Full Gap Superconductivity in Ba 0.6 K 0.4 Fe 2 As 2 Probed by Muon Spin Rotation
M. Hiraishi, R. Kadono, S. Takeshita, M. Miyazaki, A. Koda, H. Okabe, J. Akimitsu
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Full Gap Superconductivity in Ba . K . Fe As Probed by Muon Spin Rotation
Masatoshi
Hiraishi , Ryosuke Kadono , ∗ , Soshi Takeshita ,Masanori Miyazaki , Akihiro Koda , , Hirotaka Okabe and Jun Akimitsu Department of Materials Structure Science, School of High Energy Accelerator Science,The Graduate University for Advanced Studies, 1-1 Oho, Tsukuba, Ibaraki 305-0801 Muon Science Laboratory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK),1-1 Oho, Tsukuba, Ibaraki 305-0801 Department of Physics and Mathematics, Aoyama-Gakuin University, Fuchinobe, Sagamihara, Kanagawa, 229-8558
Superfluid density ( n s ) in the mixed state of an iron pnictide superconductor Ba − x K x Fe As is determined by muon spin rotation for a sample with optimal doping ( x = 0 . n s is perfectly reproduced by the conventional BCS model for s -wave paring, where the order parameter can be either a single-gap with ∆ = 8 . /k B T c = 5 . = 12 meV (fixed) [2∆ /k B T c = 7 . = 6 . /k B T c = 4 . /k B T c ) indicateextremely strong coupling of carriers to bosons that mediate the Cooper pairing. KEYWORDS: oxypnictide superconductor, order parameter, muon spin rotation
The recent discovery of high- T c superconductivity inLaFeAsO − x F x (LFAO-F, T c ≃
26 K) and of relatedcompounds has attracted broad attention regardingthe mechanism of superconductivity on Fe As layersthat show some apparent similarities with CuO layers.They have a common feature that the superconductivityoccurs upon carrier doping to the transition metal ox-ide/pnictide layers that exhibit instability towards mag-netic order at lower temperatures. In the case of LFAO-F and its family compounds, electrons are introducedby the substitution of O − with F − in the La O lay-ers. Moreover, very recent developments demonstrateincreasing variety in the methods of electron doping suchas oxygen depletion
5, 6 or Co substitution for Fe.
Incontrast, hole doping is attained in A Fe As ( A = Ba,Sr, Ca) by the substitution of divalent cations ( A )with alkali metals ( B + ). This situation providesan excellent opportunity to examine the “electron-holesymmetry” regarding the superconducting properties ofiron pnictides, which is also one of the major issues incuprates.Microscopic evidence shows that the parent compoundBaFe As exhibits magnetic order (SDW) below 140K which is accompanied by a structural phase transi-tion.
15, 16
The situation is common to Sr − x K x Fe As , and it suggests that the electronic ground state of Fe As layers in the parent compound is quite similar to thatin LaFeAsO. However, the doping phase diagram ismarkedly different from LFAO-F, as it exhibits super-conductivity over a wide range of hole content p = x/ . ≤ x ≤ . The phase di-agram is also characterized by a bell-shaped variationof T c against x , where the maximal T c ≃
38 K is at-tained near x ∼ . p ∼ . As layers sug- ∗ E-mail address : ryosuke.kadono@ kek.jp gested by theories, this difference may be attributedto that of the bands relevant to the doped carriers. Here,we report our µ SR study on Ba − x K x Fe As (BKFA)for samples with x = 0 . T c < T c ≃ x = 0 . and CaFe − x Co x AsF (CFCAF, another subclassof electron-doped iron pnictide superconductor). Polycrystalline samples of Ba − x K x Fe As with nom-inal compositions of x = 0 . Concerning the K-doped samples,reproducibility of synthesis was improved by using bar-ium and potassium arsenides as precursors. The purityof as-grown samples (sintered slabs with a dimension of ∼ × × , net weight of ∼ . x = 0 . while a minor unknown impurity phase ( ∼ x = 0 .
