Multiple superconducting gap and anisotropic spin fluctuations in iron arsenides: Comparison with nickel analog

0.42 MB·English

by  Z. Li

Multiple superconducting gap and anisotropic spin fluctuations in iron arsenides:
Comparison with nickel analog
Z.Lia,S.Kawasakib,T.Okab,T.Tabuchib,Y.Ooeb,M.Ichiokab,Z.A.Rena,Z.X.Zhaoa,J.L.Luoa,N.L.Wanga,X.C.Wanga,
Q.Q.Liua,C.Q.Jina,C.T.Linc,Guo-qingZhenga,b
aInstituteofPhysicsandBeijingNationalLabforCondensedMatterPhysics,ChineseAcademyofScience,Beijing,100190,China
bDepartmentofPhysics,OkayamaUniversity,Okayama700-8530,Japan
cMaxPlanckInstitute,Heisenbergstrasse1,D-70569Stuttgart,Germany
1
1
0
2

nAbstract
a
JWe present extensive 75As NMR and NQR data on the superconductingarsenides PrFeAs0.89F0.11 (Tc=45 K), LaFeAsO0.92F0.08
6 (Tc=27 K), LiFeAs (Tc = 17 K) and Ba0.72K0.28Fe2As2 (Tc = 31.5 K) single crystal, and compare with the nickel analog
2LaNiAsO F (T =4.0 K) . In contrast to LaNiAsO F where the superconducting gap is shown to be isotropic, the spin
0.9 0.1 c 0.9 0.1
lattice relaxation rate 1/T in the Fe-arsenides decreases below T with no coherence peak and shows a step-wise variation at
1 c
]
low temperatures. The Knight shift decreases below T and shows a step-wise T variation as well. These results indicate spin-
n c
osinglet superconductivitywith multiple gaps in the Fe-arsenides. The Fe antiferromagneticspin fluctuationsare anisotropicand
cweakercomparedtounderdopedcopper-oxidesorcobalt-oxidesuperconductors,whilethereisnosignificantelectroncorrelations
-
rinLaNiAsO0.9F0.1. WewilldiscusstheimplicationsoftheseresultsandhighlighttheimportanceoftheFermisurfacetopology.
p
uKeywords: superconductivity,ironarsenide,nickelarsenide,NMR
s
.
t
a
1. Introduction 2. Experiments
m
- The preparation of the samples of PrFeAs F
d 0.89 0.11
n (Tc=45 K), LaFeAsO0.92F0.08 (Tc=23 K), LiFeAs(Tc =
o 17 K), LaNiAsO F (T = 4.0 K), and single crystal
0.9 0.1 c
[catTthheetrreacnesnittiodnistceomvepreyraotfurseupTecrc=on2d6uKcti[v1it]yhiansLaattFreaActseOd1g−rxeFaxt B[5a,06.7,2K4,07.2,8F8e].2ANsQ2R(Tancd=NM31R.5mKea)suarreempenutbsliwsheeredcealrsreiewdhoeruet
1attention. Soonaftertheinitialwork,T wasraisedto55Kin by using a phase coherent spectrometer. The NMR spectra
c
vSmFeAsO F [2], which is the highest among materials ex- weretakenbysweepingthemagneticfieldatafixedfrequency.
1 x x
14ceptcuprate−s. Thesecompoundshavea ZrCuSiAstype struc- The spin-latticerelaxationrate 1/T1 wasmeasuredby usinga
ture (P4/nmm) in which FeAs forms a two-dimensional net- singlesaturationpulse.
