Doping evolution of the absolute value of the London penetration depth and superfluid density in single crystals of Ba(Fe 1−x Co x ) 2 As 2
R. T. Gordon, H. Kim, N. Salovich, R. W. Giannetta, R. M. Fernandes, V. G. Kogan, T. Prozorov, S. L. Bud'ko, P. C. Canfield, M. A. Tanatar, R. Prozorov
aa r X i v : . [ c ond - m a t . s up r- c on ] J un Doping evolution of the absolute value of the London penetration depth andsuperfluid density in single crystals of Ba(Fe − x Co x ) As R. T. Gordon,
1, 2
H. Kim,
1, 2
N. Salovich, R. W. Giannetta, R. M. Fernandes,
1, 2
V. G. Kogan, T. Prozorov, S. L. Bud’ko,
1, 2
P. C. Canfield,
1, 2
M. A. Tanatar, and R. Prozorov ∗ Ames Laboratory, U.S. DOE, Ames, IA 50011 Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011 Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 1110 West Green St., Urbana, IL 61801 (Dated: 10 June 2010)The zero temperature value of the in-plane London penetration depth, λ ab (0), has been measuredin single crystals of Ba(Fe − x Co x ) As as a function of the Co concentration, x , across both theunderdoped and overdoped superconducting regions of the phase diagram. For x & . λ ab (0)has been found to have values between 120 ±
50 nm and 300 ±
50 nm. A pronounced increasein λ ab (0), to a value as high as 950 ±
50 nm, has been observed for x . . λ ab (0) has allowed us to trackthe evolution of the temperature-dependent superfluid density, from which we infer the developmentof a pronounced superconducting gap anisotropy at the edges of the superconducting dome. PACS numbers: 74.25.Nf,74.20.Rp,74.20.Mn
INTRODUCTION
The zero temperature value of the London penetrationdepth is directly related to the superfluid density in theground state of a system through λ (0) ∝ / p n s (0) [1].In the clean, low scattering limit, n s (0) is equal to the to-tal density of conduction electrons, n N . There are casesin which other phases, for example itinerant magnetism,can compete with superconductivity for the same conduc-tion electrons, thus reducing the overall number of carri-ers in the superconducting state at T = 0. Given the richdoping phase diagram of the newly discovered iron-basedsuperconductors in which a long range magnetically or-dered state, with itinerant character, coexists with a su-perconducting state, questions are raised regarding theeffects of the competition between these states for thesame electrons [2–9]. One way to approach this matter isto study the doping evolution of λ ab (0) across the phasediagram of these materials and use it to infer the corre-sponding change in the superfluid density, especially inthe regime of the phase diagram where these two phasescoexist. Determination of the absolute value of the Lon-don penetration depth is also important for the correctevaluation of the normalized, temperature-dependent su-perfluid density, ρ s ( T ) = ( λ (0) /λ ( T )) . This quantitycan be calculated from various models of the supercon-ducting gap and provides insight into the pairing mech-anism.In the present study we focus on λ ab (0), which is theground state screening length associated with supercur-rent flowing in the crystallographic ab-plane as a result ofan external magnetic field applied along the c -axis. For x & . λ ab (0) have been foundbetween 120 ±
50 nm and 300 ±
50 nm. A pronouncedincrease in λ ab (0) to a value as high as 950 ±
50 nm for x . .
047 has been observed. We interpret the in-crease in λ ab (0) for samples with x . .
047 to be due tothe competition between the superconducting and itin-erant antiferromagnetic states for the same conductionelectrons.The experimental determination of λ (0) is a ratherchallenging task since only finite temperatures can bereached. There are techniques that are capable of ob-taining an estimate of its value by taking advantage ofthe small variation of λ ( T ) at low temperatures, whichcan be on the order of 1 nm/K, along with precisionmeasurements. One such technique is muon spin ro-tation ( µ SR) [10], which has produced estimates for λ ab (0) of 320 nm in (Ba − x K x )Fe As ( T c ≃ K )[11, 12], 470 nm in (Ba . K . )Fe As ( T c ≃
30 K) [13],230 nm in Ba(Fe . K . ) As ( T c ≃
38 K) [14], 250 nmin La(O − x F x )FeAs [15] and values ranging from 189 nmto 438 nm in the Ba(Fe − x Co x ) As series [16, 17].Another technique, magnetic force microscopy, has re-ported λ ab (0) = 325 ±
50 nm in Ba(Fe . Co . ) As [18].In addition, optical reflectivity measurements have beenused to estimate λ ab (0) in Ba(Fe − x Co x ) As and re-ported values of 277 ±
25 nm for x = 0 .