1. Conventional µ SR measure-ments were performed using the LAMPF spectrometerinstalled on the M20 beamline of TRIUMF, Canada.During the measurement under a zero field (ZF), residualmagnetic field at the sample position was reduced below10 − T with the initial muon spin direction parallel tothe muon beam direction [ ~P µ (0) k ˆ z ]. Time-dependentmuon polarization [ G z ( t ) = ˆ z · ~P µ ( t )] was monitored bymeasuring decay-positron asymmetry along the ˆ z -axis.Transverse field (TF) condition was realized by rotating Full Paper
Author Name A sy mm e t r y µ s 8642 ν i / M H z K x Fe As x =0.1ZF- µ SR Fig. 1. (Color online) ZF- µ SR time spectra observed at 190 Kand 2 K in Ba − x K x Fe As sample with x = 0 . T c < the initial muon polarization so that ~P µ (0) k ˆ x , wherethe asymmetry was monitored along the ˆ x -axis to obtain G x ( t ) = ˆ x · ~P µ ( t ). All the measurements under a mag-netic field were made by cooling the sample to the targettemperature after the field equilibrated.Figure 1 shows the µ SR spectra obtained upon muonimplantation to the sample with x = 0 . ν = 27 . ν =6 . µ SR study in Ba − x K x Fe As ,where they observed signals of 28.8 MHz and 7 MHz ina parent compound ( x = 0). While the quality of theirK-doped sample ( x = 0 .
45) seems to have some problemregarding homogeneity (see below), its magnetic phaseexhibits a tendency that ν is slightly reduced ( ∼ ν observed for our sample with x = 0 .
1, and naturallyunderstood as a result of enhanced itinerant characterfor d electrons in K-doped compounds. The magnitudeof internal field probed by µ SR is close to that observedin LFAO ( ∼
23 MHz and 3 MHz),
21, 25 and thereby itsuggests that the high frequency component correspondsto the signal from muons situated on the Fe As layerswhile another coming from those located near the cationsites. The onset temperature for the high frequency com-ponent is close to 140 K, which is also consistent withearlier reports.
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On the other hand, it is inferred from ZF- µ SR spec-tra in Fig. 2 that no trace of magnetism is found in thesample with x = 0 .
4. This is in marked contrast with theearlier report on µ SR measurements in a sample with x = 0 .
45 where a magnetic phase seems to dominateover a large volume fraction ( ∼ Concerning the G z ( t ) , G x ( t ) µ sZF 45K ZF 2KTF 2K Ba K x Fe As x = 0.4 Fig. 2. (Color online) ZF- µ SR time spectra observed at 45 K and2 K in Ba − x K x Fe As sample with x = 0 . T c ≃
38 K).No trace of magnetic phase is observed. The spectra under atransverse field (TF) at 2 K is displayed on a rotating referenceframe to extract the envelop function. Solid curves are fits usinga Gaussian relaxation function described in the text. bulk superconducting property, the quality of our speci-men can be assessed by looking into magnetization data,which is shown in Fig. 3a. The sharp onset as well as alarge Meissener fraction ( ≥ π for ZFC) endorses excel-lent quality of the present specimen.The µ SR time spectra under a transverse field ( µ H =0 . B ( r )] to implanted muons. The lineshape is wellrepresented by a Gaussian damping, and the analysis ismade by curve fit using the following model function, G x ( t ) = exp (cid:20) −
12 ( δ + σ ) t (cid:21) cos (2 πf s t + φ ) , (1)where σ s = γ µ h ( B ( r ) − B ) i / with B ≃ µ H beingthe mean value of the local field B ( r ), πf s ≃ γ µ B (with γ µ = 2 π × .
53 MHz/T), and δ N is the depolar-ization due to random local fields from nuclear magneticmoments. For the extraction of σ s , δ N is determined bycurve fits above T c and then subtracted from the totallinewidth obtained for the spectra below T c .The deduced linewidth, σ s , is plotted against temper-ature in Fig. 3b, where σ s is the quantity proportional tothe superfluid density n s , σ s ∝ λ = n s e m ∗ c , (2)where λ is the effective London penetration depth and m ∗ is the effective mass of the superconducting carri-ers. Compared with the results of µ SR studies in LFAO-F and that recently obtained for CFCAF, it is no-ticeable that σ s rises relatively sharply just below T c ,and becomes mostly independent of temperature below15 K ( ≃ . T c ). A curve fit using the power law, σ s = σ [1 − ( T /T c ) β ], yields β = 4 . . Phys. Soc. Jpn. Full Paper
Author Name 3 (cid:109) s (cid:3) / (cid:3) (cid:43) s - (cid:3) / (cid:3) K (cid:3) exp. (cid:3) s-BCS Ba K x Fe As x =0.4TF- (cid:43) SR a)b) Fig. 3. (Color online) a) Magnetization of Ba − x K x Fe As mea-sured on the µ SR sample with x = 0 .
