Probing the Ground State Properties of Iron-based Superconducting Pnictides and Related Systems by Muon-Spin Spectroscopy

0.28 MB·English

by  A. Amato

Probing the Ground State Properties of Iron-based Superconducting Pnictides and
Related Systems by Muon-Spin Spectroscopy
A. Amatoa,∗, R. Khasanova, H. Luetkensa, H.-H. Klaussb
aLaboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, CH-5232 VilligenPSI, Switzerland
bInstitut fu¨r Festk¨orperphysik, TU Dresden, D-01069 Dresden, Germany
9
0
0
Abstract
2
In this short review, we attempt to give a comprehensive discussion of studies performed to date by muon-spin spec-
n
atroscopy (more precisely the relaxation and rotation technique, also know as µSR) on the recently discovered layered
Jiron-basedsuperconductors. On one side, µSR has been used to characterizedthe magnetic state of different families of

6layered iron-based systems. Similarly the subtle interplay of the magnetic state and the structural transition present in
2some families has been investigated. We will also discuss the information provided by this technique on the interaction

between the magnetic state and the superconducting phase. Finally the µSR technique has been used to investigate
]
nthe magnetic penetration depth of the superconducting ground state. The study of its absolute value, temperature and
omagneticfielddependenceprovidescrucialtestsforinvestigatingpossibleunconventionalsuperconductingstatesinsuch
c
systems.
-
r
p
u
1. Introduction pnictides. Its very high sensitivity to internal magnetic
s
. fields allows one to investigate weak magnetic states and
t The recent discovery of superconductivity (SC) in lay-
a to determine very precisely the temperature dependence
mered iron pnictides [1] has triggered a surge of research
of the magnetic order parameter. As being a local probe
activity devoted to understanding their magnetic and su-
- technique, µSR is widely recognized as one of the key ex-
dperconductingstates,aswellastodisentanglingtheirfun-
periment to test for possible microscopic coexistence be-
n
damental interplay. Probably the foremost motivation of
o tweendifferentgroundstates. Inviewofthevicinityofthe
such interest is based on the apparent striking similarity
c magneticandsuperconductingstatesandoftheir possible
[between such systems and the well-studied superconduct-
interplayinthelayeredironpnictides, suchmeasurements

ing cuprates. Hence, similar to the cuprates, SC takes
2 are crucial to gain more insight on the specific formation
place mainly in crystal layers (in this case FeAs) with the
v mechanism of the superconducting ground state. Finally,
9rest of the structure acting as a charge reservoir. More- bydetecting localfielddistributions,theµSRtechniqueis
3over,aremarkableparallelwiththecupratescanbedrawn
usedtotestthenatureofsuperconductingstatesbystudy-
1from the observation that SC appears when doping away
ingthetemperatureandfielddependenceofthedensityof
3
from an antiferromagnetically ordered mother compound,
. superconductingcarriersns,directlyobtainedthroughthe
1suggesting the importance of magnetic fluctuations in the
determination of the London magnetic penetration depth
0mechanism of Cooper pairs formation.
9 λ in the vortex phase.
For the research on cuprates, the muon-spin spectros-
0
copy (µSR) technique has played a key role, on one side
:
vby investigating the interplay between magnetism and su- 2. Principle of the µSR technique
i
Xperconductivity, and on the other side by providing fun-
In µSR experiments, 100% polarized muons are im-
damental results about the nature of the superconducting
r planted in the solid sample. After a deceleration within
astate. Itisthereforenotsurprisingthatthistechniquehas
100 ps, which is too rapid to allow any significant loss of
been, at a very early stage, widely involved in the study
polarization and sufficiently rapid for the µSR time win-
of the layered iron pnictides. The aim of this article is
dow,themuoncomesatrestatinterstitiallatticesitesand
to provide a short review of the µSR studies available to
decaysafter anaveragelifetime ofτ =2.197µs, emitting
date and to discuss the main insights provided by these µ
a positron (e+) and two neutrinos.
measurements.
Theparityviolationintheweakinteractionisreflected
As developed in the next Section, the µSR technique
by an anisotropic distribution of the positron emission
possesses few features which might be exploited to pro-
withrespecttothemuon-spindirectionatthedecaytime.
vide key knowledge when studying the iron-based layered
The positron emission probability is given by
∗Correspondingauthor W(θ)dθ (1+Acosθ)dθ , (1)
∝
Preprint submittedto Elsevier January 26, 2009
where θ is the angle between the positron trajectory and They will also be identified by a µSR signal with different
the muon-spindirectionatthe momentofthe decay. This components, i.e. with different spinauto-correlationfunc-
anisotropic positron emission constitutes the basics for tions G (t). In this case the respective amplitudes (A )
i i
the µSR technique. By measuring the positron distribu- will reflect the probabilities to stop the muon at a given
tion, the original muon-spin direction can be determined. site. Therefore, great care has to be taken to differentiate
The asymmetry of W(θ) is given by A = aP (0), where this case from the occurrence of different ground states in
µ
P (0) = P (0) is the beam polarization, which is of the the sample.