06 and 315 ±
30 nmfor for x = 0 .
08 [19]. It is important to compare the val-ues of λ (0) obtained by as many different techniques aspossible because each experiment requires its own set ofassumptions and modeling procedures.Given the overall disparity between the measured val-ues of λ (0) from these different experimental techniques,it is valuable to perform a systematic study of λ (0) asa function of doping in the series of which large, highquality single crystals having homogeneous doping lev-els are available, namely the Ba(Fe − x Co x ) As series.The samples used for this study were members of theBa(Fe − x Co x ) As series and were obtained from the FIG. 1: Scanning electron microscope images of the Al coatedsamples. (a) Large scale view. The broken side is on top. (b)and (c) are zoomed in on the Al film on the edge of the brokenside. (d) A trench produced by a focused-ion beam (FIB). (e)Close-up view of the FIB trench showing the Al film and itsthickness. same source as in Ref. [3] using the same growth pro-cedure.
EXPERIMENTAL
The experimental apparatus used for obtaining all ofthe penetration depth measurements in this work was atunnel diode resonator (TDR) [20]. The essential com-ponents of the TDR are a tank circuit formed by aninductor and a capacitor, which has a resonance fre-quency f = 1 / π √ LC ≈
14 MHz, and a tunnel diode.While the diode is biased appropriately it serves as an ac power source for the tank circuit. To perform pen-etration depth measurements, the sample is mountedon a sapphire stage and inserted into the inductor coil.The magnetic field of the coil, which is ≈
10 mOe, isscreened by the sample and thus changes the induc-tance, L, and therefore also the resonance frequency byan amount ∆ f . By utilizing ∆ f ( T ) = − G πχ ( T ) = G [1 − ( λ ( T ) /R ) tanh( R/λ ( T ))], the TDR is capable ofmeasuring the variation of the penetration depth in a su-perconductor, ∆ λ ( T ) = λ ( T ) − λ (0), with a resolution ofnearly 1 ˚A, where G is a geometry dependent calibrationfactor depending on the coil volume, sample volume, de-magnetization and empty coil resonance frequency. Thiscalibration factor is measured directly by exctracting thesample from the inductor coil at its base temperature.The TDR technique, as described above, provides veryprecise measurements of the variation of the penetrationdepth, ∆ λ ( T ), but not the absolute value due to reasons described in detail in Ref. [21]. However, as proposed inthe same reference, the TDR technique can be extendedto obtain the absolute value of the penetration depth, λ ( T ). The key to obtaining λ (0) from TDR measure-ments is to coat the entire surface of the superconductorunder study with a thin film of a conventional supercon-ductor having a lower critical temperature and a knownvalue of λ (0). For this study, the aluminum films thatwere used to coat the Ba(Fe − x Co x ) As samples had T Alc ≈ t , is much less than the normal state skin depthat the TDR operating frequency of 14 MHz, where δ Al ≈ µ m for ρ Al =10 µΩ -cm [22]. By measuring the fre-quency shift upon warming from T min , which is the basetemperature of the sample, to T > T
Alc we obtain thequantity L ≡ λ eff ( T Alc ) − λ eff ( T min ), shown in Fig. 2.This quantity can be used to calculate λ (0) along withthe previously determined power-law relation for iron-based superconductors [23], ∆ λ ( T ) = βT n , and by usingthe formula for the effective magnetic penetration depthinto both the Al film and the coated superconductor for T < T
Alc , which is given by λ eff ( T ) = λ Al ( T ) λ ( T ) + λ Al ( T ) tanh tλ Al ( T ) λ Al ( T ) + λ ( T ) tanh tλ Al ( T ) , (1)where λ ( T ) is the penetration depth of the coated su-perconductor and λ Al ( T ) is the penetration depth ofthe Al film. As usual with the TDR technique, thevariation of the penetration depth with temperature,∆ λ eff ( T ) = λ eff ( T ) − λ eff ( T min ), is measured. Thismethod has been successfully demonstrated on severalcuprate superconductors [21] and has shown agreementwith measurements of λ (0) in Fe y (Te − x Se x ) crystalsobtained by different techniques [24]. Here we use anextended analysis obtained by solving the appropriateboundary value problem.The aluminum film was deposited onto each samplewhile it was suspended from a rotating stage by a finewire in an argon atmosphere of a magnetron sputteringsystem. The formation of non-uniform regions in thefilm was avoided by bonding the wire to only a portionof the narrowest edge of each sample. Each film thicknesswas checked using a scanning electron microscope in twoways, both of which are shown in Fig. 1. The first methodinvolved breaking a coated sample after all measurementshad been performed to expose its cross section. Afterthis, it was mounted on an SEM sample holder usingsilver paste, shown in Fig. 1(a). The images of the brokenedge are shown for