4, where data were obtainedafter cooling under an external field (FC) or zero field (ZFC).The total weight of the sample is 0.1 g, and the magnetizationcorresponding to 4 π is obtained by using the structural parame-ters reported in Ref. b) Temperature dependence of Gaussianlinwidth σ s = √ δ s determined by TF- µ SR measurement with H = 0 . line with the prediction of conventional BCS model for s -wave pairing. The gap parameter is obtained by a fitusing the weak coupling BCS model to yield ∆ = 8 . /k B T c = 5 . s -wave pairing, the gapparameter far exceeds the prediction of weak-couplingBCS theory (2∆ /k B T c = 3 . They report∆ ∼
12 meV on small Fermi surfaces and ∆ ∼ s -wave symmetry,
28, 29 σ s ( T ) = σ (0) − w · δσ (∆ , T ) − (1 − w ) · δσ (∆ , T ) ,δσ (∆ , T ) = 2 σ (0) k B T Z ∞ f ( ε, T ) · [1 − f ( ε, T )] dε,f ( ε, T ) = (cid:16) e √ ε +∆( T ) /k B T (cid:17) − , where ∆ i ( i = 1 and 2) are the energy gap at T = 0, w is the relative weight for i = 1, k B is the Boltzmann constant, f ( ε, T ) is the Fermi distribution function, and∆( T ) is the standard BCS gap energy. The curve fit as-suming a common T c = 38 K and a large gap fixed to12 meV (2∆ /k B T c = 7 .
3) perfectly reproduces data inFig. 3b with ∆ = 6 . /k B T c = 4 . w = 0 . σ s ,indicates that the quasiparticle excitation spectrum as-sociated with multi-gap superconductivity tends to bemerged into that of the single gap when the small gaphas a large value for 2∆ /k B T c .It has been shown in our previous µ SR studies onLFAO-F and CFCAF that the temperature depen-dence of σ s in these compounds (with a doping rangenear the boundary between magnetic and superconduct-ing phases) can be reproduced by the above mentioneddouble-gap model, where the gap parameters are consid-erably smaller than those in BKFA [e.g., 2∆ /k B T c =2 . /k B T c = 1 . x = 0 . /k B T c = 3 . /k B T c = 1 . x = 0 . d bands) that would give rise to cer-tain intricacy. Apart from the validity of applyingthe double-gap model to electron-doped iron pnictides,these figures suggest that the hole doping may occur inthe bands different from those for electron doping, wherethe characteristic energy of the Cooper pairing may differamong those bands.Finally, we point out that the superfluid density inthe optimally doped Ba − x K x Fe As does not satisfythe empirical linear relation with T c observed for under-doped cuprates. As shown in Fig. 4, the correspondingmuon spin relaxation rate [ σ s (0) = 2 . µ s − , whichyields the magnetic penetration depth λ = 155(1) nm]is more than twice as large as what is expected for com-pounds with T c = 38 K from the empirical line shown bya dashed line. The data for other iron pnictides are alsoplotted for comparison, in which we omitted those forthe compounds containing rare earth elements (Ce, Nd,Sm,...) because of the general ambiguity anticipated forextracting σ s under strong additional depolarization dueto the magnetism of rare earth ions. They show a ten-dency that σ s (and accordingly n s ) is independent of T c .This is qualitatively different from underdoped cuprates,and rather close to the behavior predicted by the conven-tional BCS theory where the condensation energy doesnot depend on n s .In summary, we have shown in a hole-doped ironpnictide, Ba − x K x Fe As , that the superconducting or-der parameter is characterized by a strong coupling toparing bosons, as inferred from large gap parameters(2∆ i /k B T c ≫ . n s ( T ), determined by µ SR is per-fectly in line with that predicted by the conventionalBCS model with fully gapped s -wave pairing. A detailedanalysis with phenomenological double-gap model indi-cates that n s ( T ) is also consistent with the presence of J. Phys. Soc. Jpn.
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Author NameFig. 4. (Color online) A plot of superconducting transition tem-perature vs muon spin relaxation rate σ s ( T → CFCAF ). The em-pirical relation is indicated by a dashed line, and the dottedline connecting points for iron pnictides is only meant for a guidefor eye. double-gap, although the large gap parameters make itdifficult to determine the multitude of energy gap solelyfrom n s ( T ).We would like to thank the TRIUMF staff for theirtechnical support during the µ SR experiment. Thiswork was partially supported by the KEK-MSL Inter-University Program for Oversea Muon Facilities and by aGrant-in-Aid for Creative Scientific Research on PriorityAreas from the Ministry of Education, Culture, Sports,Science and Technology, Japan.
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