Field and Temperature Dependence of the Superfluid Density in LaO_{1-x}F_xFeAs Superconductors: A Muon Spin Relaxation Study
H. Luetkens, H.-H. Klauss, R. Khasanov, A. Amato, R. Klingeler, I. Hellmann, N. Leps, A. Kondrat, C.Hess, A. Köhler, G. Behr, J. Werner, B. Büchner
aa r X i v : . [ c ond - m a t . s up r- c on ] A p r Field and Temperature Dependence of the Superfluid Density in LaO − x F x FeAsSuperconductors: A Muon Spin Relaxation Study
H. Luetkens, ∗ H.-H. Klauss, R. Khasanov, A. Amato, R. Klingeler, I. Hellmann, N. Leps, A. Kondrat, C. Hess, A. K¨ohler, G. Behr, J. Werner, and B. B¨uchner Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland IFP, TU Dresden, D-01069 Dresden, Germany Institute for Solid State Research, IFW Dresden, D-01171 Dresden, Germany (Dated: November 5, 2018)We present zero field and transverse field µ SR experiments on the recently discovered elec-tron doped Fe-based superconductor LaO − x F x FeAs. The zero field experiments on underdoped( x =0.075) and optimally doped ( x =0.1) samples rule out any static magnetic order above 1.6 K inthese superconducting samples. From transverse field experiments in the vortex phase we deduce thetemperature and field dependence of the superfluid density. Whereas the temperature dependenceis consistent with a weak coupling BCS s-wave or a dirty d-wave gap function scenario, the field de-pendence strongly evidences unconventional superconductivity. We obtain the in-plane penetrationdepth of λ ab (0) = 254(2) nm for LaO . F . FeAs and λ ab (0) = 364(8) nm for LaO . F . FeAs.Further evidence for unconventional superconductivity is provided by the ratio of T c versus thesuperfluid density, which is close to the Uemura line of hole doped high- T c cuprates. PACS numbers: 76.75.+i, 74.70.-b
The ongoing search for new superconductors has re-cently yielded a new family of Fe-based compounds com-posed of alternating La O − x F x and Fe As layers withtransition temperatures T c up to 28 K [1]. By re-placing La with other rare earths, T c can be raised toabove 50 K [2, 3, 4, 5, 6, 7], and thus the first non-copper-oxide superconductor with T c exceeding 50 K hasemerged. Both, recent experimental findings and theo-retical treatments [8, 9] indicate unconventional multi-band superconductivity in the layers of paramagnetic Feions, which would normally destroy superconductivity intraditional s-wave superconductors. Point contact tun-neling spectroscopy [10], specific heat [11] and magneti-zation measurements [12] point to nodal order parame-ters. High magnetic field experiments yielded evidencefor two-band effects [13]. Various scenarios for supercon-ductivity have also been discussed theoretically and dif-ferent pairing symmetries of the superconducting groundstate including spin-triplet p-wave pairing have been pro-posed [14, 15, 16, 17, 18, 19, 20]. Intriguingly, thereis evidence for a close interplay between superconduc-tivity and magnetism as it is well established for otherunconventional superconductors. A commensurate spin-density wave (SDW) has been observed below 150 K inthe undoped compound [21, 22, 23, 24], and a recent the-oretical work suggests that fluctuations associated with amagnetic quantum critical point are essential for super-conductivity in the F-doped system [25].In this Letter, we report zero field (ZF) and hightransverse field (TF) muon spin relaxation measurements( µ SR) on polycrystalline samples of LaO − x F x FeAs with x =0.075 and 0.10. Our ZF- µ SR experiments show thatno static magnetic correlations are present down to 1.6 K.Hence, the spin-density state is completely suppressed upon F-doping. Properties of the superconducting stateare determined by the TF- µ SR measurements: The weaktemperature dependence of the superfluid density below T c / − x F x FeAs and, remarkably, the data forthe Fe-based superconductors are very close to the Ue-mura line of the hole doped high- T c cuprates.Polycrystalline samples of LaO − x F x FeAs ( x = 0.075,0.1) were prepared by using a two-step solid state re-action method, similar to that described by Zhu et al.[26], and annealed in vacuum. The samples consists of1 to 100 µ m sized grains of LaO − x F x FeAs. The crys-tal structure and the composition were investigated bypowder X-ray diffraction and wavelength-dispersive X-ray spectroscopy (WDX).In order to characterize the superconducting proper-ties, zero field cooled (shielding signal) and field cooled(Meissner signal) magnetic susceptibility in externalfields H = 10 Oe . . .
