ofT* is accompanied
by a decrease of H at zero temperature which implies In summary, the superconducting data along two field
c2
larger filaments and/or an increased coupling due to a directions has allowed the determination of the texture
lower distance between the filaments. The hypothesis of of a compound,(TMTSF)2ReO4, in its phase separa-
low coupling seems no more correct as we would obtain tion regime. The presence of both a linear regime and
R 25nm which is now 40% of the inter-filament a parabolic law in the upper critical field curve have
⊥,c
distan≈ce along b’. demonstrated the regular ordering of the individual fil-
aments. This is a clear signature of a self-organization
of the charge and that the physics studied here is not
dominatedbydefectsbutonlybylongrangeinteractions
betweenthedomainswithapreciseorientationofthean-
ions. The data also demonstrate that phase separation
occurs at the mesoscopic scale.
The authors acknowledge D.J´erome for fruitful dis-
cussions. We are also grateful to P.Auban-Senzier for
her assistance for the pressure equipment. This work
is supported by the European Community under Grant
COMEPHSNo. NMPT4-CT-2005-517039. C.C.andB.S
also acknowledge this grant for financial support.
∗ Present address : Department of Chemical Physics, Ma- Rev.B 22, 4264 (1980).
terials Science Center, Nijenborgh 4, 9747 AGGroningen, 13 S.S.P.Parkin,D.J´erome,andK.Bechgaard,Mol.Cryst.
The Netherlands, e-mail : [email protected] Liq. Cryst. 79, 213 (1981).
† Department of Applied Physics, Tafila Technical Univer- 14 R. Greene, S. S. P. Parkin, and H. Schwenk, Physica B
sity, P.O.Box179, Tafila 66110, Jordan 143, 388 (1986).
1 N. Joo, P. Auban-Senzier, C. R. Pasquier, P. Monod., 15 D. Feinberg and C. Villard, Phys. Rev. Lett. 65, 919
D. J´erome, and K. Bechgaard, Eur. Phys. Journ. B 40, (1990).
43 (2004). 16 W. Lawrence and S. Doniach, in Proceedings of the 12th
2 N.Joo, P.Auban-Senzier,C.R.Pasquier,D.J´erome, and International Conference on Low Temperature Physics,
K. Bechgaard, Eur. Phys.Lett. 72, 645 (2005). edited by E. Kanda (1971), p. 361.
3 H. Schwenk, K. Andres, and F. Wudl, Phys. Rev. B 29, 17 P. Fuldeand R. A.Ferrell, Phys.Rev. 135, A550 (1964).
500 (1984). 18 A.I.LarkinandY.N.Ovchinnikov,Zh.Eksp.Teor.Fiz.47,
4 J.-P. Pouget, S. Kagoshima, T. Tamegai, Y. Nogami, 113 (1964), Sov.Phys. JETP 20,762 (1965).
K. Kubo, T. Nakajima, and K. Bechgaard, Journ. Phys. 19 N.Dupuis,Phys. Rev.B 51, 9074 (1995).
Soc. Jpn. 59, 2036 (1990). 20 P. de Gennes and M. Tinkham, Physics (N.Y.) 1, 107
5 I. J. Lee, P. M. Chaikin, and M. J. Naughton, Phys. Rev. (1964).
Lett. 88, 207002 (2002). 21 I. J. Lee, M. J. Naughton, G. M. Danner, and P. M.
6 T. Vuleti´c, P. Auban-Senzier, C. Pasquier, S. Tomi´c, Chaikin, Phys. Rev.Lett. 78, 3555 (1997).
D. J´erome, M. H´eritier, and K. Bechgaard, Eur. Phys. 22 K. Murata, M. Tokumoto, H. Anzai, K. Kajimura, and
Journ. B 25, 319 (2002). T. Ishiguro, Jpn. Journ. of Appl. Physics Suppl. 26-3,
7 C. Colin, P. Auban-Senzier,C. R.Pasquier, and K. Bech- 1367 (1987).
gaard, Eur. Phys.Lett. 75, 301 (2006). 23 J. I. Oh and M. J. Naughton, Phys. Rev. Lett. 92, 67001
8 R. Moret, J.-P. Pouget, R. Com`es, and K. Bechgaard, (2004).
Phys. Rev.Lett. 49, 1008 (1982). 24 N. Joo, P. Auban-Senzier, C. R. Pasquier, S. Yonezawa,
9 L.A. Turkevich and R.A. Klemm, Phys. Rev. B 19, 2520 H. Higashinnaka, Y. Maeno, S. Haddad, S. Charfi-
(1979). Kaddour, M. H´eritier, K. Bechgaard, et al., Eur. Phys.
10 R. Klemm, A. Luther, and M. Beasley, Phys. Rev. B. 12, Journ. B 52, 337 (2006).
877 (1975). 25 P. A. Mansky, G. Danner, and P. M. Chaikin, Phys. Rev.
11 V. M. Krasnov, A.E. Kovalev, V.A. Oboznov, and N. F. B 52, 7554 (1995).
Pedersen, Phys. Rev.B 54, 15448 (1996).
12 G. Deutscher, O. Entin-Wohlman, and Y. Shapira, Phys.