Nodal superconductivity in Ba(Fe 1−x Ru x ) 2 As 2 induced by isovalent Ru substitution
X. Qiu, S. Y. Zhou, H. Zhang, B. Y. Pan, X. C. Hong, Y. F. Dai, Man Jin Eom, Jun Sung Kim, S. Y. Li
aa r X i v : . [ c ond - m a t . s up r- c on ] J u l Nodal superconductivity in Ba(Fe − x Ru x ) As induced by isovalent Ru substitution X. Qiu, S. Y. Zhou, H. Zhang, B. Y. Pan, X. C. Hong, Y. F. Dai, Man Jin Eom, Jun Sung Kim, S. Y. Li , ∗ Department of Physics, State Key Laboratory of Surface Physics,and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, China Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Korea (Dated: November 11, 2018)We present the ultra-low-temperature heat transport study of an iron-based superconductorBa(Fe . Ru . ) As ( T c = 20.2 K), in which the superconductivity is induced by isovalent Rusubstitution. In zero field we find a large residual linear term κ /T , more than 40% of the normal-state value. At low field, the κ /T shows an H / dependence. These provide strong evidences fornodes in the superconducting gap of Ba(Fe . Ru . ) As , which mimics that in another isovalentlysubstituted superconductor BaFe (As − x P x ) . Our results show that the isovalent Ru substitutioncan also induce nodal superconductivity in BaFe As , as P does, and they may have the same origin.We further compare them with other two nodal superconductors LaFePO and LiFeP. PACS numbers: 74.70.Xa, 74.25.fc, 74.20.Rp
Since the discovery of high- T c superconductivity iniron-based compounds [1, 2], the electronic pairing mech-anism has been a central issue [3]. One key to understandit is to clarify the symmetry and structure of the super-conducting gap [4]. However, even for the most studied(Ba,Sr,Ca,Eu)Fe As (122) system, the situation is stillfairly complex [4].Near optimal doping, for both hole- and electron-doped 122 compounds, the angle-resolved photon emis-sion spectroscopy (ARPES) experiments clearly demon-strated multiple nodeless superconducting gaps [5, 6],which was further supported by bulk measurements suchas thermal conductivity [7–9]. On the overdoped side,nodal superconductivity was found in the extremely hole-doped KFe As [10, 11], while strongly anisotropic gap[9], or isotropic gaps with significantly different magni-tude [12, 13] were suggested in the heavily electron-dopedBa(Fe − x Co x ) As . On the underdoped side, recent heattransport measurements claimed possible nodes in the su-perconducting gap of hole-doped Ba − x K x Fe As with x < − x Co x ) As [9].Intriguingly, nodal superconductivity was also foundin BaFe (As − x P x ) ( T c = 30 K) [15, 16], in whichthe superconductivity is induced by the isovalent P sub-stitution for As. The laser-ARPES experiments onBaFe (As . P . ) showed isotropic gaps in the threehole pockets around the Brillouin zone (BZ) center,therefore the gap nodes must locate on the electron pock-ets around the BZ corners [17]. Moreover, previouslyLaFePO ( T c ∼ T c ∼ As slabs of iron arsenides shown in Fig. 1,instead of substituting As with P, there is an alternativeway for isovalent substitution, to substitute Fe with Ru.Indeed, superconductivity with T c up to 20 K was foundin Ba(Fe − x Ru x ) As [26] and Sr(Fe − x Ru x ) As [27].The phase diagram of Ba(Fe − x Ru x ) As is very simi-lar to that of BaFe (As − x P x ) [28, 29]. The ARPESmeasurements on Ba(Fe . Ru . ) As showed that Ruinduces neither hole nor electron doping, but the hole andelectron pockets are about twice larger than in BaFe As [30]. To investigate the superconducting gap structure inthese Ru-substituted superconductors may help to solveabove puzzle of P substitution.In this Letter, we report the demonstration ofnodal superconductivity in optimally substitutedBa(Fe . Ru . ) As by thermal conductivity mea-surements down to 50 mK. Our finding shows thatthe nodal superconducting states in P-substituted