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Hall Effect Anomalies and Phase Transitions in the Organic Superconductors, κ(BEDT-TTF)2Cu(NCS)2
and β-(BEDT-TTF)2I3
Keizo Murata
To cite this version:
Keizo Murata. Hall Effect Anomalies and Phase Transitions in the Organic Superconductors,
κ(BEDT-TTF)2Cu(NCS)2 and β-(BEDT-TTF)2I3. Journal de Physique I, EDP Sciences, 1996, 6
(12), pp.1865-1873. �10.1051/jp1:1996195�. �jpa-00247287�
Hall Elllect Anomalies and Phase Transitions in trie Organic Superconductors, ~t-(BEDT-TTF)2Cu(NCS)2
and fl-(BEDT-TTF)213
Keizo Murata
(*)
Electrotechnical
Laboratory,
1-1-4, Umezono, Tsukuba lbaraki, 305Japan
(Received
13May1996,
revised 22August, accepted
.5September1996)
PACS.74.70K
Organic superconductors
PACS.72.15Lh Relaxation limes and mean free
patins
PACS.72.15Eb Electrical and thermal conduction in
crystalline
menais andalloys
Abstract. Trie Hall coefficient, Ru
(T)
fororganic
conductors isstrongly
temperaturedepen-
dent even if they are metallic. The temperature
dependence
of Ru(T)
is found tu exhibit une-to-one
correspondence
with trie structure of the Fermi surface, hence con be called "Standard"for each surface. Ii turned Dut that the
simple temperature-independent
Ru(T)
isonly
realized in a material where trie Fermi surface is round andsimple
for these low dimensional systems.The "Standard"
Ru(T)
for each Fermi surface is obtainedempirically
by comparingRH(Tl's
of
relatively high
pressure, where low temperature navet stores or excitationsare suppressed.
In some cases,
Ru(T)
deviatesabruptly
from trie standardRu(T)-behavior,
which suggests aphase transition or lis precursor. We show the
examples
of~-(BEDT-TTF)2Cu(NCS)2
and offl-(BEDT-TTF)213
in which the anomaly inRH(T) corresponds
tu apeak (r-
GOK)
of antifer-romagnetic
fluctuation, and tu 20K-phase
transition which is a~sociated with low-Tc supercon-ductivity, respectively.
As seen in these twoexarnples,
trie Hall eflect isstrongly
influenced by trie electronic state, and therefore, can be ~ useful trot forlocating phase
transitions.1. Introduction
The Hall effect is
generally
known to show carrierdensity
in metallic andsemiconducting systems by
trierelation, RH(T)
=1/~e,
where n is trie carrierdensity
and e, trie electroncharge.
Asimple
consequence of this relation is that metallic materials show atemperature tndependent RH (T),
at least wheu trie Fermi energy is muchhigher
thon 300 K. In triepast
several years, we bave examiued trie Hall effect oforgauic
couductors audsupercouductors
fromquasi-oue-
toquasi-two-dimeusioual (QID, Q2D)
couductors aud fouud almostalways
atemperature
dependent RH (T). Although
simulations ofRH(T)
aud itsproof
are very dilficult due to restrictedexperimeutal
information audevideuce,
at least for trieQ2D system,
we fouudempirically
oue-to-ouecorrespondence
with trietemperature depeudeuce
ofresistivity, p(T),
trie temperature
dependence
of Halleffect, RH(T),
and trie structure of trie Fermisurface,
~N"hich are shown
schematically
inFigure
1.(*)
Present address:Dept.
of Mat. Sci., Fac. ofSci.,
OsakaCity
Univ., 3-3-138,Sugimoto, Sumiyoshi-
ku, Osaka 558, Japane-mail:
muratak©soi.oeaka-cu.ac.jp
@
LesÉditions
dePhysique
19961866 JOURNAL DE
PHYSIQUE
I N°12J-tYPe ~ ~ '"'~~°~
~~~
>o
~
K-type ~
'"''°~ /
< o
~
T-type ~
lin'°g
tl-(BEDT-TTF~I
~~
i~ j
4
~ og
~
20kbar 2 bar
Fermi
surface RH Vs
Temp
p vsTemp
Fig.