0
5work similar to the CuO2 plane in the cuprates case. By re-
.placing O with F, electrons are doped. After the discoveryof
1 3. ResultsandDiscussion
0ReFeAsO (Re: rare earth, so-called 1111 compound), several
1otherFe-pnictideshavebeenfoundtosuperconduct.BaFe2As2 3.1. Knightshift
1(so-called 122 compound) has a ThCr Si -type structure. By
2 2 Figure 1 shows the temperature dependence of the Knight
:
vreplacingBawithK,holesaredopedandTc canbeashighas shiftforPrFeAs F (T =45K)withthemagneticfield(H)
i38K[3]. Anotherarsenide,LiFeAs(so-called111compound) 0.89 0.11 c
X applied along the ab-direction [9]. The shift decreases below
which has Cu Sb type tetragonal structure, was discovered to
2 T and goes to zero at the T=0 limit. The Knight shift of
arshowsuperconductivityeveninstoichiometriccomposition[4]. Bca K Fe As with H parallel to the c-axis [10] also de-
Thecommonfeatureofthesethreesystemsaretheironarsenide 0.72 0.28 2 2
creases below T , as seen in Fig. 2. The behavior is quite
planewhichdominatesthepropertiesofthesecompoundsand c
similartothePrFeAs F case. Theseresultsindicatespin-
hoststhesuperconductivity. 0.89 0.11
singletsuperconductivity.
We have used nuclear magnetic resonance (NMR) and nu- However,the detailedT variationof theKnightshift isdif-
clearquadrupoleresonance(NQR)techniquestostudythepair- ferentfromthatseeninusualspin-singletsuperconductorssuch
ingsymmetryandspinfluctuationsinthenormalstate. Wefind ascopper-oxides,whereKdecreasesrapidlybelowT whichis
c
thatthesesupercondutorsareinthespin-singletstatewithmul- followedbyamilderdecreaseatlowtemperatures,asillustrated
tiple gaps, and the latter property is quite different from the bythebrokencurveinFig. 1. Incontrast, thedecreaseofthe
cupratecase. Theantiferromagneticspinfluctuationisweaker Knightshiftshowsastep-wisebehavioratatemperatureabout
thanthecupratesandareanisotropicinthespinspace. halftheT .
c
PreprintsubmittedtoJournalofPhysicsandChemistryofSolids January27,2011
0.4
%) 0.3
hift ( T
S c
ght 0.2 PrFeAsO F
ni 0.89 0.11
K H//ab
experiment
0.1
two-gap fit
one-gap fit
10 20 30 40 50 60 70 80
Temperature (K)
Figure 1: (color online) The temperature variation of 75As Knight shift of
PrFeAs0.89F0.11 withH ab. Thesolidcurveisafittingoftwod-wavegaps
k
with∆1(T = 0) = 3.5kBTC andarelative weightof0.4, and∆2(T = 0) =
1.1kBTCwitharelativeweightof0.6(seetext). ThebrokencurvebelowTcis
asimulationforthelargergapalone.
Figure3:(coloronline)Thetemperaturedependenceof19Fspin-latticerelax-
0.3 ationrate1/T1inPrFeAs0.89F0.11measuredatµ0H=1.375T.Thebrokenline
indicatesarelationofT1T =constwhichholdsforaweaklycorrelatedelectron
%) system.ThethinstraightlineillustratesthetemperaturedependenceofT3
(0.2
c
K
a”concave”shapeofT-variation.
Wefindthatatwo-gapmodelcanreproducethestep-wiseT
0.1
variationof1/T andtheKnightshift. Theunderlyingphysics
1
is that the system is dominantly governed by a larger gap for
0 T near Tc while at sufficiently low T it starts to ”notice” the
0 10 20 30 40 50 existence of a smaller gap, resulting in another drop in 1/T
1
T (K) belowT Tc/2. Inthed-wavecasewithtwogaps,wherethe
∼
densityofstates(DOS)isN (E)=N E ,theKnightshift
Faxigisu.reT2h:e(acrorloowroinnldinicea)teTsheTcK.nTighhetcsuhrifvtedbatealoowfBTac0.i7s2Ka0fi.2t8tFoea2Atws2o-wgiatphmHokdce-l and1/T1sinthesupercondus,citingstat0e,ia√reE2w−∆r2iittenas
(seetext).