µ µ
| |
order of 1, and a is an intrinsic asymmetry parameter If a static local magnetic field (B ) is present at the
µ
∼
determined by the weak decay mechanism. If all emitted µ+-site, G(t) is given by
positrons are detected with the same efficiency irrespec-
tive of their energy, an average of a = 1 is obtained. G(t)= f(B ) cos2θ+sin2θcos(ω t) dB , (6)
Practically, during µSR measuremenhtsi, only3 values up to Z µ h µ i µ
A 0.25 can be obtained. where f(B ) is the magnetic field distribution function,
≃ µ
Iftheimplantedmuonsaresubjecttomagneticinterac- θ is the angle between the local field and P (0). Hence
µ
tions, their polarization becomes time dependent [Pµ(t)]. thepresenceofinternalmagneticfieldsinasamplewillbe
The time evolution of Pµ(t) can be deduced by measur- revealed by the occurrence of frequencies νµ in the µSR
ing the positron distribution as a function of time. In signal,whichwillbe adirectmeasureofthe internalfields
the standard µSR technique, repeated measurements are as ν = ω /(2π) = γ /(2π)B , where B = B and
µ µ µ µ µ µ
made of the time interval between the µ+-implantation γ /(2π) = 135.53879( 0.7 ppm) MHz/T is the g|yro|mag-
µ
into the sample and the detection of the emitted positron netic ratio of the muon±. In practice, internal fields result-
in a particulardirection[say,in the directionof the initial ingeitherfromamagneticstate(creatingspontaneousfre-
polarization Pµ(0)]. The time histogram of the collected quencies) or from externally applied fields will have some
intervals adopts therefore the form distribution around an average value creating a depolar-
Ne+(t)=Bg+N0e−τtµh1+APPµµ((0t))i , (2) idzeinpSghuaecsnihnvgdeleoopfpoetlhaoerifzmatuhtioeonnoesisnciselelxamptloborlieyt.eµdStRo dseigtenraml,indeutehetoLtohne-
where Bg is a time-independent background, N0 is a nor- donpenetrationdepthinatypeIIsuperconductorbyper-
malization constant and the exponential accounts for the forming measurements in the vortex phase created by ap-
decay of the µ+. Pµ(t) is defined as the projection of plyingahightransverseexternalmagneticfield. Fromthe
Pµ(t) along the direction of the initial polarization, i.e. observed depolarization rate σ, usually of Gaussian char-
Pµ(t) = Pµ(t) Pµ(0)/Pµ(0) = G(t)Pµ(0) where G(t) re- acter,thepenetrationdepthcanbeobtainedrecallingthat
·
flects the normalized µ+-spin auto-correlationfunction in the clean limit:
S(t) S(0) σ λ−2 ns , (7)
G(t)= h S(·0)2 i , (3) ∝ ∝ m∗
∗
where m is the effective mass of the carriers (see for ex-
whichdependsonthedistribution,averagevalueandtime
ample[2]). Byrecordingthe temperatureandfielddepen-
evolution of the internal fields and therefore contains all
the physics of the magnetic interactions of the µ+ inside dence of σ and hence consequently ns, indication about
the likely occurrence of unconventional superconducting
the sample. Equation (2) can be written as
states can be pinpointed.
t
−τ
N (t)=B +N e µ 1+AG(t) . (4)
e+ g 0
h i 3. Characterizing the magnetic state of mother
The termAG(t) is oftencalledthe µSRsignalandthe en- compounds
velopeofG(t)isknownastheµ+-depolarizationfunction.
Since the µ+ are uniformly implanted in the sample, EarlyµSRstudieshavebeenperformedtocharacterize
the coexistence of different domains, characterizedby dif- the magnetic state of the first discovered family of FeAs
ferent types of ground states, will also be detected by the layeredsuperconductors, the so-called “1111”family with
presence of different components with distinct functions REFeAsO where RE represents a rare-earth ion. Studies
G (t). The amplitude (A ) of each components will read- havebeenreportedonsystemswithRE=La[3,4],Nd[5]
i i
ily be a measure of the volume fractions associated with andSm[6]. ThecompoundLaFeAsOhasatanearlystage
different domains,with the conditionthat they sum up to attracted interest as no complication of rare-earth mag-
the known maximal achievable asymmetry, i.e.: netic ordering is at play. Both reported measurements in-
dicatethepresenceoftwospontaneousfrequenciesfortem-
A =A . (5)
i peraturesbelowT =138K.Thetemperaturedependence
N
X
i ofthewell-definedfrequenciesindicatesthatthe magnetic
A potential difficulty is that in a particular crystallo- transitionisofsecond-orderandthatthesaturationvalues
graphicstructure,morethanonestoppingsitescanoccur. forT 0are23and3MHz. Thewell-definedfrequencies
→
2
peraturesexhibitstheoccurrenceofadditionalfrequencies
30 [6], pointing therefore to a different magnetic ordering of
the Sm-sublattice compared with the case of NdFeAsO,
where a mere shift of the main frequency was observed.
25
For all the pristine “1111” compounds investigated by
) µSR the formation of the magnetic state is confirmed to
z
H
M 20 occurinasecond-ordertransitionandwellseparatedfrom
( the temperature T 160 K where a structural transi-
y S ≃
c tion from the high-temperature tetragonal (space group
en 15 P4/nmm) phase to a orthorhombic (space group Cmma)
u
eq phase is observed[8]. A drasticallydifferent picture is ob-
r
F 10 tained when investigating by µSR the mother compounds
of the so-called “122” family. The ternary oxygen-free
5 LaFeAsO iron-basedarsenide XFe2As2 (where X = Ca, Sr, Ba) sys-
NdFeAsO temscrystallizeinahigh-temperaturetetragonalstructure
oftheThCr Si -type(spacegroupI4/mmm). Suchstruc-
2 2
0 ture contains almost identical layers of FeAs edge-sharing
0 50 100 150
tetrahedra. Instead of LaOlayersas in the “1111”family,
T (K) these layers of tetrahedra are separated by ions of type X
Figure1: Temperaturedependence ofthe highestspontaneous µSR alongthec-axis. However,the“122”familyexhibitsstrik-
frequencies recorded for two systems of the “1111” family, namely ing similarities with the “1111” series in the sense that
LaFeAsO [3] and NdFeAsO [5]. Note the change of the frequency a rather comparable tetragonal to orthorhombic (space
valueatlowtemperatureforNdFeAsOreflectingtheorderingofthe
groupFmmm)structuraltransitionisobserveduponlow-
rare-earthmoments.
ering the temperature and that a magnetic ground state
appears. Suchmagneticorderischaracterizedbyacolum-
point to the presence of a commensurate static magnetic
nar antiferromagnetic ordering of the Fe moments with a
orderandtheamplitudeoftheobservedmagneticµSRsig-
propagation vector (1,0,1). On the contrary of what has
nal implies that 100%of the sample volume orders at T .
N been observed for the REFeAsO series, for the XFs As
2 2
Suchfindingsareon-linewiththereportedmagneticstruc- systems Rotter et al. [9] convincinglyestablishedthat the
ture obtained by neutron diffraction [7]. The presence of
structuralandmagnetictransitiontransitionsoccursimul-
different components points to the occurrence of two dis-
taneously suggesting that the magnetic and orthorhombic
tinct muon stopping site, with the high frequency associ-
order parameters are strongly coupled. However, quite
ated with muons stopping near the Fe magnetic moments
some controversy still exists on the order of the phases
in the FeAs layers,whereas the lowestfrequency points to
transitions, which was first characterized to be of second-
the presence of a more remote muon stopping site, most
orderandlaterreportedtobe ofthe first-order[9,10,11].
likelyneartheLaOlayers. BycomparingdirectlytheµSR
As the space group Fmmm of the low-temperature or-
andMo¨ssbauerdataKlausset al. [3]determineastrongly
thorhombic phase is a subgroup of the space group of the
reduced iron ordered moment of 0.25(5)µ .
