arX

iv:1

106.

2829

v1 [

cond

-mat

.sup

r-co

n] 1

4 Ju

n 20

11

Multi-band superconductivity in LaFeAsO0.9F0.1 single crystals probed by high-field

vortex torque magnetometry

G. Li,1 G. Grissonanche,1 A. Gurevich,1 N. D. Zhigadlo,2 S. Katrych,2 Z. Bukowski,2 J. Karpinski,2 and L. Balicas1, ∗

1National High Magnetic Field Laboratory, Florida State University, Tallahassee-FL 32310, USA2Laboratory for Solid State Physics, ETH Zurich, CH-8093 Zurich, Switzerland

(Dated: June 16, 2011)

To probe manifestations of multiband superconductivity in oxypnictides, we measured the angulardependence of the magnetic torque τ (θ) in the mixed state of LaO0.9F0.1FeAs single crystals as afunction of temperature T and magnetic fieldsH up to 18 T. The paramagnetic contribution of the Feions is properly treated in order to extract the effective mass anisotropy parameter γ = (mc/mab)

1/2

from τ (θ). We show that γ depends strongly on both T and H , reaching a maximum value of ∼ 10followed by a decrease towards values close to 1 as T is lowered. The observed field dependencies ofthe London penetration depth λab and γ suggest the onset of suppression of a superconducing gapat H ≈ Hc2/3.

PACS numbers: 74.25.-q, 74.25.Ha, 74.25.Op, 74.70.Dd

I. INTRODUCTION

The recently discovered superconductingoxypnictides1,2 have similarities with the high Tc

cuprates, such as the emergence of superconductivityupon doping a parent antiferromagnetic compound.2–4

Theoretical models5 suggest unconventional s± pairing,consistent with Andreev spectroscopy,6 penetrationdepth,7 and photoemission measurements8 which in-dicate nodless s-wave pairing symmetry. Experimentsat high magnetic fields,8–10 penetration depth7,11,13

and heat capacity measurements,12 are consistent withmultiband s± scenarion5 Other models suggest animportant role for electronic correlations,14 and even apossibility of unconventional pairing mechanisms.15

The comparatively high critical temperatures Tc

and extremely high upper critical fields Hc2 of theoxypnictides9,16 indicate their promising prospects forapplications if, unlike the layered cuprates, a sizeable vor-tex liquid region does not dominate their temperature-magnetic field (T − H) phase diagram. It is thereforeimportant to reveal the true behavior of the anisotropicmagnetization in the vortex state of the oxypnictides,particularly the extent to which vortex properties are af-fected by strong magnetic correlations and multiband ef-fects. For instance, multiband effects in MgB2 can mani-fest themselves in strong temperature and field depen-dencies for the mass anisotropy parameter γ(T,H) =(mc/mab)

1/2 and the London penetration depth λ(T,H)even at H ≪ Hc2.

17,18 Similar effects in pnictides wouldbe consistent with the multiband pairing scenarios.5 Yet,there are significant differences between two-band super-conductivity in MgB2 and in oxypnictides: in MgB2 theinterband coupling is weak, while in the oxypnictides it isthe strong interband coupling which is expected to resultin the high Tc.

5 Thus, probing multiband superconduc-tivity in oxypnictides by magnetization measurementsrequires high magnetic fields, which can suppress thesuperfluid densities in both bands by circulating vortex

currents. In this work we address these issues, present-ing high-field torque measurements of the anisotropic re-versible magnetization in LaFeAsO0.9F0.1 single crystals.Our measurements of γ(T,H) up to 18T and extendedtemperature range, 4 < T < 15 K reveals a different be-havior in γ(T,H) as compared to recent low-field torquemeasurements.10 Ref. 10 shows a γ that increases con-tinuously as T is lowered reaching a maximum value of∼ 20 for both NdFeAsO0.8F0.2 and SmFeAsO0.8F0.2 sin-gle crystals. In contrast, our results indicate that γ inLaFeAsO0.9F0.1 reaches a maximum of ∼ 10 decreasingasymptotically towards 1 as T is lowered.Measurements of the equilibrium magnetization

m(T,H) of the vortex lattice in LaO0.9F0.1FeAs are com-plicated by the smallness of m(T,H) caused by the largeGinzburg-Landau parameter, κ = λ/ξ > 100 and bythe background paramagnetism of the normal state,19

which can mask the true behavior of m(T,H). In thiscase torque magnetometry is the most sensitive techniqueto measure the fundamental anisotropy of the param-

eters of −→m(T,−→H ) in small single crystals. The torque

−→τ = µ0−→m ×−→

H acting upon a uniaxial superconductor isgiven by

τ(θ) =HV φ0(γ

2 − 1) sin 2θ

16πµ0λ2abγ

1/3ε(θ)ln

[

ηHabc2

ε(θ)H

]