two different zoom levels in Fig. 1(b) T min Before Al coating After Al coating T Alc e ff ( m ) T (K) L= eff (T Alc )- eff (T min ) T c FIG. 2: (Color online) Main frame: Full superconductingtransition of an optimally doped Ba(Fe . Co . ) As crystalbefore and after coating. Inset: Zoomed in low-temperatureregion, T min . T . T Alc , before (green triangles) and after(red circles) the Al coating on the same sample. The overallfrequency shift through the Al transition, denoted as L , isused for the calculation of λ ab (0). and (c). The second method used a focused ion beam(FIB) to make a trench on the surface of a coated sample,with the trench depth being much greater than the Alcoating thickness, shown in Fig. 1(d). The sample wasthen tilted and imaged by the SEM that is built into theFIB system, shown in Fig. 1(e). RESULTS AND DISCUSSION
The values of λ ab (0) that were obtained using the pro-cedure described above for the Ba(Fe − x Co x ) As sys-tem are shown in the top panel of Fig. 3 for doping lev-els, x , across the superconducting region of the phasediagram, shown schematically in the bottom panel ofFig. 3. The size of the error bars for the λ ab (0) pointswas determined by considering the film thickness to be t = 100 ±
10 nm and λ Al (0) = 50 ±
10 nm. The discrep-ancy in λ ab (0) for the two samples having x = 0 . λ ab (0) values shown in the upper panel of Fig. 3has an approximately constant value of 0.2 µ m for allvalues of x , which probably indicates that the source ofthe scatter is the same for all samples. For comparison, Fig. 3 also shows λ ab (0) obtained from µ SR measure-ments (red stars) [16, 17], the MFM technique (blackstar) [18] and optical reflectivity (purple stars) [19], allin the Ba(Fe − x Co x ) As system, most of which are con-sistent with our results within the scatter. It may alsobe important to note that the λ ab (0) values from otherexperiments are all on the high side of the scatter thatexists within the TDR λ ab (0) data set. This is becauseany cracks or voids in the Al film will lead to underesti-mated values of λ ab (0). We note that we did not observean increase in λ ab (0) towards the overdoped regime as re-ported from µ SR measurements [17], although our valuesat the optimal doping do agree well.Specifically, an increase in λ ab (0) on the underdopedside below x ≈ .
047 has been observed, which is in theregion where the itinerant antiferromagnetic and super-conducting phases coexist, as is shown in the bottompanel of Fig. 3. The dependence of λ ab (0) on carrier con-centration is λ ab (0) ∝ / p n s (0), where n s is the super-fluid density, which is equal to the normal state carrierconcentration in the clean case. The proportionality be-tween λ ab (0) and n s (0) still holds if scattering is included,but n s is reduced due to a residual density of states withinthe gap. Overall, an increase in λ ab (0) is consistent witha decrease in the superfluid carrier concentration. Thereis compelling evidence suggesting that the itinerant anti-ferromagnetic spin density wave state in these materialsacts to gap a portion of the Fermi surface [2–9], whichwould remove mobile charge carriers and this qualitativeidea is consistent with our experimental observations ofthe doping dependence of λ ab (0). Changes in the Hallcoefficient for these materials, moving from the pure su-perconducting region to the coexistence region, have alsobeen interpreted as being due to the interaction betweenthese phases [25, 26]. It has been shown that the openingof a superconducting gap in the antiferromagnetic statetransfers optical spectral weight from a mid-infrared peakto a Drude peak, even when the reconstructed Fermi sur-face would be fully gapped [27]. As a result, the coexis-tence state has a finite n s , although smaller than in thepure superconducting state.In order to provide a more quantitative explanationfor the observed increase in λ ab (0) as x decreases in theunderdoped region, we have considered the case of s ± su-perconductivity coexisting with itinerant antiferromag-netism [9]. For the case of particle hole symmetry (nestedbands), the zero temperature value of the in-plane pene-tration depth in the region where the two phases coexistis λ SC + SDWab (0) = λ ab (0) s AF ∆ (2)where λ ab (0) is the value for a pure superconductingsystem with no magnetism present, and ∆ AF and ∆ are the zero temperature values of the antiferromag-netic and superconducting gaps, respectively. Deviationsfrom particle hole symmetry lead to a smaller increase in λ SC + SDWab (0), making the result in Eqn. 2 an upper esti-mate. For more information on the details of the calcula-tion and the values of ∆ AF and ∆ used, see Ref. [9, 27].The three blue dashed lines shown in the top panelof Fig. 3, which were produced using Eqn. 2, show theexpected increase in λ ab (0) in the region of coexistingphases below x ≈ .