B high-temperature tetragonal phase I4/mmm, such clas-
Thecomplicationprovidedbythe orderingoftherare-
sification could be compatible with the observed struc-
earth moments at low temperature is exemplified by the
tural phase transition. Recently a combined study on
datareportedbyAczelet al. [5]onNdFeAsO (seeFig.1).
thesystemSrFe As [12]usingthermodynamicandtrans-
2 2
In additionto havea N´eeltemperaturecomparableto the
port measurements as well as x-rays and µSR clearly de-
one ofLaFeAsO,the mainfrequencysignalexhibits above
termined the first-order character of both structural and
about5K averysimilartemperature dependence andab-
magnetic transitions. The µSR spectra in SrFe As re-
2 2
solute value to the ones observed in LaFeAsO. This indi-
semble the ones reportedfor LaFeAsO with also two well-
cates, in addition of suggesting analogous muon stopping
defined frequencies at 44 Mhz and 13 MHz, correspond-
sites, that the ordered Fe-moments for these two systems
ing to 70% and 30% of the signal, respectively. The ob-
are of the same size for temperature regions unaffected
served ratio between the highest frequencies in LaFeASO
by the rare-earthions ordering. The magnetic ordering of
and SrFe As is equal to the ratio of the hyperfine fields
2 2
the Nd sublattice is reflected by a jump of the frequency
measuredby Mo¨ssbauerindicating that in the “122”fam-
below about 5 K. The robustness of the ordering within
ily,themuonstoppingsiteneartheFeAslayersisidentical
theFeAslayersisalsodetectablebyµSRontheSm-based
as the one occurring for the “1111” systems. In addition,
mother compound SmFeAsO [6], where a similar sponta-
thetemperaturedependenceofthemagneticorderparam-
neous muon-spin precession frequency of 23.6 MHz is ob-
eter recorded by µSR (i.e. of the observed spontaneous
served for the iron-moments ordering. Here also, a clear
frequencies) is basically identical to the one characteriz-
signatureoftherare-earthorderingisobservedattemper- ing the orthorhombic distortion δ (= a /(a √2) 1 =
O T
aturesbelow5K.However,theµSRsignalatverylowtem- 1 b /(a √2), where a , a and b are the latti−ce pa-
O T T O O
−
3
rameters of basal plane for both structures) proving that
50
the magnetic and orthorhombic phase are intimately cou-
(a)
pled (see Fig. 2). Such observation strongly suggests that
the size of the orthorhombic distortion actually defines
the size of the ordered iron moment, and therefore the Hz)40 Su.)rFe2As2
muon-spin frequency, or vice versa. Interestingly, a scal- M a.
ing betweenthe values ofthe orthorhombicdistortionand y (30 e (
of the muon-spin frequency, both extrapolated at T = 0, nc ud6
holds also for the LaFeAsO compound. A similar scaling ue plit
factor of 92 MHz (equivalent to almost exactly 1 µB eq20 am4
otirodneriesdoibr∼osenrvmeodm. eLnitm) piteerdpdearctaenitsopfroerstehnotrlyhormepboicrtdeidstoforr- SR fr ourier 2
the other compounds of the “122” family, i.e. X = Ca (cid:181)10 F
0
and Ba [5, 13, 14]. The observation of clear spontaneous 0 20 40 60 80 100
µSR frequencies confirms the occurrence of well defined Frequency (MHz)
magnetic states. However, the few available points of the 0
0 50 100 150 200
temperature dependence ofthe spontaneousµSRfrequen-

cies do not allow one to draw definite conclusions on the T (K)
)
classificationorderofthemagnetictransition. Hereagain, Hz45 (b)
T = 60 K
the coincidence between the disappearance of the spon- M
(
taneous µSR frequencies and of the structural transitions y
c
clearly points to a close relation between both types of n40
e
phenomena. u
q
Another family of superconductors characterized by e
the presence of two-dimensionaliron-basedslabs has been fr35
R
also recently reported [15], i.e. the so-called “011” com-
S
posed by the α-FeSe1−x binary system. Such system is (cid:181)
characterized by stacks of edge-sharing FeSe tetrahedra,
4 30
very similar to the one found in the oxypnictides. Inter- T = 205 K
estingly, such system crystallizes in the PbO tetragonal
0.40 0.45 0.50 0.55
structure (space group P4/nmm), but presents, at least -2
(10 )
for some anion concentration, below T (of the order of
S
Figure2: (a)Temperaturedependenceofthehighestmuon-spinpre-
100 K) a structural transition into a orthorhombic phase
cession frequency recorded in SrFe2As2. Note the clear first-order
(space group Cmma) showing remarkable similarities to
transitionat205K.TheinsertrepresentsaFouriertransformofthe
that of the “1111” oxypnictides. Khasanov et al. [16] µSR signal recorded at 1.6 K, where the high and low frequencies
reported muon-spin measurements performed on a sam- areclearlyvisible. (b)ObservedscalingbetweentheµSRfrequency
and the orthorhombic distortion, with the temperature as implicit
ple with nominal concentration FeSe . In the whole
0.85 parameter. BothpanelsareadaptedfromRef. [12].
temperature region the zero-field data were found to be
well described by the single-exponential decay function.
