Unconventional multiband superconductivity with nodes in single-crystalline SrFe2(As_0.65P_0.35)2 as seen via 31P-NMR and specific heat
T. Dulguun, H. Mukuda, T. Kobayashi, F. Engetsu, H. Kinouchi, M. Yashima, Y. Kitaoka, S. Miyasaka, S. Tajima
aa r X i v : . [ c ond - m a t . s up r- c on ] M a r Unconventional multiband superconductivity with nodes in single-crystallineSrFe (As . P . ) as seen via P-NMR and specific heat
T. Dulguun, H. Mukuda,
1, 2, ∗ T. Kobayashi, F. Engetsu, H.Kinouchi, M. Yashima,
1, 2
Y. Kitaoka, S. Miyasaka,
3, 2 and S. Tajima
3, 2 Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan JST, TRIP (Transformative Research-Project on Iron-Pnictides), Chiyoda, Tokyo 102-0075, Japan Department of Physics, Graduate School of Science, Osaka University, Osaka 560-8531, Japan (Dated: November 7, 2018)We report P-NMR and specific heat measurements on an iron (Fe)-based superconductorSrFe (As . P . ) with T c =26 K, which have revealed the development of antiferromagnetic corre-lations in the normal state and the unconventional superconductivity(SC) with nodal gap dominatedby the gapless low-lying quasiparticle excitations. The results are consistently argued with an un-conventional multiband SC state with the gap-size ratio of different bands being significantly large;the large full gaps in s ± -wave state keep T c high, whereas a small gap with a nodal-structure causesgapless feature under magnetic field. The present results will develop an insight into the strongmaterial dependence of SC-gap structure in Fe-based superconductors. Superconductivity (SC) in the 122 iron-pnictides M Fe As ( M =Ba, Sr or Ca) can be induced by eitherelectron- or hole-doping, an application of pressure orchemical substitution for M , Fe, and As. The substi-tution of K +1 for Ba +2 in (Ba − x K x )Fe As (denotedas BaK122) suppresses antiferromagnetism (AFM) andstructural transition through the hole-doping, and in-duces SC with the relatively high superconducting tran-sition T c =38 K at x =0.4 [1]. Extensive experimentalworks in this compound have revealed the fully-gapped s ± -wave state [2–6]. The isovalent substitution of P forAs in BaFe (As − x P x ) (denoted as Ba122P) also ex-hibits the maximum of T c ∼
30 K at x =0.33, providinga phase diagram similar to BaK122 without changinga carrier density [7]. Notably, a nodal-gap structure inthe SC state has been reported by various experimentson Ba122P [7–12]. Relevant with this nodal-gap struc-ture, the P-NMR study on Ba122P [8] reported thegapless SC with a large fraction of residual quasiparticledensity of states (RDOS) N res at the Fermi level ( E F )with N res /N ∼ N is the DOS at E F innormal state. On the one hand, we note that a largefraction of N res /N ∼ As (Sr122) under highly hydro-static pressure[13]. It is therefore likely that the presenceof RDOS is inherent in the 122 iron-pnictides in whicha lattice contraction takes place by either the applica-tion of pressure or the chemical substitution of P for As.At the present, they are not clear which Fermi surfaces(FSs) are responsible for the existence of nodal-gap andwhy it exists there[12, 14–17].The replacement of either Sr or Ca for Ba site in M (As − x P x ) (Sr122P)resembles that for Ba122P[18], but a maximum T c de-creases to 26 K at x =0.35, and a maximum T c forCaFe (As − x P x ) (Ca122P) does to T c =15 K at x ∼ . M