50 kOe have been measured us-ing a SQUID magnetometer. The resistance has beenmeasured with a standard 4-point geometry employingan alternating DC current. Critical temperatures of T c ≈ . T c ≈
22 K for x = 0 . x = 0 . µ SR data for x = 0 . (cid:0) (cid:1)(cid:0) (cid:2)(cid:0) (cid:3)(cid:0) (cid:4)(cid:0)(cid:5)(cid:6)(cid:5)(cid:7)(cid:5)(cid:4)(cid:5)(cid:3)(cid:5)(cid:2)(cid:5)(cid:1)(cid:0) (cid:1)(cid:0) (cid:2)(cid:0) (cid:3)(cid:0) (cid:4)(cid:0) (cid:7)(cid:0)(cid:0)(cid:8)(cid:0)(cid:0)(cid:8)(cid:2)(cid:0)(cid:8)(cid:4)(cid:0)(cid:8)(cid:6) (cid:9)(cid:10)(cid:0)(cid:8)(cid:1) (cid:0)(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4)(cid:1)(cid:8)(cid:9)(cid:10)(cid:11) (cid:11)(cid:12)(cid:13)(cid:12)(cid:13) (cid:12)(cid:5)(cid:13) (cid:14)(cid:15)(cid:16) (cid:17) (cid:16) (cid:17)(cid:1)(cid:18)(cid:19) (cid:14)(cid:15)(cid:10)(cid:15)(cid:2)(cid:0)(cid:15)(cid:16)(cid:17) (cid:15) (cid:20) (cid:7) (cid:19)(cid:21)(cid:1) (cid:3) (cid:6) (cid:22) (cid:23) (cid:22)(cid:24)(cid:22) (cid:6) (cid:25) (cid:8) (cid:0) (cid:8) (cid:9) (cid:14)(cid:26) (cid:15) (cid:27) (cid:8) (cid:1) (cid:2) (cid:7) (cid:28) (cid:21) (cid:2) (cid:29) (cid:11) (cid:9)(cid:10)(cid:0)(cid:8)(cid:0)(cid:18)(cid:7) (cid:9)(cid:10)(cid:0)(cid:8)(cid:1)(cid:9)(cid:10)(cid:0)(cid:8)(cid:0)(cid:18)(cid:7)(cid:19) (cid:20) (cid:21)(cid:2)(cid:2)(cid:8)(cid:0)(cid:22) (cid:0)(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:4)(cid:1)(cid:8)(cid:9)(cid:10)(cid:11) (cid:30) (cid:1)(cid:19) (cid:22) (cid:19) (cid:6) (cid:5) (cid:31) (cid:21)(cid:1) (cid:8) (cid:9) (cid:5) (cid:7) (cid:11) (cid:15) (cid:19) (cid:20) (cid:21)(cid:2)(cid:6)(cid:8)(cid:0)(cid:22) FIG. 1: Right: temperature dependence of the resistance ofLaO − x F x FeAs at x = 0 . x = 0 .
075 in the vicinity of T c .Left: field cooled and zero field cooled magnetic susceptibilityfor x = 0 . x = 0 . are very small and can be traced back to the tiny mag-netic fields originating from nuclear moments. This im-plies that we can rule out any static SDW magnetismwith considerable magnetic moments, for both the opti-mally and the underdoped samples. Thus, our data arein striking contradiction with the prediction in Ref. 8. In-stead, our measurements show that doping the compoundLaOFeAs with electrons suppresses the SDW instability,and simultaneously promotes the superconductivity asthe new ground state. This indicates that the supercon-ducting phase is close to a quantum critical point relatedto the magnetic instability.Such a proximity of magnetism and superconductivityis also suggested by several aspects of our µ SR-data. Thefirst weak hint is a slight increase of the relaxation ratebelow T c (cf. inset Fig. 2). Further indications arisefrom the high-TF measurements on LaO . F . FeAs,as will be discussed below. M uon s p i n po l a r i z a t i on Time ( s) K T r e l a x a t i on r a t e ( M H z ) Temperature (K)
FIG. 2: Zero field µ SR spectra of LaO . F . FeAs for 1.6,10, and 30 K. The inset shows the Gaussian Kubo-Toyaberelaxation rate as a function of temperature.