1. Schematic sketch of trie Fermi Surface, trie Hall coefficient ~ers~s temperature and resistivity~ersus temperature for fl-, ~- and T-types of
quasi-two-dimensional
organic conductors.It is
interesting
to recall that Fermi surfaces of triefl-,
~-, o- and r-types can bedeveloped
from asiugle
round Fermi surface as showu luFigure
2.By
companugFigures
1 and2,
it isworth
noting
that trie Fermi surface of triefi-type
is trie mostsimple
amougail,
1.e. a round Fermi surface is locatedjust
inside trie first Brillouin zone. When trie Fermi surface foldsdue to contact with trie Brillouin zone
boundary,
there appears anearly singular
curvaturem trie Fermi surface. Arouud the
siugular
curvature lu the Fermisurface,
vF variesstrougly
withk,
audconsequently
trie rscattering
lifetime becomessensitively k-dependeut.
This is trie pnmary reasou for trie temperaturedepeudeuce
ofRH(T).
Markedexamples
of thesesiugular
curvatures are trieedges
of trie leus orbit of trie~-type,
and trieedges
of trie star-shaped
Fermi surface of trie r-type.(In
r-typecouductors,
there must be another reason for temperaturedependeuce
mRH (T).
Thesystem
con uot be treated withiu trie framework used fordegeuerate
menais due to trie Fermi energy which is in trie same order ofmagnitude
as trieroom
temperature.)
For the ideal 1D
system
withk-independent
r, m the relaxation timeapproximation
lu the semiclassical treatmeut,symmetric (in k-space)
relaù~ation time does notproduce
Hallvoltage,
smce a~y, which isproportional
to trie Hallvoltage,
vamshesaccording
to trieintegral,
a~y o~
f
dl x £, where £ = vfr[ii. Therefore,
trie Hallvoltage,
when it is detected in trie actualQID system,
it is due to the imbalance from the symmetry. In otherwords, RH (T)
is very much>-type
0
-
~
K-type
~-type
-~ ~
a-type
~ ~
example:
tx-(BEDT-TIF)~MHg(SCN)4
Fig.
2.Typical
two-dimensional Fermi surfaces reconstructed from trieoriginal
round surfaces.dominated
by
triedispersion (or diffusion) along
trie second and third conductive axes. Then trie Hallsignal
con either bepositive
ornegative irrespective
of trie value orpolarity expected
from triecharge
transfer. So it is more dilficult in lD thon in 2D to draw ont trie "standard"RH(T) correspondiug
to trie Fermi surfaces. Schematic(= rougir) image
of trie Fermi surfaceis less sulficieut to defiue
RH (T)
iiiQID.
Trieimportance
of trietransport properties aloug
trie less couductive axes arepoiuted
ont toiuterpret
trietemperature depeudeut RH(T)
iii TTF-TCNQ [2].
Auotherinterpretation
for trie temperaturedepeudent RR(T)
is, forinstance,
interms of a precursor of trie
phase
transition or of collectiveexcitation,
such as CDW in TTF-TCNQ
[2] and SD~V in(DMET)2Au(CN)2 [3,4].
Theseapparently
different causesresulting
in trie
temperature dependent RH (T)
areactually
uotiudepeudeut,
siuce triedispersion along
trie less couductive axes
strougly
influences trie variation of trie Hall effect as well as triephase
transitions. It is a matter of course that materials with lowerdimeusiouality
are morelikely
to show lowtemperature
iustabilities. lu otherwords,
materialsproperties
at lower dimension are more sensitive to trie 2ud aud 3rd axes trausfer euergy or to triewarpiug
of trie Fermi surface. This situation makes it more dilficult to draw outtypical
aud standardRH(T)
for lower dimeusioual materials. Eveu lu trie 2D materials, withiucreasiug
pressure,low temperature iustabilities are more
suppressed,
audthus,
"standard"RH (T)
for each Fermisurface,
eveuthough
it isschematic,
isrelatively easily
obtaiued.lu this paper, we revisited
RH (T)
of trie~-type
andfl-type
couductors and show thatRH (T)
ceases
chaugiug
with pressure abeyoud
certain pressure, where atypical
aud "StandardRH (T)
for each Fermi surface are realized. Wheu suddeu deviatious from those
RH(T)
arefouud,
it1868 JOURNAL DE
PHYSIQUE
I N°12~
5
~ .9
)
~
Î~
~ ~
É
#'
~
i
# 1
à
~'
0 50 100 150 200 250 300
Temperature (K)
Fig.