+τm sin 2θ, (1)

where V is the sample volume, φ0 is the flux quan-tum, Hab

c2 is the upper critical field along the ab planes,η ∼ 1 accounts for the structure of the vortex core, θ

is the angle between−→H and the c-axis, ε(θ) = (sin2 θ +

γ2 cos2 θ)1/2 and γ = λc/λab is the ratio of the Londonpenetration depths along the c-axis and the ab-plane.The first term in Eq. (1) was derived by Kogan in theLondon approximation valid at Hc1 ≪ H ≪ Hc2,

20 whilethe last term describes the torque due to the backgroundparamagnetism, for which τm = µ0(χc − χa)V H2/2 andχc and χa are the normal state magnetic susceptibilitiesalong the c-axis and ab- plane, respectively. In general,

γ = (mc/mab)1/2 6= λc/λab, (where mc and mab are the

2

Ginzburg-Landau superconducting effective masses) butboth ratios are assumed to be equal in the model lead-ing to Eq. 1. As will be shown below, the paramagneticterm in Eq. (2) in LaO0.9F0.1FeAs can be larger thanthe superconducting torque, which makes extraction ofthe equilibrium vortex magnetization nontrivial. In thiswork we propose a method, which enables us to resolvethis problem and measure the true angular dependence

of the superconducting torque as a function of both−→H

and T , probing the concomitant behavior of γ(T,H) andλab(T,H) and manifestations of multiband effects.

II. EXPERIMENTAL

Underdoped single crystals of LaO1−xFxFeAs withtypical sizes of 80 × 60 × 5 µm3 were grown by the fluxmethod described in Ref. 21. The samples had a criti-cal temperature Tc ≃ 15 K as determined by the SQUIDmagnetometry, and as shown in Fig. 1. The width ofsuperconducting transition, measured by a commercialSQUID magnetometer under a field H = 10 Oe aftercooling the crystal under zero field, is ∆Tc ∼ 3.5 K. Thisrelatively broad transition may not reflect the samplequality but mostly results from the penetration of vor-tices in a plate-like crystal which has a large demagne-tization factor and thus reduced lower critical field. Al-though in some crystals from the same batch the widthof the resistive transition, from the very onset of the re-sistive transition to the zero resistance state, is observedto be as large as ∆T ≃ 3 to 4 K , consistent with thevalues reported in the literature for crystals with simi-lar composition22. The fraction of F quoted here, corre-sponds to a nominal value since its precise content is verydifficult to determine in such small single crystals. How-ever, a superconducting transition temperature Tc ≃ 15K, see Fig. 1, firmly places these crystals within the un-derdoped state, following the overall phase diagram dis-playing Tc(x) as a function of the F content x.24 As ar-gued in Ref. 23, F is expected to be inhomogeneously dis-tributed throughout the samples. Samples were attachedto the tip of a piezo-resistive micro-cantilever placed in arotator inserted into a 3He cryostat. The ensemble wasplaced into a 18 T superconducting solenoid. Changesin the resistance of the micro-cantilever associated withits deflection and thus a finite magnetic torque τ wasmeasured via a Wheatstone resistance bridge.

III. RESULTS AND DISCUSSION

Fig. 2 (a) shows the angular dependence of the torqueτ(θ) at T = 8 K and underH = 5 T for a LaFeAsO0.9F0.1

single crystal. Hysteresis, resulting from the irreversiblemagnetization due to vortex pinning is observed be-tween increasing and decreasing angular sweeps. Blackline depicts the average value of both traces, τrev(θ) =(τ(θ)up + τ(θ)down)/2 defined as an equilibrium magne-

5 10 15 20 25-8

-6

-4

-2

0

2

Raw data Average

M (e

mu)

x 1

08

T (K)

crystal La-690, L2

LaFeASO0.9

F0.1

FIG. 1. (color online) (a) Magnetization M as a function oftemperature for a typical LaO0.9F0.1FeAs single crystal mea-sured under an external field of 10 Oe. The small mass of thesingle crystal, of just a few micrograms, leads to the observedlarge scattering in the data points. Red markers correspondto M(T ) averaged over 20 raw data points.