K ∂f(E)
s = N (E) dE (1)
K Z s ∂E
N
3.2. T inthesuperconductingstate
1
The step-wise decrease of the Knight shift is also reflected T1N = 2 N (E)N (E )
in the temperature dependence of the 19F spin-lattice relax- T1s XkBT Z Z s,i s,i ′
ationrate1/T [9],andisalsoseeninLaFeAsO F (T =23
1 0.92 0.08 c
K)[11]andthehole-dopedBa0.72K0.28Fe2As2(Tc=31.5K)[10]. f(E) 1 f(E′) δ(E E′)dEdE′ (2)
Figure3showsthetemperaturedependenceof1/T measured − −
1 (cid:2) (cid:3)
by19FNMRinPrFeAs F (T =45K),andFig. 4shows where f(E)istheFermidistributionfunction. Wefindthatthe
0.89 0.11 c
thetemperaturedependenceof1/T1measuredby75AsNQRin parameters2∆1(0) = 7.0kBTc, 2∆2(0) = 2.2kBTc and κ = 0.4
LaFeAsO0.92F0.08 (Tc=23K). Below Tc, thereis nocoherence canfit thedata ofboththeshiftand1/T1 verywell, asshown
peak for both samples. Moreover, a bending feature is seen bythesolidcurvesinFig. 1andFig. 3,where
around T T /2 [9, 11]. This behavior is not expected in a
single-gap∼supecrconductor. κ= N0,1 (3)
N +N
Figure 5 shows the temperature dependence of 1/T mea- 0,1 0,2
1
sured by75As NMR with the magneticfield appliedalongthe is the relative DOS of the band(s) with larger gap to the total
c-axis in Ba K Fe As (T = 31.5 K) single crystal [10]. DOS.
0.72 0.28 2 2 c
1/T also shows a ”knee”-shape around T T /2. Namely, Application of the same model to LaFeAsO F gives
1 c 0.92 0.08
∼
the sharp drop of 1/T just below T is gradually replaced by 2∆ (0)= 8.4k T ,2∆ (0)= 3.2k T ,andκ = 0.6[11]. Onthe
1 c 1 B c 2 B c
a slower change below T 15 K, then followed by another otherhand,forBa K Fe As ,2∆ (0)=9.0k T ,2∆ (0)=
0.72 0.28 2 2 1 B c 2
∼
steeper drop below. This ”convex” shape is clearly different 1.62k T ,andκ=0.69wasobtained[10]. Thesamemodelcan
B c
fromthecaseofsuperconductorswithasinglegapwhichshows alsofittheKnightshiftdata,asseeninFig. 2.
2
10
100 T
c
Tc
10
)
1
1 -c
e
1 ) (s
- c 1
e T
(s 1/ 1 Ba0.72K0.28Fe2As2
T1
H//c
/

1 two-gap d-wave
two-gap s(+-) with impurity
0.1
0.1
LaFeAsO0.92F0.08
75 10 100
As-NQR
T (K)
d-wave
(2 gap fit)
0.01
–s-wave Figure 5: (color online) T-dependence of 1/T1 in Ba0.72K0.28Fe2As2. The
(Bang et al.) curvesbelowTc(indicatedbythearrow)arefitstotwo-gapmodels(seetext).
10 100
wavemodelshowsthatthegapvalueofLiFeAsissmallerthan
Temperature (K)
other compounds, but the impurity scattering is much larger
Figure4: (coloronline)75As(1/T1)inLaFeAsO0.92F0.08. Thesolidcurveis
atwogapfitassumingad-wavesymmetrywithparameters,∆1(0)=4.2kBTc, (η = 0.26kBTc) [16]. The gap parameters for all Fe-arsenide
∆2(0)=1.6kBTc,andκ =0.6(seetext). Thedottedcurveisasimulationas- samples are summarized in Tab. 1. To summarize, the multi-
sumingtwos-wavegapsthatchangesignswithparameters,∆1(0)=3.75kBTc, ple gap featureis universalto all Fe-arsenids, which probably
∆2(0)=1.5kBTc,andκ=0.38. associatedwiththemultipleelectronicbands[18].