047 by normalizing to three differentvalues of λ ab (0) in the pure superconducting state, withthose being 120 nm, 180 nm and 270 nm. This theorydoes not take into account changes in the pure supercon-ducting state, so for x > .
047 the dashed blue lines arehorizontal. These theoretical curves were produced us-ing parameters that agree with the phase diagram in thebottom panel of Fig. 3 [9, 28], which includes a shift ofthe coexistence region to lower values of x by an amountof 0.012, and given the simplifications of the model, theagreement with the experimental observations is quitereasonable.While the exact functional form of λ ( x ) is unknown,the solid gray line in Fig. 3 serves as a useful guide to theeye (of the form A+B/ x n ), which does indeed illustratea dramatic increase of λ ab (0) in the coexistence regionand also a relatively slight change in the pure supercon-ducting phase. It should be noted that a dramatic in-crease in λ ab (0) below x ≈ .
047 cannot be explained byimpurity scattering, which would only lead to relativelysmall corrections in the magnitude of λ ab (0) (but, indeed,significantly affects the temperature dependence of λ ( T )[31]).Values of λ ab (0) obtained here can be used to calcu-late the actual penetration depth, λ ab ( T ) = ∆ λ ab ( T ) + λ ab (0), where ∆ λ ab ( T ) has been measured for eachBa(Fe − x Co x ) As crystal used in this study before Alcoating [29, 30]. In the top panel of Fig. 4, we exam-ine λ − ab ( T ) ∝ n s ( T ) /m ∗ as a function of temperature infour different samples; with x = 0 .
038 corresponding tothe two far underdoped samples having different mea-sured values of λ ab (0) in the region of coexisting phases, x = 0 .
074 being close to optimal doping and x = 0 .
10 be-ing an overdoped concentration, all of which were usedto determine the values of λ ab (0) shown in the top panelof Fig. 3. It should be noted that the orange and blackcurves in Fig. 4 for x = 0 .
038 were made using the same∆ λ ab ( T ) data, but different values of λ ab (0) because thetemperature dependence of only one of the two samplesshown in the top panel of Fig. 3 was measured beforealuminum coating. As can be seen in the top panel ofFig. 4, the values of λ − ab ( T →
0) are quite large for x & .
047 (red diamonds and green triangles) relativeto those with x . .
047 because the measured values of λ ab (0) are much smaller than 1 µ m, i.e. 0.182 nm and0.270 nm. However, for x . .