tization, where θup and θdown indicate either increasingor decreasing angle sweeps, respectively. This reversibletorque contains both superconducting and paramagneticcontributions. Given that vortex pinning and concomi-tant hysteresis are bound to disturb the equilibrium mag-netization, we have checked that our definition of τrev(θ)leads to reproducible traces, by re-measuring τ(θ) forboth θup and θdown within two distinct angular ranges,as shown in Figs. 2 (b) and 2 (c). The respective τrev(θ)traces, i.e. blue and magenta traces, are plotted in Fig.2 (d) together with the original τrev(θ) from Fig. 2 (a).As seen, all traces overlap almost perfectly. Both sharpspikes seen at either side of θ = 90◦ are likely due topinning effects.Fig. 3 (a) shows the angular dependence of the

torque τ(θ) at T = 10 K and H = 5 T for a sec-

ond LaFeAsO0.9F0.1 single crystal. In this crystal andat this temperature one does not observe any structurethat might be attributable to pinning and which wouldcompromise a fit attempt of the resulting τrev(θ) (brownline) to either Eq. (1) or Eq. (2). As shown in Fig. 3(b),the paramagnetic term τm sin 2θ increases rapidly as thefield increases, preventing a direct fit of τrev(θ) to Eq.(1) since τm sin 2θ interferes with the sin 2θ harmonicsof the first term. Yet the superconducting parametersγ(T,H) and λ(T,H) can be unambiguously extractedfrom the data adding a 90◦ translation of τrev(θ) to itself,i.e. τrev(θ) + τrev(θ+90◦), where the paramagnetic termin τ(θ) cancels out:

τ+ = τ(θ) + τ(θ + 90◦) =V φ0(γ

2 − 1)H sin 2θ

16πµ0λ2abγ

1/3

×[

1

ε(θ)ln

(

ηHabc2

ε(θ)H

)

− 1

ε⋆(θ)ln

(

ηHabc2

ε⋆(θ)H

)]

, (2)

3

FIG. 2. (color online) (a) Magnetic torque τ for a LaO0.9F0.1FeAs single crystal for increasing and decreasing angle (θ) sweeps(red lines), at H = 5 T and T = 8 K. Arrows indicate either increasing (θup) or decreasing (θdown) angles. Black line is thereversible torque component or τrev(θ) defined here as the average between both traces. (b) Same as in (a) but in a smallerangular range. (c) Same as in (a) and in (b) but in an even shorter angular range. (d) The resulting τrev(θ) from Figs. (a), (b)and (c).

where ε⋆(θ) = (cos2 θ + γ2 sin2 θ)1/2. This procedure isillustrated by Fig. 3 (c) which shows τ+(θ) as a functionof θ for all curves in Fig. 3 (b). Notice that the amplitudeof τ+(θ) is considerable smaller than that of τrev(θ).

Since τ+(θ) in Eq. (2) depends on three fit param-eters, γ, λ and ηHc2, different sets of parameters maygive equally good descriptions of the experimental data.One can circumvent this difficulty by extracting ηHc2

from the amplitude of τ+(θ)/H plotted as a functionof ln(1/H) for several values of θ, as shown in Fig.4 (a). If at a given temperature, these measurementsare performed up to high enough fields, the extrapo-lation of τ+(θ)/H to zero evaluates the value H⋆ atwhich

(

ηHabc2 /ε(θ)H⋆

)

= 1. From the two extrapolatedvalues of H⋆ for θ1 = 110◦ and θ2 = 120◦, we ex-clude γ and obtain (ηHc2)

2 = H2⋆ (θ1)H

2⋆ (θ2) sin(θ2 −

θ1) sin(θ2 + θ1)/[H2⋆ (θ1) cos

2 θ1 − H2⋆ (θ2) cos

2 θ1], whichyields ηHab

c2 ≃ 27 T for T = 10 K. This simple methodprovides a thermodynamic estimate for Hab

c2 without theneed of extremely high magnetic fields, H ≃ Hc2(θ). Fur-thermore, with ηHab

c2 ≃ 27 T we obtain excellent and sta-ble two-parameter fits of τ+(θ) to Eq. (2) for virtually allfield values, as shown in Fig. 4 (b). Here the parametersγ and λ no longer interfere in the fit as λ affects onlythe magnitude but not the shape of τ+(θ). We confirmed

that the extracted parameters lead to a small differencein the logarithmic terms of Eq. (2) at H = H⋆.