By strong contrast, the nickel analog of LaFeAsO F ,
1 x x
For the case of s±-gap [12, 13], recent calculations have namely,LaNiAsO0.9F0.1 hasdifferentbehavior.[19]Asse−enin
shown that scattering between the differentbands may reduce Fig. 7, 1/T shows a well-defined coherence peak just below
1
thecoherencepeakjustbelowTc [14,15]. FollowingRef.[15], Tc,whichisafingerprintofsuperconductorswithanisotropic
wecalculated1/T1forthes±-gapmodel,byintroducingtheim- gap. Thisis insharpcontrastto variousFe-arsenidesreported
purityscatteringparameterηintheenergyspectrum,E =ω+iη. so far[9, 11, 10, 20, 21, 22]. At low temperatures, 1/T de-
1
Theparameters2∆1(0)= 7.5kBTc,2∆2(0)= 3.0kBTc,κ = 0.38 creasesasanexponentialfunctionofT.ThesolidcurvesinFig.
andη=0.15kBTc,canwellfitthedata,asshowninFig.4.where 7arecalculationsusingtheBCSmodel.FollowingHebel[23],
weconvoluteN (E)withabroadeningfunction B(E)whichis
πn (N +N )V2 s
η= imp 1 2 (4) approximatedwitharectangularfunctioncenteredat E witha
1+π2(N +N )2V2
1 2 heightof 1/2δ. The solid curvesbelow T shown in Fig. 7 is
c
In the equation, nimp is the impurity concentration and V is calculationwith2∆(0) = 3.2kBTc andr ≡ ∆(0)/δ=5. SuchT-
the scattering potential at the impurity. A similar set of pa- dependenceof 1/T1 in the superconductingstate is in striking
rameters(2∆ (0) = 7.2k T , 2∆ (0) = 1.68k T , κ = 0.6 and contrast to that for Fe-arsenide where no coherence peak was
1 B c 2 B c
η=0.22k T )canfitthedataofBa K Fe As ,seeFig. 5. observedandtheT-dependenceatlow-T doesnotshowanex-
B c 0.72 0.28 2 2
The results for LiFeAs[16] (Fig. 6) are shown in Fig. 6. ponentialbehavior. Thestrikingdifferencemaybeascribedto
We measuredtwoLi FeAssampleswithnominal x = 0.8and thedifferenttopologyoftheFermisurfaces.ForFe-arsenides,it
x
1.1. ThephysicalpropertiesincludingtheNMRresultsarethe hasbeenproposedthatd-wave[24,25]orsignreversals-wave
same. Thissupportsthatonlystoichiometriccompoundcanbe gap[12,13]canbestabilizedduetonestingbytheconnecting
formed.[17] 1/T1 below Tc shows a qualitatively similar be- wave vector Q = (π,0). In LaNiAsO0.9F0.1, however,there is
havior as the previous three samples, but the behavior at low nosuchFermisurfacenesting[26],andthusthemechanismfor
temperaturesis a little different. Namely, 1/T1 becomesto be the proposed gap symmetry does not exist. Given that the Tc
proportional to T below T Tc/4, which indicates that a fi- ismuchlowerinLaNiAsO1 xFx,ourresultsuggeststheimpor-
≤ −
niteDOSisinducedbytheimpurityscattering.Obviously,this tantroleoftheFermi-surfacetopologyinthesuperconductivity
would occur in a d-wave case. On the other hand, it is also ofFe-arsenides.
possible in the s case provided that the scattering between Finally,forcomparison,1/T normalizedbythevalueatT
± 1 c
theelectron-andhole-pocketisstrong. Calculationbythe s - areshowninFig. 8asafunctionofreducedtemperatureforall
±
3
Table1:Thegapparameters.κ=N1/(N1+N2),η= 1π+nπim2p(N(N11++NN22)2)VV22,wherenimpistheimpurityconcentrationandVisthescatteringpotentialattheimpurity.
d-wave s -wave
±
∆ /k T ∆ /k T κ ∆ /k T ∆ /k T κ η/k T
1 B c 2 B c 1 B c 2 B c B c
PrFeAsO F 3.5 1.1 0.4
0.89 0.11
LaFeAsO F 4.2 1.6 0.6 3.75 1.5 0.38 0.15
0.92 0.08
Ba K Fe As 4.5 0.81 0.69 3.6 0.84 0.6 0.22
0.72 0.28 2 2
LiFeAs 3.0 1.3 0.5 0.26
100 10
LaNiAsO F
T 0.9 0.1
c
75
As - NQR
~ T
10 1
1 ) Tc
-1 T (sec) 1 1 - 1 / T (s 1 0.1
1/
0.1 LixFeAs 0.01 experiment
s-wave fit
nominal x=0.8
(0) = 3.2 k T
B c
nominal x=1.1
0.001
0.01 s(+-)-wave 1 10
T (K)
1 10 100
Figure7: (coloronline)TheT dependenceofthespinlatticerelaxationrate,
T (K)
1/T1,forLaNiAsO0.9F0.1. ThearrowsindicateTc. Thebrokenstraightlines
Figure 6: (color online) The T-dependence of 1/T1 measured by NQR for showtherelation1/T1∝T,andthecurvesbelowTcarefitstotheBCSmodel
Li0.8FeAsandLi1.1FeAs. ThecurvesbelowTcarefitstothes±-wavemodel withthegapsizeindicatedinthefigure.