ironarsenides are not that special, and suggests a commonorigin of the nodal superconductivity induced by isova-lent substitutions, at least in Ba(Fe − x Ru x ) As andBaFe (As − x P x ) .Single crystals of optimally substitutedBa(Fe . Ru . ) As were grown using a self-fluxmethod [31]. Plate-shaped crystals with shiny surfaceswere extracted mechanically. The Ru substitutinglevel was determined by energy dispersive X-ray spec-troscopy. The dc magnetic susceptibility was measuredat H = 10 Oe, with zero-field cooled, using a SQUID(MPMS, Quantum Design). The sample was cleavedto a rectangular shape of dimensions 1.50 × in the ab -plane, with 70 µ m thickness along the c -axis. Contacts were made directly on the samplesurfaces with silver paint, which were used for bothresistivity and thermal conductivity measurements. Thecontacts are metallic with typical resistance 200 mΩat 1.5 K. In-plane thermal conductivity was measuredin a dilution refrigerator, using a standard four-wire FIG. 1: (Color online). Crystal structure of BaFe As . Thereare two ways for isovalent substitution in the Fe As slabs,substituting As with P, or Fe with Ru. Both substitutionscan induce superconductivity, and result in similar phase di-agrams. steady-state method with two RuO chip thermometers,calibrated in situ against a reference RuO thermometer.Magnetic fields were applied along the c -axis. To ensurea homogeneous field distribution in the sample, all fieldswere applied at temperature above T c .Fig. 2a shows the in-plane resistivity ρ ( T ) of ourBa(Fe . Ru . ) As single crystal. The magnitude andshape of ρ ( T ) are consistent with previous report [28].The normalized magnetization was plotted in the in-set, which displays a nice superconducting transitionat about 20 K. According to the phase diagram ofBa(Fe − x Ru x ) As [28, 29], no static magnetic order ex-ists in our optimally substituted sample. The resistivitydata between 30 and 90 K are fitted to ρ ( T ) = ρ + AT n ,which gives a residual resistivity ρ = 43.7 ± µ Ωcmand n = 1.31 ± ρ ( T ) is similar to that observed inBaFe (As − x P x ) near optimal substitution, which mayreflet the presence of antiferromagnetic spin fluctuationsnear a quantum critical point [32].The low-temperature part of ρ ( T ) is plotted in Fig.2b. The zero-resistance point of the resistive tran-sition is at T c = 20.2 K, which is in good agree-ment with the diamagnetic superconducting transitionshown in the inset of Fig. 2a. To estimate the up-per critical field H c , the resistivity in H = 3, 6, 9,and 14.5 T with H || c were also measured, as seen inFig. 2b. Fig. 2c shows the temperature dependenceof H c , defined by ρ = 0 and ρ = 0 . ρ N , respec-tively. For comparison, the H c ( T ) of the electron-dopedBa(Fe . Co . ) As single crystal with T c ≈
22 K is re-produced from ref. [33]. One can see that although the T c of our Ba(Fe . Ru . ) As is only slightly lower thanBa(Fe . Co . ) As , its H c ( T ) is significantly lower. ForBa(Fe . Co . ) As , extrapolation of the H c ( T ) datasuggests H c (0) between 40 and 50 T, much larger thanthat obtained from Werthamer-Helfand-Hohenberg for-mula H W HHc (0) = − . T c dH c /dT | T = T c [33]. For our H = 14.5 H = 9 H = 6 H = 3 H = 0 T (b) r ( mW c m ) T (K) zero 10%10% Ba(Fe Co ) As Ba(Fe Ru ) As Ba(Fe Ru ) As (c) H c ( T ) T (K) (a) r ( mW c m ) T (K) - M / M ( K ) FIG. 2: (Color online). (a) In-plane resistivity ofBa(Fe . Ru . ) As single crystal. The solid line is a fitof the data between 30 and 90 K to ρ ( T ) = ρ + AT n . Inset:normalized magnetization. (b) Low-temperature resistivityin H = 0, 3, 6, 9, and 14.5 T with H || c . (c) Temperaturedependence of the upper critical field H c . The squares andcircles represent H c of Ba(Fe . Ru . ) As defined by ρ = 0and ρ = 0 . ρ N , respectively. The triangles represent H c ofBa(Fe . Co . ) As with T c ≈