Using the method outlined above, we extracted thefield and the temperature dependencies of γ(T,H),λab(T,H). An example, is given by the orange line inFig. 5 (a) for H = 6 T and T = 10 K. Having fixedγ, λ, and ηHab

c2 we can now fit the original τrev(θ) toEq. (1) (red line), leaving the amplitude of the param-agnetic component τm as the only adjustable parameter(magenta line). Figure 5 (b) depicts the resulting ampli-tudes for both τm and the superconducting contributionτK ∝ H/λ2

ab in Eq. (1) as a function of field for T = 10 K.The amplitude of τK follows the expected linear in fielddependence up to H = 8 T, from which point it starts todecline continuously. On the other hand, τm follows theexpected H2 dependence characteristic of the torque ofan anisotropic paramagnetic background. To our knowl-edge, this is the first magnetometry method which allowsan independent extraction of the parameters of a mag-netic superconductor.

The curves τ(θ) measured for T > 4 K, indicatethat ηHab

c2 (T ) is described by ηHabc2 (T ) = ηHab

c2 (0)[1 −(T/Tc)

2]. As seen in Fig. 5, the irreversible componentin τ(θ) grows quickly as the temperature is lowered. AtT = 4 K despite the observed large irreversibility, the

4

FIG. 3. (color online) (a) Magnetic torque τ for aLaO0.9F0.1FeAs single crystal for increasing (clear blue line)and decreasing (blue line) angle (θ) sweeps, at H = 3 T andT = 27 K. (b) τrev(θ) for several field values at T = 10 K.(c) The symmetrized component τrev(θ)+ τrev(θ+90◦) of thetorque due solely to the reversible vortex magnetization.

resulting reversible component in τ(θ) is still nearly per-fectly described by Eq. (1), see Fig. 6 (a). However, asthe temperature is lowered to T = 1.5 K additional struc-tures emerge in τ(θ) for θ close to 90◦, see Fig. 6 (b). Weascribe these features to the intrinsic pinning of vorticesby the planar structure of the material, which preventsa reliable extraction of the reversible component in τ(θ)below T ∼ 4 K. A detailed analysis and discussion willbe provided elsewhere.25

Figure 7 (a) shows the resulting temperature depen-dence of the total superfluid density ns ∝ λ−2

ab mea-sured under a field H = 5 T. A field of 5 T is highenough to suppress the irreversible component in thetorque as compared to the reversible one, and to ne-glect demagnetization factors and geometrical barriersfor the penetration of magnetic flux through the sam-ple. Our torque magnetometer was not calibrated, sowe could only measure the temperature dependency ofλab(T ) but not the absolute values of λab or ns. Despitethe unavailability of points at the lowest T s, the tem-perature dependence of ns(T ) exhibits a positive curva-ture as seen in penetration depth measurements in thecompounds RFeAsO0.9F0.1 (R=La, Nd, with Tcs of 14and 45 K, respectively).26 But it contrasts with penetra-

90 120 150 180 210 240 270

-0.02

-0.01

0.00

0.01

0.02

-3 -2 -1 00

1

2

3

4

T = 10 K

rev(

)+re

v(+9

00 ) ()

(degrees)

H = 4 T H = 10 T H = 18 T Kogan fit

(b)

1000

1100

1200

1300

Linear Fit

[re

v()+

rev(

+900 )]

/H (m

/T)

ln (1/H) (lnT-1 )

25 T23.22 T

Habc2

27 T

(a)

FIG. 4. (color online) (a) The amplitude of [τrev(θ)+ τrev(θ+90◦)]/H as a function of ln(H−1) for several angles, takenfrom the data in Fig. 1 (c). Red lines are linear extrapolationsof [τrev(θ) + τrev(θ + 90◦)]/H → 0 for θ = 110◦ and 120◦,which yields ηHab

c2 ≃ 27 T for LaFeAsO0.9F0.1 at T = 10K. (b) With the value ηHab

c2 ≃ 27 we obtain excellent fits ofτrev(θ) + τrev(θ + 90◦) to Eq. (2) for all field values.