with∆+1 =3.0kBTc,∆−2 =1.3kBTc,andtheimpurityscatteringrateη=0.26
kBTc(seetext).
the increasing is very small. The 1/T T of stoichiometric
1
LiFeAs is almost constant. While 1/T T of LaNiAsO F
samples. 1 0.9 0.1
decrease with decreasing temperature. These results sug-
3.3. Normalstateproperties gest that the antiferromagnetic spin fluctuations are stronger
in Ba K Fe As and LaFeAsO F , but quite weak in
Next, we discuss on the character of spin fluctuations. 0.72 0.28 2 2 0.92 0.08
LiFeAs and LaNiAsO F . This difference may be under-
Figure 9 shows the temperature variation of 1/T T in 0.9 0.1
1
stoodbythedifferenceoftheFermisurfacetopology.Thereare
Ba K Fe As . Onenoticesthat,inthenormalstateabove
0.72 0.28 2 2
notonlyhole-pocketsandelectron-pocketsbutalsonestingbe-
T , 1/T T increaseswith decreasingT, whichisanindication
c 1
ofantiferromagneticelectroncorrelation,sincebothKaandKc tweentheminBa0.72K0.28Fe2As2 andLaFeAsO0.92F0.08 ,which
can promote spin fluctuations. While in LiFeAs there is no
slightlydecreasewithdecreasingT,butbecomesaconstantbe-
suchnesting,althoughtherearestillhole-pocketsandelectron-
lowT 70K[10],whichresemblescloselythecuprate[27]or
∼ pockets. Lackingofsuchnestingmakethespinfluctuationbe-
cobaltatecases[28].
comeweakerthanBa K Fe As andLaFeAsO F . In
Figure 10 compares 1/T T for four samples. The data 0.72 0.28 2 2 0.92 0.08
1
LaNiAsO F there is no hole-pockets, then nesting can not
for LaFeAsO F , LiFeAs, LaNiAsO F are measured 0.9 0.1
0.92 0.08 0.9 0.1
happen,thereforethespinfluctuationsarenotexpected.
by NQR, which correspond to H c-axis, since the princi-
ple axis of the NQR tensors is alokng the c-axis. The data Finally,wediscusstheanisotropyofthespinfluctuations.In
for Ba0.72K0.28Fe2As2 is measured by NMR with H c- ageneralform,1/T1T iswrittenas
k
axis. The 1/T T of hole-doped Ba K Fe As increase
1 0.72 0.28 2 2
1 πk γ2 χ (q,ω)
wdoitpheddeLcareFaesAinsgOt0e.9m2Fp0e.0r8atualrseoasshdoiwscussimseidlaarbboevhea.vTiohre,eallethcotruognh- T1T = (γeB~)n2 Xq A2hf ′⊥′ω , (5)
4
2.0
As
H//a
1
1.5
Fe
-1K) H//c Fe
1
-c 75As NMR in
e
T (s 1.0 H//a Ba1-xKxFe2As2
T 1 0.1 T1
)/ Tc 1/ H//c x=0.28
1 0.50
T
(
x=0
PrFeAsO0.89F0.11
LaFeAsO0.92F0.08 0.0
0.01 0 50 100 150 200 250 300
Ba0.72K0.28Fe2As2
T (K)
LiFeAs
LaNiAsO0.9F0.1
s-wave fit Figure 9: (color online) The quantity 75(1/T1T) in the normal state of
Ba0.72K0.28Fe2As2 (circles) andintheparamagnetic state ofBaFe2As2 (dia-
monds).Thearrowsintheinsetillustratethelargercomponentofthefluctuat-
0.001 ingfieldofFeandthatseenbytheAssite.