3.Temperature dependence
of Hall coefficient ofK-(BEDT-TTF)2Cu(NCS)2
ai ambient and other pressures.Magnetic
field isperpendicular
tu trieplane.
is an indication of a
phase
transition or somepeaking
in electronic excitation. Thus trie Hall effect is a useful and sensitive tool forobserviug
aphase
transition.2.
~z-(BEDT-TTF)2Cu(NCS)2
This material shows a
hump
in theresistivity
versustemperature
around loo K and under- goes asuperconducting
transition at 10 K. Theresistivity hump
had been controversial untila series of materais from trie
insulating
to more metallic onesappeared systematically.
It is understood since that trie materials con becategorized
from insulator to metal in trie or-der, N-(BEDT-TTF)2Cu[N(CN)2)Cl, N-(d~, BEDT-TTF)2Cu[N(CN)2)Br, ~-(h8, BEDT-TTF)2 Cu[N(CN)2)Br,
andN-(BEDT-TTF)2Cu(NCS)2.
Thisinsulating
state is drivenby
electroncorrelation,
like a Mott insulator which bas been discussed in correction with NMRexperi-
ments
[à-7j
as well astheoretically [8j.
Triehump
at 100 K inN-(BEDT-TTF)2Cu(NCS)2
con then be understood as a crossover from trie Mott insulator to a metal
by lowering
trietemperature.
In ail of trie
N-compounds, (TIT)~~
of~~C-NMR
exhibitsa
peak.
In~-(BEDT-TTF) 2Cu(N CS)2
and in~-(BEDT-TTF)2Cu[N(CN)2)Br,
thispeak
is located around 55 60 Kindicating
a maximum in trie
antiferromagnetic
fluctuation but net trie real transition because trie fineshape
of NMR is still visible below 55 60 K. Previous to these NMRstudies,
there bave been several reports that indicate anomalouschange
around 60 70 K, which bave been referred to m reference[9j.
Trie Hallcoefficient, RH(T),
which ispositive, gradually
increases ondecreasmg
trie
RH(T) temperature.
Below 60 70K,
trieslope
of(dRH(T)/dT( suddenly
increases and shows apeak
around 10 K[9,10j.
Noappreciable change
is observed around 100 Ksimilarly
toNMR-(TIT)~~
and to staticsusceptibility [5, 6j.
This sudden increase m(dRR(T)/dT(
below 60 70 K coincidesexactly
with triepeak
in(TIT)~~
of~~C-NMR.
Now trie 60 70 K
transition,
we con compare trieRH(T)
studied underhigher
pressures.If we
overlap
trieRH(T)
of P = 0 with otherRH (T)
ofhigher
pressures, it is quite evident that trie 60 70 K isreally
an anomalous temperature as shown mFigure
3. We therefore could bave astrong implication
of a transition around 60 70 K net from trieslope change
mjdRH(T)/dT(
but rallier from trie contrast between trie ambient andhigher
pressures m trie Hall effect. We exammed triespecific
heat across thistemperature
range, but could trot detectany
singular signal il ii.
This is reasonable if trie 60 Iianomaly
is ofpurely
electronicorigin.
In such a case, an
anomaly
mspecific heat,
even if oneexists,
can be buried in trie lattice contribution to triespecific
heat.Moreover,
this is consistent with trie fact that this is triepeak
in theantiferromagnetic
fluctuation in~-(BEDT-TTF)2Cu(NCS)2
but trot trie transition obtained from observation of thefine-shape
of NMR[12].
The suppression
by
pressure of the 60 70 K "transition" observedby
Hall effectstudy
under pressure in
~-(BEDT-TTF)2Cu(NCS)2
mayactually
occur. In a similarmaterial,
~-(BEDT-TTF)2Cu[N(CN)2)Br,
thesuppression
of themagnetic
fluctuationpeak by
pressureis observed
by (TIT)~~
of NMR[6].
About the "standard"
RH(T),
Sushko et ai. studied in~-(BEDT-TTF)2Cu[N(CN)2)Cl
in trie pressure range of 4.5 10kbar,
and found almost nochange
mRH(T)
with pressure[13].
It is
important
to note that this is trie pressure region wherealready superconductivity
issuppressed similarly
as m~-(BEDT-TTF)2Cu(NCS)2.