This points either to the existence of fast electronic fluc- of the “1111” family, where trivalent cation and oxygen
tuations measurable within the µSR time window or to are respectively replaced by divalent alkaline earth metal
a static magnetic field distribution caused by diluted and (Ca or Sr) and fluorine. The crystal structure is compa-
randomly oriented magnetic moments. However, it was rable to the “1111” oxypnictides with similar FeAs lay-
found that an externally applied longitudinal field allows ers(ZrCuSiAs-typestructure,spacegroupP4/nmm),but
one to quench the depolarization due to internal fields, divalent alkaline earth metal - fluoride layers replace the
proving therefore their static character. By comparing rare-earth - oxide layers. In this family, the fluoride ions
the µSRdatawithmagnetizationstudies,Khasanovetal. are thought to provide weaker magnetic exchange path-
conclude that the magnetism observed is, most probably, waysbetweentheFeAslayersthanfortheabovedescribed
caused by traces of Fe impurities. “1111” oxypnictides or “122” families. Again similarly to
Finally, µSR studies of the magnetic properties of the oxypnictides, one observes for the parent compounds
the oxygen-free compounds SrFeAsF and CaFeAsF have astructuraltransitiontoalow-temperatureorthorhombic
been reported [17, 18]. These compound can be classi- structure (Cmma) below (T 175 K for SrFeAsF [20]
S
≃
fied as the parent compound of a newly discovered se- and T 134 K for CaFeAsF [21]).
S
≃
ries of fluoropnictide superconductors, where the doping Concerning SrFeAsF, and based on Mo¨ssbauer stud-
on the divalent metal site may lead to superconductivity, ies [20], it was speculated that the structural transition
as for example Sr0.5Sm0.5FeAsF which superconducts be- was accompanied by a concomitant magnetic transition.
low T = 56 K [19]. Such family represents a variation
c
4
However, Baker et al. [17] clearly demonstrate by µSR 4. Evolution of the magnetic state upon doping
that SrFeAsF possesses an even greater separation be- and its interplay with superconductivity
tween the structural and magnetic ordering temperatures
(TS TN 50 K) than in the “1111” oxypnictide family Like the cuprate high-Tc superconductors, the super-
and−that t≃he magnetic transition is of second-order. In- conducting state in the iron-based layered systems is
terestingly,theobservedspontaneousfrequenciesobserved reached upon charge doping the magnetic parent com-
below T are slightly lower that in LaFeAsO but in simi- pound. Such doping can be achieved through electron
N
larproportion,suggestingthatthemagneticstructureand doping by creating oxygen deficit, substituting oxygen by
ordered moments are comparable to LaFeAsO, and also fluorine in the RE-oxygen layers, or even replacing iron
points to related muon stopping sites. A difference with by e.g. cobalt in the FeAs layers. Another route is hole
the oxypnictides is furnished by the temperature depen- doping,achievedbyapartialsubstitutionoftherare-earth
dence of the frequencies, which can also be fitted by a ions(e.g. LabySr). Asinthecuprates,suchdopingleads
conventionalpowerlawν (T)=ν (T)[1 (T/T )α]β but toaweakeningofthe magneticstateasthe superconduct-
i i,0 N
withparameterβ =0.22(3)representinga−slightlysharper ing state emergesraising the question of the nature of the
phase transition suggesting a more two-dimensional mag- interplay between both ground states. As µSR studies
netic interactionsthan in oxypnictide compounds. This is have provided unique information on the evolution of the
consistentwiththeincreasedseparationT T andwith magnetismupondopingincuprates[25],itisofnosurprise
S N
theexpectationthattheinterplanarexchang−emediatedby thatearlyandextensiveµSRinvestigationshavealsobeen
a fluoride layer is weaker than that mediated by an oxide devotedto the searchof possible genericfeatures common
layer in the “1111” family. to cuprates and iron-based layered systems, which could
For the CaFeAsF compound, Takeshita et al. [18] ob- shade more light on the understanding of the mechanisms
served a second order magnetic transition around 120 K, of high-Tc superconductivity.
below which a single spontaneous µSR frequency appears Much interest has been first dedicated to the study of
and which saturates at about 25 MHz. Hence, the magni- the lanthanum member of the “1111” family, as the lack
tude of the internal field is again rather close to the ones of a 4f-electrons contribution allows one to gain a clearer
observed for the oxypnictides “1111” family. viewontheevolutionoftheFe-momentsmagnetism. First
To complete the picture, a careful study of the possi- µSRdataondopedbutstillmagneticLaFeAsO1−xFxwere
bleimpurityphases(namely,FeAsandFeAs )inpnictides reported by Carlo et al. [4]. By doping with 3% fluo-
2
compounds containing FeAs layers has been reported by rine, the ZF-µSR spectra exhibit a change from the sim-
Bakeretal. [22]. FeAsisknowntoexhibitanhelimagnetic ple cosine signals observed in undoped LaFeAsO towards
orderbelowT =77K[23],whereasFeAs haspreviously a Bessel function line shape. Such a change hints to a
N 2
been shown not to order down to 5 K [24]. The spon- crossoverfromacommensuratemagneticstructure(CMS)
taneous µSR frequencies observed in FeAs for T 0 K towardsanincommensurateone(IMS).Whereas,forCMS
are both strongly damped and have values of 2→3 MHz sharp distributions are present due to the constant phase
(correspondingto70%ofthesignal)and 38MH∼zforthe between the muon-stopping site and the spin modulation,
remaining signal amplitude. Above T t∼he µSR signal is for IMSthe field distributionseenby the muonrepresents
N
weakly damped as expected in the paramagnetic phase. a sinusoidal distribution of internal fields and is given by
The 23 MHz signal observed for FeAs is similar to that [26]:
in the “1111” family and in the SrFeAsF compound (see 2 1
for B <B
afrbeoqvuee)n.cyHosiwgenvaelr,,atnhdea“1m11u1c”hcloowmeproduanmdspihnagverantoe.hAiglhseor, fIMS(B)= πpB2−Bm2ax max (8)
the23MHzsignalinthe“1111”compoundspersistsallthe 0 otherwise.
way up to TN 140 K, twice that of FeAs. Consequently, 
Baker et al. ≃concluded that the local environments for By combining Eq. 8 and Eq. 6, one can easily calcu-
implanted muons are relatively similar in FeAs and the late that the time evolution of the muon polarization is
“1111” family, but FeAs impurities cannot produce the given by the J0 Bessel function. Carlo et al. [4] as-
observed signal. A similar conclusion can be drawn for sociate such change to the one observed in the cuprate
SrFeAsF, where the observed 23 MHz signal persists up La2CuO4 at the 1/8 doping when the formation of spin
to T 120 K and therefore∼is not related to FeAs im- stripes occurs [27]. In the cuprates, such stripe order in-
N
purities≃. The µSR studies of the impurity phase FeAs volves a spatial segregation of doped holes. This results
2
confirm the absence of static ordering, with the observa- into a persistence of antiferromagnetic hole-poor regions.