0.1 1
4. Conclusion
T/Tc
Figure 8: (color online) The normalized T-dependence of 1/T1 for In summary, we have presented the NMR and NQR results
PrFeAs0.89F0.11 (Tc=45K), LaFeAsO0.92F0.08 (Tc=23 K),Ba0.72K0.28Fe2As2
(Tc=31.5K).LiFeAs(Tc=17K),LaNiAsO0.9F0.1(Tc=4.0K). on the electron-doped Fe-arsenides PrFeAs0.89F0.11 (Tc = 45
K), LaFeAsO F (T = 23 K), stoichiometric LiFeAs(T
0.92 0.08 c c
=17K),andthehole-dopedFe-arsenideBa K Fe As (T
0.72 0.28 2 2 c
= 31.5 K). We find there are multiple gaps in iron arsenides
where Knightshift and 1/T does not follow a simple power-
1
lawnorexponentialfunction. However,the1/T oftheNickel
1
whereχ′′(q,ω)istheimaginarypartofthedynamicalsuscepti- analog LaNiAsO0.9F0.1 shows a well-defined coherence peak
bilitype⊥rpendiculartotheappliedfield. Theanisotropicratioin just below Tc and an exponential behavior at lower tempera-
theformof qAchf(q)2χ′c′(q) forBa K Fe As andparentcom- tures. These properties indicate that it is a conventionalBCS
PqAahf(q)2χ′a′(q) 0.72 0.28 2 2 superconductor. The difference between the Fe-arsenides and
pound are sPhown in Fig.11. The larger magnitude of 1/T T
1 theNi-analogmaybeunderstoodbythediffereneoftheFermi
along the a-axis direction than that along the c-axis direction
surfacetopology,andthereforehighlightstheimportantroleof
indicates that there are stronger fluctuations along the c-axis
theFermi-surfacetopologyinpairingsymmetryoftheironar-
direction seen by the As-site. Neutronexperimentfoundthat,
senidessuperconductors.
intheundopedBaFe As compound,theorderedFemagnetic
2 2 In the normalstate, all iron arsenides show weak antiferro-
momentisalongthea-directionandformsastripe[29]. Since
magneticspincorrelations. Ourdataalsoshowthatthesample
the As atom sits in the position above (below) the middle of
withweakercorrelationshasalowerT ,andthismayimplythe
c
fourFe-atoms,ourresultimpliesthat,intheFesite,astronger
T hasarelationshipwiththestructureofFermisurface.More-
c
fluctuatingfieldsexistalongthea-axisdirection,asillustrated
over,thespinfluctuationsareanisotropicinspinspace,which
intheinsetofFig.9.Itisremarkablethattheantiferromagnetic
isdifferentfromcuprates.
fluctuationsofFeareanisotropicinspinspace. Namely,χ (Q)
′′ WegratefullyacknowledgethesupportfromCAS,National
ismuchlargerthanχ (Q),wherezisalongthec-axisdirec±tion
′z′z ScienceFoundationofChina,JSPSandMEXTofJapan.
and Q is the spin fluctuation wave vector. This is in contrast
tothehigh-T cuprateswherethespinfluctuationsarebelieved
c
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LiFeAs
LaNiAsO F
0.9 0.1
1
T
1
T
1/
0.5
0
0 50 100 150 200 250
T
Figure 10: (color online) TheT-dependence of1/T1T forLaFeAsO0.92F0.08
(Tc=23 K),Ba0.72K0.28Fe2As2 (Tc = 31.5 K), LiFeAs(Tc = 17 K),
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T
N
ac T)-(1/TT)/21 c 1/TT)/2122..05 TC BaFe2As2 45 qcq"(q) /
T1 ( a"
1/ (q
( )
1.5 Ba K FeAs 3
0.72 0.28 2 2
1.0 2
0 50 100 150 200 250 300
T (K)
Figure11:(coloronline)TheTdependenceoftheanisotropyofthespinfluctu-
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PqAahf(q)2χ′a′(q) Pqχ′a′(q)
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