047 (black circles andorange squares) the values of λ − ab (0) vary much less be- T ( K ) AFM SC
SC+AFM x TDR SR MFM Reflectivity Theory Fit ab ( ) ( m ) FIG. 3: (Color online) Top panel: The zero temperature Lon-don penetration depth, λ ab (0), as a function of the Co con-centration, x . The three dashed blue lines are theoreticalcurves obtained using Eq. 2 for three different values of λ ab (0)in the pure superconducting state. The solid gray line is aguide to the eye (in the form of A+B/ x n ). Also shown arevalues of λ ab (0) obtained by other experiments for compari-son explained in the text. Bottom panel: Phase diagram forBa(Fe − x Co x ) As [2, 3, 9, 28]. cause λ ab (0) becomes closer to 1 µ m, i.e. 0.673 nm and0.921 nm.Using the same penetration depth data that was usedin the top panel of Fig. 4, we construct the normalized su-perfluid density (phase stiffness), ρ s ( T ) = ( λ (0) /λ ( T )) ,which is commonly used to analyze penetration depthdata and a quantity which is fairly easy to calculate foran arbitrary gap structure. The bottom panel in Fig. 4shows ρ s ( T ) for the same samples shown in the top panel.The black and orange curves were constructed using thesame ∆ λ ab ( T ), but different λ ab (0) values for the heav-ily underdoped sample, x =0.038, and the red and greencurves are the data for optimally doped and overdopedcompositions, respectively. Also shown for comparisonare the ρ s ( T ) curves for a single band s-wave supercon-ductor (dotted blue line) and a d-wave superconductor(dotted gray line), both in the clean limit. From Fig. 4, ρ s ( T →
0) and ρ s ( T → T c ) behave quite differently forthe members of the Ba(Fe − x Co x ) As series comparedto the standard, single gap s-wave and d-wave clean limitcases. Impurity scattering would turn the d-wave curvequadratic at low temperatures, while leaving s-wave al-most intact.The data for all doping levels show an overall similartrend of the evolution of ρ s ( T ) across the phase diagram.A special feature of this behavior is the negative curva-ture just below T c . This behaivor suggests that below T c the superconducting gap develops slower than it doesin the case of a single gap, which is a feature consistentwith the behavior of ρ s ( T ) in a two-gap superconduc-tor [32]. Furthermore, the normalized ρ s ( T ) curve forthe optimally doped sample over the entire temperaturerange stays above the curves for both heavily underdopedand overdoped samples. This distinction between thedifferent Co-doping compositions suggests that the gapanisotropy, which is generally considered as being eitherthe actual angular variation in k − space and/or the de-velopment of an imbalance between the gaps on differ-ent sheets of the Fermi surface, notably increases in theoverdoped and underdoped compositions. This is con-sistent with the measurements of the specific heat jump[33] and the residual term [34], as well as with measure-ments of thermal conductivity [35, 36]. Thermal con-ductivity measurements with heat flow along the c -axisactually suggest that nodal regions develop in the super-conducting gap in heavily under- and over-doped compo-sitions. Indeed, measurements of λ c in a closely relatedBa(Fe − x Ni x ) As , also suggest the existence of nodes inthe superconducting gap [37]. CONCLUSION
In conclusion, the zero temperature value of the in-plane London penetration depth, λ ab (0), has been mea-sured for the Ba(Fe − x Co x ) As series across the super-conducting “dome” of the phase diagram using an Alcoating technique along with TDR measurements. Thereis a clear increase in λ ab (0) below x ≈ . λ ab (0) were also used to construct the nor-malized superfluid density (phase stiffness), ρ s ( T ), andstudy its evolution with doping. The negative curvatureof ρ s ( T ) just below T c for samples across the supercon-ducting dome of the phase diagram implies two-gap su-perconductivity. A notable suppression of ρ s for heavilyunderdoped and slightly overdoped samples with respectto samples with optimal doping suggests a developinganisotropy of the superconducting gap toward the edgesof the superconducting dome, consistent with the behav-ior found in specific heat and thermal conductivity stud-ies.We thank J. Schmalian and A. Kreyssig for useful dis-cussions. Work at the Ames Laboratory was supported - ( m - ) T (K) =0.921 m) 