tion ofa weakdepolarizationmostprobablyreflectingthe An alternativeroute to explainthe incommensurabilityof
effect of the atomic-moments fluctuations within the µSR the magnetic structure upon doping is to consider that
time-window. the increase of electron doping changes slightly the topol-
ogy of the different Fermi surfaces thereby modifying the
length of the antiferromagnetic nesting vector responsible
forthe magneticorder[28]. Suchexplanationwasinvoked
5
by Luetkens et al. [29] as they reported the observation
of a similar Bessel function in a LaFeAsO F sam-
0.96 0.04
ple. Such view point appears somewhat corroborated by
the observation, at very low doping, of a smooth evolu-
tion of both the magnetic order temperature transition
and the ordered value of the magnetic moment [29]. The
rathersystematicstudy ofthe evolutionofthe magnetism
upon doping in the LaFeAsO1−xFx series presented by
Luetkens andcoworkers[29]also clearly demonstratesthe
total absence of any coexistence between magnetism and
superconductivity. Hence, for a fluorine doping x between
0.04and0.05,asharpfirst-order-liketransitionfromspin-
density wave magnetic order towardssuperconductivity is
observed. The abrupt change of the ground state is visi-
ble in the transition temperatures T and T (see Fig. 3),
N c
as well as on the magnetic order parameter. It this work
the abrupt change was not only mapped out by µSR but
also by Mo¨ssbauer spectroscopy. Interestingly, such first-
order-like transition is also observed on the orthorhom-
bic distortion which also disappears at the same doping,
as demonstrated by x-ray diffraction on the same sam-
ples. Thisconfirmstheclosecorrelationbetweenthestruc-
turaldistortionandthe magneticgroundstate properties.
Moreover,thesteplikebehaviorofthesuperconductingor-
der parameter, between x = 0.04 and 0.05 suggests that
the key element for superconductivity is the suppression
of the orthorhombicdistortion, and therefore of the static
Figure3: Phasediagramsasafunctionoffluorineconcentration for
magnetic order, rather than the moderate increase of the
different systems of the “1111” family REFeAsO1−xFx. The data
chargecarrierdensitybythefluorinedoping. Moreimpor- withRE=La[29]andRE=Sm[6]areobtainedbyµSR,whereasthe
tantly, the study of Luetkens and coworkers rules out the dataonRE=Cewereobtainedbyneutrondiffraction[30]. Dashed
occurrence of a magnetic quantum critical point, at least lines and circles: Tc; Solid lines and squares: TN. Note the first-
order-liketransitionfortheRE=Lasystem,theapparentquantum
in La-based “1111” systems.
critical point for RE = Ce and the coexistence for the RE = Sm
Note that in a recent neutron scattering study of the system(shadedarea).
dopingdependenceoftheorthorhombicdistortionandthe
magnetic order in CeFeAsO1−xFx [30] a gradual suppres-
istswithsuperconductivityandslowmagneticfluctuations
sion of T as a function of the fluorine doping within the
N
persist into the superconducting state [32, 33], the max-
orthorhombicphasewasobserved,pointingtothepresence
of a quantum critical point (see Fig. 3). However, sub- imal Tc is almost double that of the LaFeAsO1−xFx sys-
tems, where spin fluctuations are hardly detectable in the
sequent µSR experiments on the very same sample with
superconducting samples by µSR. As mentioned above,
the magnetically ordered composition close to the phase
slow spin fluctuations emerging at the boundaries of a
boundary (x=0.06) reveals an increased magnetic order-
magnetic state can induce and/or enhance the Cooper
ing temperature [31]. A similar systematic µSR study as
pairs formation mechanism usually connected with a un-
the one performed for the La-based system is therefore
conventional superconducting order parameter [34]. In
urgently needed for the Ce-based system.
view of the results reported by Khasanov et al. [33] the
Finally, in the Sm-based system of the “1111” family,
question is raised about the origin of the observed slow
µSR studies appear to reveal a third type of behaviour.
fluctuationsforhigh-doping. Hence,oneobservesthatthe
Hence, a microscopic coexistence of bulk magnetic order
temperature dependence of the fluctuation rate is charac-
and superconductivity [6], connected with a gradual sup-
terized by an activation energy, most probably reflecting
pressionofN´eeltransitiontemperatureandthepersistence
the thermal population of samarium crystal-field levels.
of slow magnetic fluctuations, was observed in the doping
This is supported by the value of the fitted activation en-
range0.10<x<0.17(seeFig.3). Itmustbenoticedthat
ergy of 23 meV, which is in good agreement with the
forthehigh-Tc cupratesasimilarpictureoccursastheon- first exci∼ted crystal field level of the Sm3+ ions deduced
set of superconductivity gives rise to a suppression of the
fromthe observationofSchottky anomaliesin the specific
local magnetic order and the emergence of slow magnetic
heat [35]. Luetkens et al. [29] suggested that the origin
fluctuations, persisting welldeeply into the superconduct-
for the difference between the Sm and Ce-based systems
ing state. In view of their results, Drew et al. [6] noticed
thatintheSm-basedsystemwherestaticmagnetismcoex- to the LaFeAsO1−xFx ones might be related to a strong
6
electroniccouplingtotherare-earthmagneticmomentsor indicateanhomogeneousdistributionofthedopantatoms
possibly to a different level of local structural distortions and that the average potassium content was experimen-
at the x-dependent crossover from the low temperature tally determined by looking at the functional dependency
orthorhombic lattice structure to the tetragonal phase. of the lattice parameters.