122 iron-pnictides.In this paper, we present P-NMR results on singlecrystalline SrFe (As . P . ) (Sr122P) with T c =26 K,which unravels the development of AFM correlations inthe normal state and the unconventional gapless SC withnodes. Specific heat measurement in SC state revealsthat the fraction of RDOS at E F are mostly induced bythe external field. Although the low-lying quasiparticleexcitations are gapless in a small gap even when H =0, thefully-gapped s ± -wave state in other bands is not affectedsignificantly. Such multiband effect plays a significantrole in keeping T c relatively high in this compound.Single crystalline samples of SrFe (As − x P x ) ( x =0.35and x =0.5) were synthesized by self-flux method[7, 20].We used small pieces of single crystals that are supercon-ducting at T c =26 K for x =0.35 with a sharp transitionwidth ∆ T c < P-NMR measurement for x =0.35 wasperformed at fields H =1 ∼ c -axis using the aligned single crystalline samples. TheKnight shift K was measured with respect to a reso-nance field in H PO ( K =0 in Fig. 1). For comparison,these measurements were also performed on x =0.5 with T c =8 K in the overdoped regime.Figure 1 shows a temperature ( T ) dependence of P-NMR spectrum at H =14.0088 T for x =0.35. The NMRspectral shape does not change down to T c ( H )=23 Kwith a full-width at half maximum (FWHM) of 55 kHzat ∼
14 T and 250 K, which corresponds to ∆
K < . T c , its peak shifts to alow frequency side and the FWHM increases owing to theappearance of SC diamagnetism[8]. As indicated in theinset of the figure, K is nearly T -invariant in the nor-mal state, but decreases below T c ( H ). In the x =0.5, the (b)
30 K240 K180 K100 K50 K20 K10 K f ( MHz ) SrFe (As P ) K =0 (a) x=0.35x=0.5 K ( % ) T ( K ) T c( ) P - N M R I n t en s i t y ( a . u . ) FIG. 1: (Color online) (a) T dependence of P-NMR spec-tra for Sr122P( x =0.35) at H =14.0088 T. (b) T dependenceof Knight shift K , which is T -invariant, but decreases be-low T c ( H )=23 K. The K for x =0.5 is slightly smaller thanthat of x =0.35 in the normal state, which is attributed to thesubtle reduction of DOS at E F [21]. FWHM becomes 95 kHz at 100 K, being broader thanthat of x =0.35, due to the higher doping level. The K in the normal state is smaller than that of x =0.35, whichis attributed to the subtle reduction of DOS at E F , beingin good agreement with the result in Ba122P[21]. (b) SC t ( s ) 3 K12 K 20 K
170 K 110 K m ( t )
45 K(a) Normal
FIG. 2: (Color online) Nuclear spin-lattice relaxation rate1 /T was obtained from the recovery of nuclear magnetizationby fitting with a simple exponential recovery curve of m ( t ) =[ M − M ( t )] /M = exp( − t/T ) in (a) normal and (b) SC statefor x =0.35 at H ∼
14 T.
Nuclear spin-lattice relaxation rate 1 /T for both sam-ples was obtained from the recovery of nuclear magnetiza-tion by fitting with a simple exponential recovery curve of m ( t ) = [ M − M ( t )] /M = exp( − t/T ) for P ( I = 1 / M and M ( t ) are the respective nuclear magneti-zations of P for the thermal equilibrium condition andat a time t after the saturation pulse. Typical recovery Sr122P (x=0.5) ( H =14.5T) H = 2.9 T H = 14.0 T T (K) P - N M R - ( T T ) - ( s - K - ) Sr122P ( x =0.35 ) T c BaFe (As P ) ( T c = 30K) P-NMR
Nakai et al. Ba K Fe As ( T c = 38K) Fe-NMR
Yashima et al. ( T T ) - / ( T T ) - T = K FIG. 3: (Color online) T dependence of P-NMR ( T T ) − inthe normal state for Sr122P along with the results for Ba122Pwith T c =30 K[21] and for BaK122 with T c =38 K [4]. Here,the data for P( Fe)-NMR ( T T ) − in Ba122P(BaK122) arenormalized by the value at 250 K. Solid curve is a fit forSr122P( x =0.35) on the assumption of ( T T ) − = a/ ( T + θ )+ b with parameters a =8.7, b =0.38, and θ = − .