tion depth results for PrFeAsO1−y (Tc ≃ 35 K)27 andfor SmFeAsO0.8F0.2 (Tc ≃ 44) K7, which finds evidencefor a superconducting state characterized by more thanone (non-nodal) gap. In Ref. 26 such an upward cur-vature was explained in terms of the s± scenario, withthe superconducting gap ratio ∆1/∆2 ≃ 1/3. As fol-lows from Fig. 7 (b), the associated λab(T ) in our lim-ited temperature range follows a T 2 dependence at lowand intermediate temperatures, in contrast to the lin-ear dependence expected for a nodal gap as observedin LaFePO28, or the nearly exponential behavior ex-pected for a clean s-wave superconductor, as reported forSmFeAsO0.8F0.2

7 and PrFeAsO1−y.27 One important de-

bate concerning the Fe arsenides is precisely the origin ofthese differences, since a common pairing mechanism5,14

has been proposed for all compounds based on the pre-sumed similarity of their electronic structure. At thesame time, it was recently argued that the extended s-wave scenario can lead to either nodeless or nodal gaps,depending on the interplay between intraband and in-terband interactions.29 Penetration depth measurementsover an extended region in reduced temperatures (T/Tc)also revealed a T 2-dependence for λab in RFeAsO0.9F0.1

(R =La, Nd)26 as well as in Ba1−xKxFe2As2.13 This

5

0 2 4 6 8 10 12 14 16 18 200

1

2

3

0

20

40

60

80

100

0 30 60 90 120 150 180

-30

-20

-10

0

10

20

K (m

)

H (T)

m (m

) H2

(b)

(m)

(degrees)

H = 6 T Fit to Eq. (1)

T = 10 K

(a)

FIG. 5. (color online) (a) Reversible torque τrev(θ) for aLaFeAsO0.9F0.1 single crystal (blue markers) at H = 6 Tand T = 10 K. Orange line shows the reversible vortex torqueτK and the magenta line shows the paramagnetic torque ex-tracted from the data shown in Fig. 3 using the deconvolutionprocedure described in the text. Red line shows the sum ofτK with the paramagnetic term. (b) The amplitude of τKnormalized by (γ2

− 1)/γ1/3 (blue markers) and that of theparamagnetic term (clear blue markers) as functions of H .At lower fields, τK(H,θ) increases linearly with H , while theparamagnetic term exhibits a H2 dependence.

power-law temperature dependence was deemed to beconsistent with the s± muti-gap scenario, if either stronginterband impurity scattering30 or pair-breaking effects31

are important. Our observation of a ns ∝ T 2 is limited bythe restricted temperature range imposed by the pinningeffects at lower T s, yet we believe that it is importantto expose the agreement for the anomalous temperaturedependence of the penetration depth between magnetictorque and surface impedance measurements in the caseof LaFeAsO0.9F0.1. Given the width of the superconduct-ing transition≃ 3−4 K, it is possible that local variationsof Tc due to an inhomogeneous distribution of F, couldaffect the dependence of ns on T at higher temperatures.In addition, given that our measurements of ns(T ) wereperformed under a field of 5 T, we cannot completely ruleout that the temperature dependence of Hc2(T ) mightinfluence the power law dependence for ns(T ) reportedhere, particularly at higher temperatures.Figure 7 (b) also displays the temperature dependence

of the mass anisotropy parameter γ, which starts at γ ≃ 7for T ≤ Tc, increases toward a maximum of ∼ 10 at T ≃

0 30 60 90 120 150 180

-0.4

-0.2

0.0

0.2

0.4-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

(degrees)

()

H = 5 TT = 1.5 K(b)

()

H = 5 TT = 4 K

(a)

FIG. 6. (color online) (a) τ as a function of the angle θ andrespectively for increasing (blue line) and decreasing (orangeline) angle scans at T = 4 K and under a field H = 5 T.Black line corresponds to the average between both traces.(b) Same as in (a) but for T = 1.5 K. Notice the emergenceof sharp peaks in τ (θ) (red arrows) for θ close to 90◦ resultingfrom the intrinsic pinning by the planar structure.

0.75 Tc, and then decreases to ≈ 1 as T is lowered (as ithappens in nearly all Fe based superconductors, see Refs.9 and 16). Our unpublished transport measurements inLaFe1−xCoxAsO indicate a very similar T -dependencefor γH = Hab

c2 /Hcc2.