Theconnectionbetweenthepresenceofrare-earthions Such a presence of magnetic and superconducting
in the system and the observation of coexistence between ground states in the Ba1−xKxFe2As2 systems is at first
magnetism and superconductivity does not hold for the sight similar to the situation reported for the cuprates
fluoropnictide system Ca(Fe1−xCox)AsFe. As shown by high-Tc in the underdoped regime. However, for the
Takeshita et al. [18], the substitution of iron by cobalt cuprates both ground states appear to coexist at the mi-
leads to a weakening of the magnetic state and a meso- croscopiclevel(seeforexample[25]),whereasamesoscopic
scopic coexistence between both ground states. However, phase separationis observedin the iron-layeredsupercon-
one also observes that upon doping the magnetic order ductors.
is no more characterized by well defined frequencies, but To add more complexity to the picture of the doping-
rather by a fast depolarization, most probably reflecting dependence of the magnetic state in the “122” family, we
a large disorder of the magnetic structure connected with note that, very recently, Hiraishi et al. [39] reported µSR
the iron ions substitution. data on a Ba1−xKxFe2As2 polycrystalline sample with a
Concerningthe“122”family(XFe As ,whereX=Ca, nominalx=0.4composition,wherenotraceofmagnetism
2 2
Sr, Ba – see above), severalµSR measurements havebeen wasfounddowntothelowesttemperaturesandwithasu-
devotedtothestudyoftheholedoping,whichresultsinto perconducting volume fraction of 100%. It remains to be
a weakening of the magnetic state and the occurrence of seen whether such apparent divergence between the re-
superconductivity. Suchdopingcanbeenobtained,forex- porteddataisaresultofasamplesqualityissueand/orof
ample, through the substitution of divalent cations (X2+) difference of doping between nominal and effective values.
through potassium as in Ba1−xKxFe2As2. For this latter
system, quite some divergence appears when comparing
5. On the nature of the superconducting state
the available µSR studies. In line with transport, x-ray
andneutrondiffractionstudies(seeforexample[36]),some As said above, in a type-II superconductors, the ab-
µSRstudies[5,13,37]reportthatthe magneticorderand
solute value and temperature dependence of the London
the superconductivity overlap in the intermediate compo-
magneticpenetrationdepthλcanbedeterminedfromµSR
sition range. However, all µSR data appear to exclude
transverse-fieldexperimentsbymonitoringthedepolariza-
any microscopic coexistence between both ground states,
tion of the µSR signal arising from the dephasing created
which are therefore spatially separated, with a magnetic
by the flux-line lattice. The temperature dependence of
order exhibiting a rather large correlationlength >100˚A.
thesuperconductingdensityn ,whichisdirectlyrelatedto
s
Early measurements by Aczel et al. [5] suggest that up to
the penetration depth (see Eq. 7), provides indications on
80% of the volume of a x = 0.45 single-crystalline sam- the topology of the superconducting gap. Such technique
∼
ple maintain a magnetic ground state and that supercon-
hasbeenwidelyusedtocharacterizedthesuperconducting
ductivity is limited to the microscopically separated non-
state of cuprates (see for example [40]) and has also lead
magnetic fraction. As for the “1111”family a shift froma
to the so-called Uemura universal scaling (“Uemura plot”
commensurate to an incommensurate magnetic structure
[41]) between the superconducting transition T and the
c
isevidencedbytheoccurrenceofaBesselratherthanaco-
superconducting carriers density. The BCS theory pre-
sine function to characterize the µSR spectra (see Eq. 8).
dicts that T is related to the energy scale of attractive
c
Goko et al. [13] report that for a x = 0.5 sample, i.e.
interaction, while only a weak and indirect dependence is
possessing a nominal optimal doping, the magnetic frac- expected on n . The observed scaling is taken as indica-
s
tion is still 50% at low temperature, i.e. well below the
tionthatthecondensationincupratesisrelatedtoaBose-
∼
superconducting transition temperature. Finally, Park et
Einstein condensation mechanism of pre-formed pairs. In
al. [37] state that in a x = 0.41 sample, the supercon-
view of the apparent similarities between cuprates and
ducting fraction is about 1/4 of the total volume, with
iron-based pnictides, much interest has been focused on
50% still occupied by the usual magnetic state and the
the characterization of the superconducting state by µSR
∼
rest presenting a so far unknown “disordered magnetic
on these latter systems.
phase” persisting up to room temperature. Such “hid-
Let us first discuss the specific information obtained
den” order, which cannot be explained by impurities of by the temperature dependence of the penetration depth.
Fe As phase, is tentatively ascribed to the presence of
2 Forthe“1111”family,themostcompletepicturehasbeen
a weakly temperature-dependent density-wave-like order
obtained on the La-based systems [42, 29]. Here again,
observed by ARPES technique in the very same sample
the absence of 4f magnetic contribution at low tempera-
[38]. As for the previous measurements, one observes a
turesprovidesacleareranswerthaninrare-earthanalogs.
gradualincrease of the magnetic fraction below T rather
N In anisotropicsuperconductors like “1111”family [43] the
than a sharp phase transition as in the undoped sample
muon depolarization rate can be converted into λ , the
ab
[5, 13, 14, 12]. Note that for the last study, XRPD data
7
in-plane magnetic penetration depth, and Eq. 7 becomes
[2]:
FeSe
λ−2 = σ ns . (9) 6 0.85
ab 0.0355Φ γ ∝ m∗
0 µ
)
Luetkens et al. [42, 29] found that λ−2 follows, for x be- -2 m
ab (cid:181) 4
tween 0.05 and 0.10, a nearly temperature independent (
behavior below T /3 indicative of a low density of states -2 ab
c
inthe superconductinggap. Whereasthe temperaturede-
pendence couldbe compatiblewithaconventionalBCSs- 2
wavegap,thefielddependenceofλ−2 pointstothe occur- s-wave
ab
rence of a dirty d-wave gap or a multi-gap superconduct-
s+s wave
ing state. This later possibility is backed, for example, by
0
high-field measurements [44] and recent NQR results [45]. 0 2 4 6 8 10
Moreover, the clear concave curvature of λ−ab2 for higher T (K)
x-concentrationnearTc [29]appearsalsoasasignatureof Figure4: Temperaturedependenceofλ2abobtainedonFeSe0.85 from
multi-band effects (see for example [46]). A similar con- thedepolarizationrateoftheµSRsignal. Thecurvesrepresentsfits
clusion was obtained by Takeshita et al. on a x = 0.06 assumingasingles-wavegap symmetry (dashed line)and adouble
sample [47]. s-wavegap(solidline). AdaptedfromRef.[16].
The presence of multi-gaps as a common feature
among iron-based layered systems is also supported by
gap with ∆ = 8.35(6) meV, or double-gap structure with
the reported µSR measurements performed on the “122”
∆ =12 meV and ∆ =6.8(3) meV.