3.
fl-(BEDT-TTF)213
As seen
Figure 4, RH (T)
of this material variesextremely
little with temperature down to 20 K.Although
this result isquite simple,
and looks more like standardmetal,
tt is worthremarktng,
since flot
RH (T)
isexceptional
among theQ2D organic
couductors.By comparing
withRH (T)
aud the Fermi surface of other
types,
it is noticed that this standard behavior ofRH(T)
is causedby
the fact that the Fermi surface does not touch the first Brillouin zoneboundary, leaving
nosingular
area in the Fermi surface. In otherwords,
noparticularly
anomalousr-(mean
freetime)
area inkF-space
is found.Another
interesting
feature in thisregion
is that eventhough p(T)
andRH (T)
exhibit metallicbehavior,
the mean freepath, t,
calculatedby
a=
ne~r/m
is smaller than trie lattice constant around 300K;
t= 0.13
À
for 300 K and 130 attemperature just
abovesuperconducting
T~
[14, là]. (The
lattice constants are 6.6À,
9.1 in the 2Dplane
and 15.3perpendicular
to the
plane.)
The mobilities are p=
RH
x a is 0.2cm~ IV
s at roomtemperature
and 80cm~
Vs at 20 K. From such
high
to lowtemperatures
ailthrough, RH (T)
is constant as if it iscontiuuously
a coherent metal. It is net well understoodyet why
metallic behavior isexhibited with such
parameters
inhigh (= room) temperature.
Turning
back to the relation between the Hall effect aud thephase transitions,
we compare theRH(Tl's
studied under vanous pressures. FromFigure 4, RH(Tl's
are identical above 7kbar,
and we can thus obtain trie "standard"RH(T)
for this material.By comparing
withthis,
anomalies mRH(T)
arequite
dear at 17à K[14]
and 20 K[14-16].
This material bas twosupercouductiug
transitiontemperatures,
8 K and 1-à K[17,18].
Triesuperconductivity
of1.à K is associated with trie incommensurate
superstructure
fouudby Emge
et ai.[19]
witha wave vector of
(0.08,
0.27,0.20à)
that appear at 17à K. Triesuperconductivity
at 1.à K isa metastable state
[20, 21]
which can be converted to 8 K statethrough
2 Kby annealing
triesample
at around 103 K in trie time scale of 100 hours[22, 23].
As for trie
properties
and rotes of trie Halleffect, first,
ii isinteresting
from trieviewpoint
of trietransport property
itself thatalready
at 17àK,
where nosiguificaut change
in trie Fermisurface relative to trie Brillouin zone
boundary
isexpected,
trieRH (T)
is influenced(reduced) by
8Slo. Next, a new transition wasstrongly implied
at 20 Kby observing
asharp
kink thereand > 40Yo
drop
mRH (Ti
below 20 K[14]
which was then confirmed as a transition but nottrie crossover of trie
scattenng
mechanismby specific
heat measurement[24].
Since this 20K transition was obvions m
RH(T)
and inspeofic heat,
it is noted that trieRH(T) study
isthus a
po~v"erful
tool forlocating phase
transitions.Looking
around at other works concernmg trie 20 Kanomaly,
we are remmded of trie NMRKorringa relation,
which does net continue187o JOURNAL DE
PHYSIQUE
I N°125
Ù w+
~
~ OOOO'OOO°OaO
f
~ ,,,
Îf
~Î__
#
g
à1
~Î~"~
h'~>
~ '
a)
50 100 150 200 250 300Temperature (K)
~'%
~
~ l '
~
~
~ °
' Q
c©
j O
£ -
>
O >
~ fl
~
>
'perature (K)
Fig.
4.Temperature dependence
of Hall coefficient offl-(BEDT-TTF)213
ai anibient and orner pressures for T= o 300 K
la)
and ils expansion for low temperature16). Magnetic
field is perpen- dicular to trieplane.
The values of pressure in aclamp
cellcorrespond
to low temperature. Inour
pressure medium and equipment, room temperature is
always
1.5 kbindependent
ofroom temperature values. Arrow
in
(b)
shows aexample
of ananomaly
m RH(T)
for 5 kb. Data for 3 -10 kbare for
trie same
sample.
TO fit with o kb data of a dilferent sample, trie value ai 100 K is adjusted takinginto account trie data from reference [28].
across this
temperature [2à,26].
Trie~H-NMR
relaxation behavior becomesnon-siugle
audthat situation is
comphcated [27].