Figures 7 (c) and 7 (d) show the field dependencies ofγ and ns for T = 10 K. Here γ increases by nearly afactor of 2, from ∼ 8 at small fields to ∼ 15 at H = 18 T.On the other hand, ns remains nearly constant in fieldsup to Hv = 8 T, and then decreases at higher fields, ex-trapolating to ns = 0 at H(10 K) ≈ 25 T. The completesuppression of ns at this value is consistent with our pre-vious estimate of ηHc2 ≈ 27 T obtained above. The sup-pression of ns(H) upon application of magnetic field isconsistent with the onset of orbital pair-breaking by cir-culating vortex currents as the spacing between the vor-tex cores becomes smaller than ≈

√3 of the vortex spac-

ing at Hc2 where superconductivity is fully suppressed.For instance, the single-band Ginzburg-Landau theorypredicts λ−2 ∝ ns(H) ≃ ns(0)(1−H/Hc2) for T close toTc.

32 Interestingly, the ratio Hv/Hc2 ≃ 1/3 turned out tobe approximately equal to the ratio of the superconduct-ing gaps on the electron and hole pockets of the Fermisurface as observed in Ref. 26. Around H = 6 - 7 T,there is a spike in λ and/or a dip in ns, the origin ofwhich remains unclear.

6

0

1

2

3

4

0 2 4 6 8 10 12 14 1602468

10

1.52.02.53.03.5

LaFeAsO0.9

F0.1

-2 ab

(Arb

. Uni

ts)

T (K)

H = 5 T

T 2

ab (A

rb. Units)

0 5 10 15 20 250

1

2

3

02468

10121416

1/2 ab

(Arb

. Uni

ts)

H (T)

LaFeAsO0.9

F0.1

TC 15 K

T = 10 K

Habc2

27 T

(d)

(c)

(b)

(a)

FIG. 7. (color online) (a) Temperature dependence of thesuperfluid density ns ∝ λ−2

ab extracted from the torque dataat H = 5 T. (b) Temperature dependence of both γ (clearblue markers) and λab (blue markers). Here λab(T ) exhibitsa quadratic dependence on T . (c) γ as a function of magneticfield as extracted from the fittings in Fig. 2 (b). (d) Thesuperfluid density ns ∝ λ−2

ab as a function of H at T = 10 K.

We described our data using the simplest Eq. (1) forthe torque in a uniaxial superconductor, assuming thatthe angular dependencies of λ and ξ are controlled bythe single anisotropy parameter γ. A more complicatedexpression for τ with two different anisotropy parame-ters γH = Hab

c2 /Hcc2 and γλ = λab/λc was suggested

for multiband superconductors,33 However given that theformula for τ of Ref. 33 was obtained on phenomenolog-ical grounds, and the angular dependencies of λ(θ) andHc2(θ) derived from the multiband BCS theory are much

more complicated,34 we believe that the use of that ex-pression for τ with different γH and γλ may not unam-biguously reveal any new physics as compared to the sim-pler Eq. (1). Indeed, the fit of our data with τ from Ref.33 gave behaviors qualitatively similar to those shownabove: γH ≃ 10 |T≈Tc

increases to a maximum valueof 18 before decreasing to much lower values as T → 0.Meanwhile γλ = 1.4 |T≈Tc

exhibits a mild decrease to-wards 1 as T → 0. This common tendency of γ to ap-proach a value close to 1 upon decreasing T , observed onmany Fe-based superconductors, indicates the increasingcontribution of the Pauli pair-breaking effects at lowerT s which is neither taken into account in Eq. (1) nor inthe expression for τ of Ref. 33 .

In conclusion, we report the torque measurements ofreversible magnetization of LaO0.9F0.1FeAs single crys-tals from which the field dependent mass anisotropy pa-rameter γ and the reduced London penetration depthλ(H,T )/λ(0, T ) were measured. The significant field de-pendencies of γ and λ(H,T )/λ(0, T ) are consistent withmultiband pairing while the observed quadratic temper-ature dependence of λ(H,T )/λ(0, T ) at low and interme-diate T is consistent with the s± pairing with interbandimpurity scattering.

IV. ACKNOWLEDGEMENTS

We acknowledge S. Weyeneth for the SQUID measure-ments. The NHMFL is supported by NSF through NSF-DMR-0084173 and the State of Florida. L. B. is sup-ported by DOE-BES through award de-sc0002613. Workat ETH was supported by the Swiss National ScienceFoundation and the NCCR program MaNEP.