22 K [33].
Ba(Fe . Ru . ) As , H W HHc (0) ≈ H c (0).We can only roughly estimate the bulk H c (0) ≈
23 T,defined by ρ = 0, by linearly extrapolating the data be-tween 6 and 14.5 T in Fig. 2c. Note that a slightlydifferent H c (0) does not affect our discussion below.Fig. 3 shows the temperature dependence of the in-plane thermal conductivity for Ba(Fe . Ru . ) As in H = 0, 1, 2, 4, 6, 9, and 12 T magnetic fields, plottedas κ/T vs T . All the curves are roughly linear, as pre-viously observed in BaFe . Ni . As [8], KFe As [10],and overdoped Ba(Fe − x Co x ) As single crystals [9, 12].Therefore we fit all the curves to κ/T = a + bT α − with α fixed to 2. The two terms aT and bT α represent contri- L / r H = 12 H = 9 H = 6 H = 4 H = 2 H = 1 H = 0 T k / T ( m W / K c m ) T (K)
FIG. 3: (Color online). Low-temperature in-plane thermalconductivity of Ba(Fe . Ru . ) As in magnetic fields ap-plied along the c -axis ( H = 0, 1, 2, 4, 6, 9 and 12 T). Thesolid lines are κ/T = a + bT fit to all the curves, respectively.The dash line is the normal-state Wiedemann-Franz law ex-pectation L / ρ , with L the Lorenz number 2.45 × − WΩK − and ρ = 43.7 µ Ωcm. butions from electrons and phonons, respectively. Herewe only focus on the electronic term.In zero field, the fitting gives a residual linear term κ /T = 0.266 ± − cm − . This valueis more than 40% of the normal-state Wiedemann-Franz law expectation κ N /T = L / ρ = 0.56 mW K − cm − , with L the Lorenz number 2.45 × − WΩK − and ρ = 43.7 µ Ωcm. For another isovalently substi-tuted BaFe (As . P . ) single crystal, similar value of κ /T ≈ − cm − was obtained, which is about30% of its normal-state κ N /T [16]. The significant κ /T of Ba(Fe . Ru . ) As in zero field is a strong evidencefor nodes in the superconducting gap [34].The field dependence of κ /T may provide furthersupport for the nodes [34]. In Fig. 4, the normal-ized ( κ /T ) / ( κ N /T ) of Ba(Fe . Ru . ) As is plottedas a function of H/H c , with the normal-state κ N /T = 0.56 mW K − cm − and bulk H c = 23 T. Simi-lar data of the clean s -wave superconductor Nb [35], anoverdoped d -wave cuprate superconductor Tl-2201 [36],and BaFe (As . P . ) [16] are also plotted for com-parison. For a nodal superconductor in magnetic field,delocalized states exist out the vortex cores and dom-inate the heat transport in the vortex state, in con-trast to the s -wave superconductor. At low field, theDoppler shift due to superfluid flow around the vorticeswill yield an H / growth in quasiparticle density ofstates (the Volovik effect [37]), thus the H / field depen-dence of κ /T . From Fig. 4, the behavior of κ ( H ) /T inBa(Fe . Ru . ) As clearly mimics that in Tl-2201 andBaFe (As . P . ) . In the inset of Fig. 4, the κ ( H ) /T of Ba(Fe . Ru . ) As obeys the H / dependence atlow field, which supports the existence of nodes in the Tl2201 Ba(Fe Ru ) As Nb BaFe (As P ) ( k / T ) / ( k N / T ) H/H c2 ( k / T ) / ( k N / T ) (H/H c2 ) FIG. 4: (Color online). Normalized residual linear term κ /T of Ba(Fe . Ru . ) As as a function of H/H c . Sim-ilar data of the clean s -wave superconductor Nb [35], anoverdoped d -wave cuprate superconductor Tl-2201 [36], andBaFe (As . P . ) [16] are also shown for comparison. Thebehavior of κ ( H ) /T in Ba(Fe . Ru . ) As clearly mimicsthat in Tl-2201 and BaFe (As . P . ) . Inset: the samedata of Ba(Fe . Ru . ) As and Tl-2201 plotted against( H/H c ) / . The lines represent the H / dependence. superconducting gap.To our knowledge, previously there are five iron-based superconductors displaying nodal superconductiv-ity, KFe As [10, 11], underdoped Ba − x K x Fe As ( x < (As − x P x ) [15, 16], LaFePO [18–20],and LiFeP [21]. Here we only consider the “in-planenodes”, not counting the “ c -axis nodes” in underdopedand overdoped Ba(Fe − x Co x ) As as suggested by c -axisheat transport experiments [38]. For the extremely hole-doped KFe As , the nodal superconductivity may resultfrom the intraband pairing via antiferromagnetic fluc-tuations, due to the lack of electron pockets [10]. Forunderdoped Ba − x K x Fe As , it is still not clear howthe superconducting gap transforms from nodeless tonodal at x ≈ .