3.8% Co ( =0.673 m) 7.4% Co ( =0.270 m) 10% Co ( =0.182 m) s = ( ) / ( T ) T/T c s-waved-wave FIG. 4: (Color online) Top panel: λ − ab ( T ) for samples of dif-ferent Co concentrations, x , from the Ba(Fe − x Co x ) As se-ries constructed from previously measured ∆ λ ab ( T ) curvesand λ ab (0) from this study. Bottom panel: Normalized su-perfluid density, ρ s ( T ), for the same samples shown in thetop panel along with the standard s-wave and d-wave casesfor low impurity scattering. by the division of Materials Science and Engineering, Ba-sic Energy Sciences, Department of Energy (USDOE),under Contract No. DEAC02-07CH11358. Work atUIUC was supported by the Center for Emergent Super-conductivity, an Energy Frontier Research Center fundedby the USDOE Office of Science, Basic Energy Sciencesunder Award Number DE-AC0298CH1088. R.P. ac-knowledges support from the Alfred P. Sloan Foundation. ∗ corresponding author: [email protected][1] M. Tinkham, Introduction to Superconductivity (Dover,New York, 1996), 2nd ed.[2] P. C. Canfield and S. L. Bud’ko, Annu. Rev. Condens.Matter Phys. , 11.1-11.24 (2010).[3] N. Ni, M. E. Tillman, J. Q. Yan, A. Kracher, S. T. Han- nahs, S. L. Bud’ko, P. C. Canfield, Phys. Rev. B ,214515 (2008).[4] A. J. Drew, Ch. Niedermayer, P. J. Baker, F. L. Pratt,S. J. Blundell, T. Lancaster, R. H. Liu, G. Wu,X. H. Chen, I. Watanabe, V. K. Malik, A. Dubroka,M. R¨ossle, K. W. Kim, C. Baines, and C. Bernhard, Nat.Mater. , 310 (2009).[5] D. K. Pratt, W. Tian, A. Kreyssig, J. L. Zarestky, S.Nandi, N. Ni, S. L. Budko, P. C. Canfield, A. I. Gold-man, and R. J. McQueeney, Phys. Rev. Lett. , 087001(2009).[6] A. D. Christianson, M. D. Lumsden, S. E. Nagler, G.J. MacDougall, M. A. McGuire, A. S. Sefat, R. Jin, B.C. Sales, and D. Mandrus, Phys. Rev. Lett. , 087002(2009).[7] Y. Laplace, J. Bobroff, F. Rullier-Albenque, D. Colson,and A. Forget, Phys. Rev. B , 140501 (2009).[8] T. Goko, A. A. Aczel, E. Baggio-Saitovitch, S. L. Bud’ko,P. C. Canfield, J. P. Carlo, G. F. Chen, Pengcheng Dai,A. C. Hamann, W. Z. Hu, H. Kageyama, G. M. Luke, J.L. Luo, B. Nachumi, N. Ni, D. Reznik, D. R. Sanchez-Candela, A. T. Savici, K. J. Sikes, N. L. Wang, C. R.Wiebe, T. J. Williams, T. Yamamoto, W. Yu, and Y. J.Uemura, Phys. Rev. B , 024508 (2009).[9] R. M Fernandes, D. K. Pratt, W. Tian, J. Zaretsky,A. Kreyssig, S. Nandi, M. G. Kim, A. Thaler, N. Ni,P. C. Canfield, R. J. McQueeney, J. Schmalian, andA. I. Goldman, Phys. Rev. B , 140501(R) (2010).[10] J. E. Sonier, Rep. Prog. Phys. , 1717 (2007).[11] R. Khasanov, V. Evtushinsky, A. Amato, H. H. Klauss,H Luetkens, Ch. Niedermayer, B. B¨uchner, G. L. Sun,C. T. Lin, J. T. Park, D. S. Inosov, V. Hinkov, Phys.Rev. Lett. , 187005 (2009).[12] D. V. Evtushinsky, D. S. Inosov, V. B. Zabolotnyy,M. S. Viazovska, R. Khasanov, A. Amato, H. H. Klauss,H. Luetkens, Ch. Niedermayer, G. L Sun, V. Hinkov,C. T. Lin, A. Varykhalov, A. Koitzsch, M. Knupfer,B. B¨uchner, A. A. Kordyuk, S. V. Borisenko, New J.Phys. , 055069 (2009).[13] A. A. Aczel, E. Baggio-Saitovitch, S. L. Bud’ko,P. C. Canfield, J. P. Carlo, G. F. Chen, PengchengDai, T. Goko, W. Z. Hu, G. M. Luke, J. L. Luo,N. Ni, D. R. Sanchez-Candela, F. F. Tafti, N. L. Wang,T. J. Williams, W. .Yu, and Y. J. Uemura, Phys. Rev. B , 214503 (2008).[14] M. Hiraishi, R. Kadono, S. Takeshita, M. Miyazaki, A.Koda, H. Okabe, J. Akimitsu, J. Phys. Soc. Jpn. , 2(2009).[15] H. Luetkens, H. H Klaus, 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. B¨uchner, Nature Mater. , 305 (2009).[16] T. J. Williams, A. A. Aczel, E. Baggio-Saitovitch,S. L. Bud’ko, P. C. Canfield, J. P. Carlo, T. Goko,J. Munevar, N. Ni, Y. J. Uemura, W. Yu, andG. M. Luke, Phys. Rev. B , 094501 (2009).[17] T.J. Williams, A.A. Aczel, E. Baggio-Saitovitch, S.L.Bud’ko, P.C. Canfield, J.P. Carlo, T. Goko, H.Kageyama, A. Kitado, J. Munevar, N. Ni, S.R. Saha, K. Kirschenbaum, J. Paglione, D.R. Sanchez-Candela, Y.J.Uemura, G.M. Luke, arXiv:1005.2136 (unpublished)[18] L. Luan, Ophir M. Auslaender, Thomas M. Lippman,Clifford W. Hicks, Beena Kalisky, Jiun-Haw Chu, JamesG. Analytis, Ian R. Fisher, John R. Kirtley, and KathrynA. Moler, Phys. Rev. B , 100501R (2010).[19] M. Nakajima, S. Ishida, K. Kihou, Y. Tomioka, T. Ito,Y. Yoshida, C. H. Lee, H. Kito, A. Iyo, H. Eisaki, K. M.Kojima, and S. Uchida, Phys. Rev. B , 104528 (2010).[20] C. T. Van Degrift, Rev. Sci. Inst.