∗ balicas@magnet.fsu.edu1 Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono,J. Am. Chem. Soc. 130, 3296 (2008); H. Takahashi, K.Igawa, K. Arii, Y. Kamihara, M. Hirano, and H. Hosono,Nature 453, 376 (2008); X. H. Chen, T. Wu, G. Wu, R.H. Liu, H. Chen , D. F. Fang, Nature 453, 761 (2008).

2 G. F. Chen, Z. Li, D. Wu, G. Li, W. Z. Hu, J. Dong, P.Zheng, J. L. Luo, and N. L. Wang, Phys. Rev. Lett. 100,247002 (2008).

3 Y. Takabayashi, M. T. McDonald, D. Papanikolaou, S.Margadonna , G. Wu, R. H. Liu, X. H. Chen, K. Pras-sides, J. Am. Chem. Soc. 130, 9242 (2008).

4 C. de la Cruz, Q. Huang, J. W. Lynn, Jiying Li, W. RatcliffII, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N.L. Wang, and P. C. Dai, Nature 453, 899 (2008).

5 I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du,Phys. Rev. Lett. 101, 057003 (2008).

6 T. Y. Chen, Z. Tesanovic, R. H. Liu, X. H. Chen, and C.L. Chien, Nature 453, 1224 (2008).

7 L. Malone, J. D. Fletcher, A. Serafin, A. Carrington, N.D. Zhigadlo, Z. Bukowski, S. Katrych, and J. Karpinski,Phys. Rev. B 79, 140501 (R) (2009).

8 H. Ding, P. Richard, K. Nakayama, K. Sugawara, T.Arakane , Y. Sekiba, A. Takayama, S. Souma, T. Sato,

T. Takahashi, Z. Wang, X. Dai, Z. Fang, G. F. Chen, J. L.Luo, N. L. Wang, Europhys. Lett. 83, 47001 (2008).

9 F. Hunte, J. Jaroszynski, A. Gurevich, D. C. Larbalestier,R. Jin, A. S. Sefat, M. A. McGuire, B. C. Sales, D. K.Christen, D. Mandrus, Nature 453, 903 (2008).

10 S. Weyeneth, R. Puzniak, U. Mosele, N. D. Zhigadlo, S.Katrych, Z. Bukowski, J. Karpinski, S. Kohout, J. Roos,H. Keller, J. Supercond. Nov. Magn. 4, 325 (2009); S.Weyeneth, R. Puzniak, N. D. Zhigadlo, S. Katrych, Z.Bukowski, J. Karpinski, and H. Keller, ibid, 347 (2009).

11 K. Hashimoto, T. Shibauchi, T. Kato, K. Ikada, R.Okazaki, H. Shishido, M. Ishikado, H. Kito, A. Iyo, H.Eisaki, S. Shamoto, and Y. Matsuda, Phys. Rev. Lett. 102,017002 (2009).

12 P. Popovich, A. V. Boris, O. V. Dolgov, A. A. Golubov,D. L. Sun, C. T. Lin, R. K. Kremer, and B. Keimer, Phys.Rev. Lett. 105, 027003 (2010).

13 C. Martin, R. T. Gordon, M. A. Tanatar, H. Kim, N. Ni, S.L. Bud?ko, P. C. Canfield, H. Luo, H. H. Wen, Z. Wang, A.B. Vorontsov, V. G. Kogan, and R. Prozorov, Phys. Rev.B 80, 020501(R) (2009).

14 K. Haule, J. H. Shim, and G. Kotliar, Phys. Rev. Lett.100, 226402 (2008); Q. Si and E. Abrahams, Phys. Rev.Lett. 101, 076401 (2008)

7

15 P. A. Lee, X. G. Wen, Phys. Rev. B 78, 144517 (2008).16 Y. J. Jo, J. Jaroszynski, A. Yamamoto, A. Gurevich, S.

C. Riggs, G. S. Boebinger, D. Larbalestier, H. H. Wen, N.D. Zhigadlo, S. Katrych, Z. Bukowski, J. Karpinski, R. H.Liu, H. Chen, X. H. Chen, and L. Balicas, Physica C 469,566 (2009); J. Jaroszynski, J. Jaroszynski, S. C. Riggs, F.Hunte, A. Gurevich, D. C. Larbalestier, G. S. Boebinger,F. F. Balakirev, A. Migliori, Z. A. Ren, W. Lu, J. Yang,X. L. Shen, X. L. Dong, Z. X. Zha, R. Jin, A. S. Sefat, M.A. McGuire, B. C. Sales, D. K. Christen, and D. Mandrus,Phys. Rev. B 78, 064511 (2008).