1 2
Ba1−xKxFe2As2. The clearest two-gap signature is fur- The observation of possible multi-gap features on the
nished by the measurements of Khasanov et al. [48]. On
temperaturedependenceofn isin-linewithARPESstud-
s
a single-crystal with T = 32 K, they report the exper-
c ies consistent with the fact that superconductivity occurs
iments performed in an external magnetic fields applied
oncomplex Fermisurfaces consistingof manybands, that
in parallel and perpendicularly to the crystallographic c-
would give rise to a intricate temperature dependence of
axis, allowingthem to separatethe in-plane (λ ) andthe
ab the density of superconducting carriers. In addition, the
out-of-plane (λ ) components of penetration depth λ and
c observeddependence of the gap values as a function of T
c
to reconstruct its anisotropy γ = λ /λ . Note that the
λ c ab is fully compatible with different ARPES studies [49, 50].
anisotropyforthe “122”familyisaboutoneorderofmag-
Concerning the temperature dependence of n mea-
s
nitude lower than for “1111” systems. From the temper-
suredby µSR,andforcompleteness,oneshouldalsomen-
ature dependence of λ−2, and the observation of a clear
ab tioned the measurements on the “011” family [16], on the
inflection point at T = 7 K, they deduce a multi-gap
oxygen-freefluoropnictides[18]andontheLiFeAs(“111”)
behavior with zero-temperature values of the gaps esti-
system[51]. Forthe “011”systemFeSe ,clearevidence
0.85
mated to be ∆ = 9 meV and ∆ = 1.5 meV. The tem-
1 2 for nodeless superconductivity was reported. Here again,
perature behavior of the anisotropywas found to increase
thecurvatureobservedinn (T)pointstotheoccurrenceof
s
upon decreasing temperature from γ = 1.1 at T to 1.9
λ c twogapsofs-wavecharacter,orpossiblytothepresenceof
at T 1.7 K. This resembles very much the situation
ananisotropics-wavegap[16](see Fig.4). Measurements
≃
in double-gap MgB where the anisotropy of the penetra-
2 performed on CaFe1−xCoxAsF for x = 0.075 and 0.150
tion depth was found to be equal to the anisotropy of the
show that also in the fluoropnictides the T-dependence of
critical fields at T , but has an opposite temperature de-
c n cannotbe reproducedby a singles-waveBCSgap, but
s
pendence.
require an approach invoking at least a two-gap model
OthermeasurementsonBa1−xKxFe2As2 systems were [18]. Finally, for the “111” system LiFeAs, which is a
reported in Reference [5] and [39]. Whereas the measure-
newvariantofiron-basedlayeredsuperconductorswithout
ments by Aczel et al. [5] on a T 30 K do not allow a
c lanthanide-oxidelayer,againn (T)cannotbedescribedby
reliable detailed study of the T-de≃pendence of n λ−2, s
s a simple s-waveBCS model as n increases monotonically
∝ s
due to the strongly reduced superconducting volume frac-
upon cooling below T [51].
c
tion, they clearly point to the absence of points or nodes
In Fig. 5, we report the µSR data available to date
on the superconducting gap(s). A clearer picture was ob-
for iron-based layer systems on a “Uemura” plot. As dis-
tained on a T 38 K sample by Hiraishi et al. [39],
c cussed above, the extracted penetration-depth parameter
where ns λ−2 w≃asfound below 0.4Tc to be mostly inde- λ2 is directly proportional to the supercarriers density
∝ ab
pendentoftemperature,confirmingthenodelesscharacter
n . Although no perfect single scaling is observed, one
s
of the superconducting gaps. Hence, Hiraishi et al. re-
can tentatively extract the following trends. The “1111”
portedthatthe temperaturedependence ofn isperfectly
s and “122” families are found to follow rather closely the
reproduced by the conventional BCS model for s wave
scaling observed for hole-doped cuprates. For the “111”
−
paring, where the order parameter can be either a single-
8
is common. Hence fundamental differences remain, as the
100
possibility to induce superconductivity in the Fe layersby
substitutingCoorNiionsdirectlyintotheFesites. Thisis
80 LaFeAsO1-xFx in deepcontrastwith the caseofcuprates,where the dop-
NdFeAsO1-xFx ing with Zn ions with one extra electron into Cu sites de-
60 FeSe1-x stroys superconductivity. Also, at least in the “122” fam-
K) SmFeAsO1-xFx ily, the antiferromagnetic order of the parent compound
(
T c CeFeAsO1-xFx XFe2As2 can be destroyed by external pressure, which in-
40 duces superconductivity without external doping. Such
LiFeAs
effect which is not present for cuprates stresses the role of
CaFe1-xCoxAsF
thestructuralparameterasakeyfactorfortheoccurrence
20 Ba1-xKxFe2As2
of high temperature superconductivity.
0
0 20 40 60 80 6. Conclusions
-2 -2
ab ((cid:181)m ) Asforthecupratesystems,theµSRtechniquehasvery
Figure 5: Uemura plot for the iron-based layered systems with quicklyprovidedvaluableinformationonthe groundstate
some of data obtained to date. The scalings observed for the high- propertiesofthesenewhigh-T superconductors. Thespe-
c
Tc cuprates is provided for comparison (solid line for hole doping; cific advantages of the technique were exploited in partic-
dashedlineforelectrondoping). LaFeAsO1−xFxdatafromRef.[29]
ular to disentangle the interplay between magnetism and
–Notethe“boomerang”behavioruponincreasingthefluorinedop-
ing(curved arrow); SmFeAsO1−xFx data from Ref.[6](green) and superconductivity,connectedtogroundstateswithalmost
[33](red);NdFeAsO1−xFxtakenfromRef.[4](green)and[33](red); degenerate condensation energies. In particular, and in
LiFeAs takenfromRef.[51];CaFe1−xCoxAsFtaken fromRef.[18]; almost all cases, one does not observe a microscopic co-
Ba1−xKxFe2As2takenfromRef.[13](green)and[48](red);FeSe1−x
existence of both phases, as in the cuprates, but rather
taken fromRef.[16].
a mesoscopic phase separation. However, the systems
SmFeAsO1−xFx seem to represent an exception as µSR
family, one seems to observe lower values than the trend data point to a microscopic coexistence of both phases.