We come back to this discussion later.One of trie
advantages
of trieRH(T) study
is that we caneasily
extend trie work under pressure. Since anomalies arealways
seen inRH (T),
as shownby
an arrow inFigure
4b for à kb forexample,
we cauplot
thosetemperatures agamst
pressuretogether
withT~'s
of triesuperconductivity,
as shown inFigure
à. It is seen that triepoint
at 20 K at P= 0
cannot be couuected to other points associated with trie
high T~'s. By annealing
at 103 K forà0 -loo
hours,
8 Ksupercouductivity
is observedby specific heat,
aud 20 Kanomaly
inRH (T) disappears [28].
What is known fromFigure
5 is that 1.5 Ksuperconductivity
is related with lîà Kthrough
20 Kanomaly,
while 8 Ksuperconductivity
is relatedthrough
la Kanomaly.
With this
figure,
asN-(BEDT-TTF)2Cu(NCS)2 superconductivity
issuppressed
whereRR(T)
ceases
changiug
with pressure, it issuggestive
that triesuperconductivity
is assisted with non-conventional electromc excitation.
Although
trie reason to reahze 1-à Ksuperconductivity
m trie basicbackground
of 8 K bas uot beeu solvedyet,
weproposed previously
that triedeusity
of states for the 1-à K state is25
J'-(BEDT-TIF)~l~
Çi
R~(T)
Î 15
~ é
Î
la Low Tempf
Metallic region~ ~
O 2 4 6 8 la 12
Pressure (kbar)
Fig.
5. Trie temperature-pressurediagram
offl-(BEDT-TTF)213 plotted
with Tc(superconductiv- ity)
and THaii(Hall
elfectanomaly).
Ii is seen that ai Tuait ai 20 K for low Tc, trie store does non continue to triepoints
associated with triehigh
Tc state. The metallic region below trie temperature of trie Hall elfectanomaly
is shown as "low temperature metallicregion".
This demonstrates trieambiguity
m trie definition of trie anomalous temperature.smaller thon that of trie 8 K at trie 20 K transition
through possible nesting
of trie Fermi surface[14, 24].
Thisdeusity
of state scenario can not be consistent with trie~H-NMR results,
which tells about3%/kbar/kbar
decrease in triedeusity
of states inspite
of some relaxationanomaly
at P= o
through
around 20 K[2à].
Very recently,
Kanoda et ai. bavereported
a detailed staticsusceptibility
and~~C-NMR
concemiug trie 20 K transition[29]
which renewed trieprevious reports
oususceptibility [30].
Trie static
susceptibility
decreases withtemperature
aud levels off below 20 K.By auuealiug
at 103
K,
trie level-offsusceptibility
iucreased. This is consistent with ourprevious deusity
of statepicture implied
ou trie Hall effect measurement. Further. incommensurate structure are seeu to besuppressed by
trie NMR fineshape by aunealing
in trie time scale of 700 tirs.4. Conclusion
The Hall effect of
orgauic
metaiiic couductors aregenerally
verytemperature depeudent.
This is due to trie low dimensional nature of these inaterials. If trie materials are lower indimension, RH (T)
as well as trie low dimensional instabilities are moresensitively
influencedby
trie transfer energyalong
trie less conductive axes. This situationmight
be trie reason that we cari obtaintypical
"standard"RH(T)
for eachtypical
Fermi surfaceespecially
for 2D materials underrelatively higher
pressures, where delicate transfer energy structure is lessimportant.
Among these, fl-(BEDT-TTF)213
is triespecial
case, which shows almost temperature Inde-pendent RH (T).
It isexplained
that trie Fermi surface is trie mostsimple
without anysingular point
ink-space
lu terms ofscatteriug
lifetime.We note that for ail trie cases
~-(BEDT-TTF)2Cu(NCS)2, ~-(BEDT-TTF)2Cu[N(CN)2)Cl
and
fl-(BEDT-TTF)213, RH(T)
isalready
constant with pressure wheresuperconductivity
issuppressed.
Thismight
indicate that triesuperconductivity
is realized in trie environment of novel low dimensional instabilities.1872 JOiÎRNAL DE
PHYSIQUE
I N°12Finally regarding
trie standardRH(T),
trie anomalies inRH(T)
which areusually
related tophase
transitions areclearly
found. Thus the Hall effect is a useful tool forlocating phase
transitions.
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