17 M. Angst, R. Puzniak, A. Wisniewski, J. Jun, S. M. Kaza-kov, J. Karpinski, J. Roos, and H. Keller, Phys. Rev. Lett.88, 167004 (2002); A. V. Sologubenko et al. Phys. Rev.B 65, 180505(R) (2002); S. L. Bud’ko and P. C. Canfield,ibid. 65 212501 (2002)

18 R. Cubitt, M. R. Eskildsen, C. D. Dewhurst, J. Jun, S. M.Kazakov, and J. Karpinski, Phys. Rev. Lett. 91, 047002(2003); M. Angst, D. Di Castro, D. G. Eshchenko, R.Khasanov, S. Kohout, I. M. Savic, A. Shengelaya, S. L.Bud?ko, P. C. Canfield, J. Jun, J. Karpinski, S. M. Kaza-kov, R. A. Ribeiro, and H. Keller, Phys. Rev. B 70, 224513(2004).

19 M. Tegel, S. Johansson, V. Weiss, I. Schellenberg, W. Her-mes, R. Pottgen, D. Johrendt, Europhys. Lett. 84, 67007(2008).

20 V. G. Kogan, Phys. Rev. B 24, 1572 (1981).21 N. D. Zhigadlo, S. Katrych, Z. Bukowski, and J. Karpinski,

J. Phys.: Condens. Matter 20, 342202 (2008).22 H. Kim, C. Martin, M. E. Tillman, S. K. Kim, S. L. Budko,

P. C. Canfield, M. A. Tanatar, R. Prozorov, Physica C 470,S363 (2010).

23 C. J. van der Beek, G. Rizza, M. Konczykowski, P. Fertey,I. Monnet, T. Klein, R. Okazaki, M. Ishikado, H. Kito, A.Iyo, H. Eisaki, S. Shamoto, M. E. Tillman, S. L. Bud?ko,P. C. Canfield, T. Shibauchi, and Y. Matsuda, Phys. Rev.B 81, 174517 (2010).

24 H. Luetkens, H.H. Klauss, M. Kraken, F. J. Litterst, T.Dellmann, R. Klingeler, C. Hess, R. Khasanov, A. Am-ato, C. Baines, M. Kosmala, O. J. Schumann, M. Braden,J. Hamann-Borrero, N. Leps, A. Kondrat, G. Behr, J.Werner, and B. Buchner, Nat. Mater. 8, 305 (2009).

25 G. Li, G. Grissonnanche, B. S. Conner, L. Balicas, et al.

(unpublished)26 C. Martin, M. E. Tillman, H. Kim, M. A. Tanatar, S. K.

Kim, A. Kreyssig, R. T. Gordon, M. D. Vannette, S. Nandi,V. G. Kogan, S. L. Bud?ko, P. C. Canfield, A. I. Goldman,and R. Prozorov, Phys. Rev. Lett. 102, 247002 (2009).

27 K. Hashimoto, T. Shibauchi, T. Kato, K. Ikada, R.Okazaki, H. Shishido, M. Ishikado, H. Kito, A. Iyo, H.Eisaki, S. Shamoto, and Y. Matsuda, Phys. Rev. Lett. 102,017002 (2009).

28 J. D. Fletcher, A. Serafin, L. Malone, J. G. Analytis, J.-H. Chu, A. S. Erickson, I. R. Fisher, and A. Carrington,Phys. Rev. Lett. 102, 147001 (2009).

29 A. V. Chubukov, M. G. Vavilov, and A. B. Vorontsov,Phys. Rev. B 80, 140515(R) (2009).

30 A. B. Vorontsov, M. G. Vavilov, and A. V. Chubukov,Phys. Rev. B 79, 140507(R) (2009).

31 R. T. Gordon, H. Kim, M. A. Tanatar, R. Prozorov, andV. G. Kogan, Phys. Rev. B 81, 180501(R) (2010).

32 E. H. Brandt, Rep. Prog. Phys. 58, 1465 (1995).33 V. G. Kogan, Phys. Rev. Lett. 89, 237005 (2002).34 A. Gurevich, Phys. Rev. B 82, 184504 (2010); ibid. 67,

184515 (2003); A. A. Golubov, A. E. Koshelev, Phys. Rev.B 68, 104503 (2003).