line of the other systems. As pointed out by Pratt et al. Thecloseconnectionbetweenthestructuraltransitionand
[51], two lines of thoughts can obviously be invoked to magnetism has been clearly evidenced by µSR in partic-
explain such deviation. Either such systems possess su- ular on LaFeAsO1−xFx systems. Moreover a scaling be-
percarriers densities that are enhanced over the expected tweenT andthesuperconductingcarriersdensity,similar
c
values on the basis of their Tc’s, or, alternatively, super- to the one observed on cuprates, appears also to occur in
conductivity is somehow suppress on those systems. Such the iron-basedlayeredpnictides. Itremainshowevertobe
reduction could be linked to crystal structure considera- seen whether such scaling has a similar origin.
tions. For all the families, the superexchange between Fe
atoms through As is thought to provide the main contri-
References
bution to the exchange interaction [52] and therefore one
expectadependenceoftheelectronicpropertiesonthean- [1] Y.Kamiharaet al.,J.Am.Chem.Soc.130,3296(2008).
gle between two legs of the tetrahedron formed by the As [2] E.H.Brandt,Phys.Rev.B37,2349(1988).
ions around the iron ions. Hence, one observe a clear de- [3] H.-H.Klausset al.,Phys.Rev.Lett. 101,077005(2008).
[4] J.P.Carloet al.,arXiv:0805.2186v1.
creaseof this angle (and thereforeshortening ofthe As-Fe
[5] A.A.Aczelet al.,Phys.Rev.B78,214503(2008).
distance) going from the “1111”, through the “122” (pre- [6] A.J. Drew et al., arXiv:0807.4876 and Nature Materials, in
sentingalmostregularAstetrahedra)andto“111”family. press.
Roughly speaking, it is expected that a weaker Fe-As hy- [7] C.delaCruzet al.,Nature453,899(2008).
[8] T.Nomuraet al.,Supercond.Sci.Technol. 21,125028(2008).
bridizationcausesadecreaseoftheconductionbandwidth,
[9] M.Rotter et al.,Phys.Rev.B78,020503(R) (2008).
accompaniedby an increasein the density of states atthe [10] Q.Huanget al.,Phys.Rev.Lett. 101,257003(2008).
Fermi level N(E ) and the occurrence or strengthening [11] C.Krellneret al.,Phys.Rev.B78,100504(R) (2008).
F
of the superconducting state. Within a family, it is sug- [12] A.Jescheet al.,Phys.Rev.B78,180504(R) (2008).
[13] Y.J.Gokoet al.,arXiv:0808.1425v1.
gestedthatanydeviationfromthe regularAstetrahedron
[14] Y.J.Uemuraet al.,arXiv:0811.1546v1.
isdetrimentalforsuperconductivity[53]. Forexample,for [15] F.C.Hsuet al.,Pro.Natl.Acad.Sci.USA105,14262(2008).
the LaFeAsO1−xFx, a so-called boomerang effect is ob- [16] R.Khasanovet al.,Phys.Rev.B78,220510(2008).
served for high fluorine concentration. [17] P.J.Bakeretal.,arXiv:0811.4598v1andPhys.Rev.B,inpress.
[18] S.Takeshitaet al.,arXiv:0812.1670v2.
AlthoughthesimilaritiesbetweentheUemuraplotsfor
[19] G.Wuet al.,arXiv:0811.0761v2.
cuprates and iron-based layer superconductors are appar- [20] M.Tegelet al.,Europhys.Lett.84,67007(2008).
ently striking, it remains to be seen whether the under- [21] Y.Xiaoet al.,arXiv:0811.4418v2.
[22] P.J.Bakeret al.,PhysicalReviewB78,212501(2008).
laying mechanism to promote the superconducting state
[23] K.Selteet al.,ActaChem.Scand. 26,3101(1972).
9
[24] M.Yuzuriet al.,J.Phys.Soc.Jpn.48,1937(1980).
[25] See for example: C. Niedermayer et al., Phys. Rev. Lett. 80,
3843(1998).
[26] J.Majoret al.,HyperfineInteract. 31,259(1986).
[27] A.T.Saviciet al.,Phys.Rev.B66,014524(2002).
[28] T.A.Maieret al.,arXiv:0805.0316v1.
[29] H.Luetkensetal.,arXiv:0806.3533v1andNatureMaterials,in
press.
[30] J.Zhaoetal.,NatureMaterials7,953(2008).
[31] P.DaiandY.J.Uemura,privatecommunication,unpublished.
[32] A.J.Drewet al.,Phys.Rev.Lett. 101,097010(2008).
[33] R.Khasanovet al.,Phys.Rev.B78,092506(2008).
[34] M.Katoet al.,J.Phys.Soc.Jpn57,726(1988).
[35] P.J.Bakeretal.,arXiv:0811.2494v1andNewJ.Phys.,inpress.
[36] H.Chenet al.,Europhys.Lett. 85,17006(2009).
[37] J.T.Parket al.,arXiv:0811.2224v1.
[38] V.B.Zabolotnyy et al.,arXiv:0808.2454v1.
[39] M.Hiraishiet al.,arXiv:0812.2069v2.
[40] J.E.Sonieret al.,Rev.ModernPhys.72,769(2000).
[41] Y.J.Uemuraet al.,Phys.Rev.Lett.66,2661(2008).
[42] H.Luetkens et al.,Phys.Rev.Lett.101,097009 (2008).
[43] S.Weyeneth et al.,arXiv:0811.4047v2.
[44] F.Hunteet al.,Nature453,903(2008).
[45] S.Kawasakiet al.,Phys.Rev.B78,220506(R) (2008).
[46] R.Khasanovet al.,Phys.Rev.Lett. 99,237601(2007).
[47] S.Takeshitaet al.,J.Phys.Soc.Jpn.77,103703(2008).
[48] R.Khasanovet al.,arXiv:0901.2329v1.
[49] D.V.Evtushinsky et al., arXiv:0809.4455v1and Phys. Rev. B,
inpress.
[50] H.Dinget al.,Europhys.Lett. 83,47001(2008).
[51] F.L.Prattet al.,arXiv:0810.0973v1.
[52] T.Yildirim,Phys.Rev.Lett.101,057010 (2008).
[53] C.H.Leeet al.,J.Phys.Soc.Jpn.77,083704(2008).
10