The results of the analysis of the magnetic field depen-dent and temperature dependent TF- µ SR measured inthe vortex phase
H > H c1 ≈
40 Oe are displayed in Fig- ures 3 and 4. From the muon spin polarization P ( t ) wedetermined the Gaussian relaxation rate σ which is thesum of a nuclear contribution σ nm and a contribution σ sc proportional to the second moment of the magnetic fielddistribution of the vortex lattice, i.e. σ = σ sc + σ nm . Inorder to extract the σ sc which measures the superfluiddensity, i.e. σ sc ∝ /λ ∝ n s /m ∗ [28], we determinedthe small nuclear relaxation rate σ nm = 0 . LaO F FeAs BCS s-wave B C2 = 32 T d-wave with non-linear/non-local effects LaO F FeAs R e l a x a t i on r a t e sc ( M H z ) Magnetic field H (T)
FIG. 3: Field dependence σ sc at 1.6 K for LaO . F . FeAsand LaO . F . FeAs. The dashed line is the expected behav-ior for an s-wave BCS superconductor with µ H c2 = 32 Taccording to Eq. 1. The solid line is a fit of the data withEq. 2 indicative for nodes in the gap function. Figure 3 shows the obtained field dependence of σ sc for both LaO − x F x FeAs samples at 1.6 K. Each mea-surement was performed after cooling the sample in thefield from above T c .We restrict our discussion of σ sc ( H ) to the optimallydoped sample since the data for x = 0 .
075 are clearlyinfluenced by additional contributions. In particular, af-ter a small decrease we find that σ sc ( H ) starts to in-crease with increasing field, which is incompatible withthe suppression of the superfluid density in high magneticfields. Analogous behavior has been observed in high- T c cuprates [29, 30], where an external field can promotethe magnetic correlations leading to spurious magnetismin the otherwise superconducting sample. The upturnof σ sc as a function of magnetic field is therefore mostlikely produced by an additional magnetic contributionand does not reflect a field dependence of the superfluiddensity.In contrast, the data for x = 0 . σ sc , that is purely originating from the second momentof the field distribution of vortex lattice. At low fields amaximum in σ sc ( H ) is observed followed by a decreaseof the relaxation rate up to the highest fields. At firstglance this appears to be consistent with a BCS s-wavesuperconductor. However, a quantitative analysis takinginto account the large critical fields reveals strong dis-crepancies.In a conventional s-wave superconductor the penetra-tion depth λ is field independent and σ sc increases withincreasing magnetic field up to H ≃ H c1 . At higherfields a weak field dependence according to Eq. 1 is ex-pected in an ideal triangular vortex lattice [28]: σ sc [ µ s − ] = 4 . × (1 − h )[1 + 3 . − h ) ] / λ − [nm] . (1)Here, h = H/H c2 and H c2 is the upper critical field whichhas been reported to be as large as 32 . . .
65 T in opti-mally doped LaO − x F x FeAs [13, 26, 31]. We note thathigh field studies on our sample corroborate these largevalues [32]. Taking these critical fields, the theoreticalBCS behavior has been calculated. It is shown by thedashed line in Fig. 3. The decrease of σ sc at µ H & . µ H c2 = 5 T is assumed.For unconventional superconductors with nodes in thegap, λ depends on the field. This leads to a decreaseof σ sc ( H ) for H > H c1 , which is generally observed forvarious high- T c superconductors [33]. This observation isnicely described by theories taking non-local/non-lineareffects into account. In this case, the field dependence ofthe superfluid density can be described by [34, 35]: λ − ( H ) λ − ( H = 0) = σ sc ( H ) σ sc ( H = 0) = 1 − K √ H , (2)where K is the parameter depending on the strength ofthe non-linear effects. Applying this model, our dataare well described by Eq. 2 with K = 0 . − . indicative for superconductivity with nodes in the gapfunction [47]. F FeAs s-wave BCS power law LaO F FeAs sc ( M H z ) ~ / ~ n s / m * Temperature (K)
FIG. 4: Temperature dependence of σ sc measured in a field of µ H = 0 .
07 T for LaO . F . FeAs and LaO . F . FeAs.The σ sc ( T ) were fitted using a standard BCS curve and apower law 1 − ( T /T c ) n . In case of LaO . F . FeAs thepoints below 4 K were omitted in the fit.