599 (1975).[21] R. Prozorov, R. W. Giannetta, A. Carrington,P. Fournier, R. L. Greene, P. Guptasarma, D. G. Hinks,and A. R. Banks, Appl. Phys. Lett. , 4202 (2000).[22] J. J. Hauser, J. Low Temp. Phys. , 314 (1972).[23] R. T. Gordon, H. Kim, M. A. Tanatar, R. Prozorov, andV. G. Kogan, Phys. Rev. B , 180501(R) (2010).[24] H. Kim, C. Martin, R. T. Gordon, M. A. Tanatar, J.Hu, B. Qian, Z. Q. Mao, Rongwei Hu, C. Petrovic, N.Salovich, R. Giannetta, and R. Prozorov, Phys. Rev. B , 180503R (2010).[25] E. D. Mun, S. L. Bud’ko, N. Ni, A. N. Thaler, and P. C.Canfield, Phys. Rev. B , 054517 (2009).[26] Lei Fang, Huiqian Luo, Peng Cheng, Zhaosheng Wang,Ying Jia, Gang Mu, Bing Shen, I. I. Mazin, Lei Shan,Cong Ren, and Hai-Hu Wen, Phys. Rev. B , 140508(R)(2009).[27] R. M. Fernandes and J. Schmalian, arXiv:1005.2174 (un-published).[28] S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes,D. K. Pratt, A. Thaler, N. Ni, S. L. Bud’ko, P. C. Can-field, J. Schmalian, R. J. McQueeney, and A. I. Goldman,Phys. Rev. Lett. , 057006 (2010).[29] R. T. Gordon, N. Ni, C. Martin, M. A. Tanatar,M. D. Vannette, H. Kim, G. Samolyuk, J. Schmalian,S. Nandi, A. Kreyssig, A. I. Goldman, J. Q. Yan,S. L. Bud’ko, P. C. Canfield, and R. Prozorov, Phys.Rev. Lett , 127004 (2009).[30] R. T. Gordon, C. Martin, H. Kim, N. Ni, M. A. Tanatar,J. Schmalian, I. I. Mazin, S. L. Bud’ko, P. C. Canfield,and R. Prozorov, Phys. Rev. B , 100506(R) (2009).[31] R. T. Gordon, H. Kim, M. A. Tanatar, R. Prozorov,V. G. Kogan, Phys. Rev. B , 180501(R) (2010).[32] V. G. Kogan, C. Martin, and R. Prozorov, Phys. Rev. B , 014507 (2009).[33] S. L. Bud’ko, N. Ni, and P. C. Canfield, Phys. Rev. B , 220516 (2009).[34] K. Gofryk, A. S. Sefat, M. A. McGuire, B. C. Sales, D.Mandrus, J. D. Thompson, E. D. Bauer, and F. Ronning,Phys. Rev. B , 184518 (2010).[35] M. A. Tanatar, J.-Ph. Reid, H. Shakeripour, X. G. Luo,N. Doiron-Leyraud, N. Ni, S. L. Bud’ko, P. C. Can-field, R. Prozorov, and L. Taillefer, Phys. Rev. Lett. ,067002 (2010).[36] J.-Ph. Reid, M. A. Tanatar, X. G. Luo, H. Shakeripour,N. Doiron-Leyraud, N. Ni, S. L. Bud’ko, P. C. Canfield,R. Prozorov, and Louis Taillefer, arXiv:1004.3804.[37] C. Martin, H. Kim, R. T. Gordon, N. Ni, V. G. Kogan,S. L. Bud’ko, P. C. Canfield, M. A. Tanatar, and R. Pro-zorov, Phys. Rev. B81