16 [14]. The rest three compounds,BaFe (As − x P x ) , LaFePO, and LiFeP, have stimulatedvarious interpretations of the effect of isovalent P substi-tution on the superconducting gap structure [22–25].Our new finding of nodal superconductivity inBa(Fe . Ru . ) As reveals the similarity between theisovalently Ru- and P-substituted iron arsenides, there-fore the P substitution is not that special for inducingnodal superconductivity. In this sense, the mystery ofP substitution in iron-based superconductors has beenpartially unwrapped. What next one needs to do is tofind out whether there is a common origin for the nodalsuperconductivity in these isovalently substituted com-pounds.Due to the smaller size of P ion than As ion, one com-mon structural feature of the P-substituted compoundsis the decrease of pnictogen height and increase of As-Fe-As angle [32, 40, 41]. The substitution of larger Ru ionfor Fe ion in Ba(Fe − x Ru x ) As results in the increaseof a lattice parameter and decrease of c lattice parame-ter, thus the decrease of pnictogen height and increase ofAs-Fe-As angle too [28]. Therefore, both the P and Rusubstitutions cause the same trend of structure change iniron arsenides.LaFePO and LiFeP belong to the “1111” and “111”systems, respectively, and the P ions have fully substi-tuted As ions in LaFeAsO and LiFeAs. This is differentfrom the partial P and Ru substitution in superconduct-ing BaFe (As − x P x ) and Ba(Fe − x Ru x ) As . In fact,both the fully substituted BaFe P and BaRu As arenonsuperconducting [42, 43]. Another difference is themuch lower T c of LaFePO and LiFeP, 6 and 4.5 K, re-spectively. For LaFePO, Kuroki et al. have attributedthe low- T c nodal pairing to the lack of Fermi surface γ around ( π, π ) in the unfolded Brillouin zone, due to thelow pnictogen height [22]. Hashimoto et al. also relatedthe nodal superconductivity in LiFeP to the pnictogenheight [21].For Ba(Fe − x Ru x ) As and BaFe (As − x P x ) , thesubstitutions start from the same parent compoundBaFe As , and result in similar phase diagrams [28, 29].The highest T c at optimal substitution, 20 and 30 K, arealso close. Furthermore, the Fermi surface structures areroughly similar, with hole pockets around BZ center andelectron pockets around BZ corners [17, 30]. All thesesimilarities suggest that the origin of the nodal supercon-ductivity in Ba(Fe − x Ru x ) As and BaFe (As − x P x ) may be the same. Suzuki et al. have proposed three-dimensional nodal structure in the largely warped holeFermi surface and no nodes on the electron Fermi surface[25]. However, these seem inconsistent with the ARPESresults, which have constrained the nodes on the electronpockets [17]. More careful considerations of the struc-tural parameters, band structure, and local interactionsare needed to clarify whether there is a common originfor the nodal superconductivity in all these isovalentlysubstituted iron arsenides.In summary, we have measured the thermal conductiv-ity of Ba(Fe . Ru . ) As single crystal down to 50 mK.A large κ /T at zero field and an H / field dependenceof κ ( H ) /T at low field give strong evidences for nodalsuperconductivity in Ba(Fe . Ru . ) As . Comparingwith previous P-substituted iron arsenides, our new find-ing suggest that the nodal superconductivity induced byisovalent substitutions may have the same origin, at leastin Ba(Fe − x Ru x ) As and BaFe (As − x P x ) . Findingout this origin will be important for getting a completeelectronic pairing mechanism of the iron-based high- T c superconductors.This work is supported by the Natural ScienceFoundation of China, the Ministry of Science andTechnology of China (National Basic Research Pro-gram No: 2009CB929203), Program for New Century Excellent Talents in University, Program for Professorof Special Appointment (Eastern Scholar) at ShanghaiInstitutions of Higher Learning, and STCSM of China(No: 08dj1400200 and 08PJ1402100). ∗ E-mail: shiyan [email protected] [1] Y. Kamihara et al. , J. Am. Chem. Soc. , 3296 (2008).[2] J. Paglione and R. L. Greene, Nature Physics , 645(2010).[3] Fa Wang and Dung-hai Lee, Science , 200 (2011).[4] P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin,arXiv:1106.3712, and references therein.[5] H. Ding et al. , EPL , 47001 (2008).[6] K. Terashima et al. , Proc. Natl. Acad. Sci. , 7330(2009).[7] X. G. Luo et al. , Phys. Rev. B , 140503(R) (2009).[8] L. 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