It is well established that nodes in the gap function alsoinfluence the temperature dependence of the superfluiddensity n s /m ∗ ∝ /λ . This temperature dependence n s ( T ) is directly obtained from the temperature depen-dent TF- µ SR measurements. To ensure an accurate de-termination of λ ( T ) it is mandatory to measure slightlyabove the maximum of σ sc ( H ) where Eq. 1 is valid todetermine the absolute value of λ . Therefore, the mea-surements were done with an external field of 700 G. Theresults for σ sc ( T ) are shown in Figure 4.Surprisingly, and in contrast to our conclusions fromthe field dependence, the results follow the s-wave weakcoupling BCS temperature dependence as shown by thedashed curve. However, the data are also reasonably welldescribed by a power law 1 − ( T /T c ) . , which is sim-ilar to the prediction for the dirty limit d-wave model1 − ( T /T c ) [36]. Other gap symmetries such as a cleanlimit d-wave or a non-monotonic d-wave have been testedalso, but were found to be inconsistent with the data. Inparticular, it is difficult to account for the very weak tem-perature dependence of σ sc at low T within such mod-els. Considering both field and temperature dependenceof σ sc , the dirty-limit d-wave model appears to be mostcompatible with the data. It it important to note, thatwe observe a strong reduction of the high-TF Knightshift below T c . This points to significant reduction ofthe spin susceptibility in the superconducting state whichexcludes triplet pairing.The temperature dependence for the underdoped com-pound LaO . F . FeAs resembles that of the opti-mum doped sample, with the difference that an upturnof σ sc is observed below 4 K. When measuring σ sc ( T ) ina higher field of 0.6 T, the upturn of σ sc ( T ) is already ob-served at higher temperatures T . λ ( T = 0) and the in-plane penetration depth λ ab . For LaO . F . FeAs wedetermine a zero temperature relaxation rate σ sc (0) =0 . λ (0) = 333(2) nm. ForLaO . F . FeAs we analogously determined the lowtemperature relaxation rate to σ sc (0) = 0 . λ (0) = 477(10) nm. Forpowdered samples the experimentally extracted λ is ageometrically averaged penetration depth. However, inLaO − x F x FeAs a rather large anisotropy can be expectedfrom recent band structure calculations predicting e.g. aresistivity ratio of ρ c /ρ ab ≈ −
15 [37]. In our TF- µ SR measurements a large anisotropy of λ is confirmedby the observation of a symmetric Gaussian shape ofthe field distribution p ( B ). In contrast, for an isotropicsuperconductor a typical nonsymmetric shape of p ( B )with a van Hove singularity is found [33]. It has beenshown [38] that for large anisotropies the measured effec-tive penetration depth λ becomes independent on theactual anisotropy and is solely determined by the in-plane penetration depth λ ab and can be expressed by λ = 1 . λ ab . Therefore we obtain the in-plane penetra-tion depth of λ ab (0) = 254(2) nm for LaO . F . FeAs and λ ab (0) = 364(8) nm for LaO . F . FeAs, respectively.In Fig. 5 we display our data in the so-called Uemuraplot, which nicely demonstrates the linear relation of su-perfluid density and T c for under and optimally doped su-perconductors [39]. We compare our data to the cupratefamily. The data for LaO − x F x FeAs are close to theUemura line for hole doped cuprates, indicating thatthe superfluid is also very dilute in the oxypnictides.This observation is in accordance with its small normalstate charge carrier density [26, 40, 41] and provides fur-ther evidence for the unconventional superconductivityin LaO − x F x FeAs. T C ( K ) -2ab ( m -2 ) La214Y123 Bi2223NCCO SLCOh-dopedcupratese-dopedcupratesPCCO
FIG. 5: Uemura plot for hole and electron doped high T c cuprates. Points for the cuprates are taken from [42, 43, 44,45, 46]. The stars are showing the data for LaO − x F x FeAsobtained in this work.
In conclusion, we have performed zero field and hightransverse field muon spin relaxation measurements onpolycrystalline samples of LaO − x F x FeAs with x =0.075and 0.10. Our ZF- µ SR experiments show that the spin-density state is completely suppressed upon F-doping,which suggests a close proximity of the superconductingphase to a magnetic quantum critical point. TF- µ SRmeasurements reveal a weak temperature dependence ofthe superfluid density below T c /