5, indicating thecloseness to the AFM QCP. curves of x =0.35 are presented for normal- and SC statein Figs. 2(a) and 2(b), respectively. The m ( t ) can bedetermined by a single component of T for both x =0.35and 0.5. Figure 3 shows the T dependence of P-NMR1 /T T in the normal state, which increases significantlyupon cooling down to T c . In general, 1 /T T is describedas, 1 T T ∝ X q | A q | χ ′′ ( q , ω ) ω , where A q is a wave-vector ( q )-dependent hyperfine-coupling constant, χ ( q , ω ) a dynamical spin suscepti-bility, and ω an NMR frequency. Since the Knightshift does not change in the normal state, the increaseof 1 /T T upon cooling is due to the development ofAFM correlations as well as the case in Ba122P[21] andBaK122[4]. We assume two-dimensional (2D) AFM cor-relations model that predicts a relation of 1 /T T ∝ χ Q ( T ) ∝ / ( T + θ ) when a system is close to an AFMquantum critical point (QCP)[22]. Here, the staggeredsusceptibility χ Q ( T ) with an AFM propagation vector q = Q follows a Curie-Weiss law. Since 1 /T T divergestowards T → θ = 0, θ is a measure of how closea system is to an AFM QCP. Actually, as shown by thesolid curve in Fig. 3, the T dependence of 1 /T T for x =0.35 can be fitted by assuming 1 /T T = a/ ( T + θ ) + b with parameters a =8.7, b =0.38, and θ = − . θ is nearly zero for x =0.35,indicating the closeness to the AFM QCP as well as inBa122P with a ∼ θ ∼ b ∼ TABLE I:
Superconducting characteristics and lattice param-eters for SrFe (As . P . ) (Sr122P)[18] along with thoseof Ba . K . Fe As (BaK122) [1] and BaFe (As . P . ) (Ba122P)[7, 8]. BaK122[1] Ba122P[7, 8] Sr122P( x =0.35)[18] T c [K] 38 30 26Type of SC Gap Full gapless gapless a [˚A] 3.917 3.92 3.92 † c [˚A] 13.3 12.8 12.23 † h Pn [˚A] 1.38 1.32 1.32 † † ) The values for x =0.35 are interpolated from the data in ref[18]. critical enhancement of 1 /T T disappears in x =0.5, asshown in Fig. 3.We address why the enhancement of 1 /T T at low T becomes distinct in going from Sr122P, Ba122P, toBaK122 as seen in Fig. 3. As listed in table I, the iso-valent substitution of P for As largely reduces the c -axislength and a pnictgen height ( h P n ), whereas the a -axislength remains constant, which may be equivalent to ap-plying an uniaxial stress along the c -axis for (Fe P n ) − layers. The band-structure calculation for Ba122P haspredicted that one of the hole FSs mainly derived fromthe XZ/Y Z/Z orbitals exhibits three dimensional (3D)features when h P n becomes lower in the 122 compounds,whereas the hole FS from X − Y orbital keeps a quasi-2D character[16]. Although the local lattice parametersof (Fe P n ) − resemble for both Ba122P and Sr122P, thereduction of c -axis length is more significant for Sr122P.In this context, appearance of three-dimensionality inthe electronic structure may cause the nesting of FSs toweaken in some of the multiple bands.Next, we present the SC characteristics inSr122P( x =0.35) with T c =26 K. Figure 4(a) showsa plot of P-NMR T ( T c ) /T versus T /T c for Sr122Palong with the results for Ba122P[8] with T c =30 Kand BaK122[4] with T c =38 K. The 1 /T s for Sr122P( x =0.35) decrease steeply below T c without a coherencepeak and follow a T -linear dependence below T /T c < H = 14 T. The 1 /T T normalized by the valueat T c remains a finite, as shown in Fig. 4(b). Althoughit shows a weak H dependence, it still remains a finiteeven in low H limit at T ∼ . T c , as seen in the inset ofFig. 4(b), pointing to a gapless SC dominated by a largecontribution of low-lying quasiparticle excitations at E F .It is in contrast with the power-law behavior without T -linear dependence in 1 /T in BaK122 despite of theapplication of high external field (12 T), which wasconsistently accounted for by the fully-gapped s ± -wavestate[4]. Generally, the 1 /T T in the gapless SC state isrelated to the square of RDOS at E F ( N ), and hencethe fraction of RDOS ( N res /N ) to a normal-state DOS -4 -3 -2 -1 Ba K Fe As Yashima et al. (
H ~
12 T)
BaFe (As P ) Nakai et al. ( H ~ 4 T) H = 1.0T H = 2.9T H = 14.0T ~ T (b) SrFe (As P ) ~ T T ( T c ) / T ~ T (a) ( T T ) - / ( T T ) - T = T c T / T c model B N ( E ) / N (c) ( E - E F ) / model A (d) ( E - E F ) / N res / N o H (T)
T~ 0.2T c FIG. 4: (Color online) (a) Plots of P-NMR T ( T c ) /T and(b) ( T T ) − / ( T T ) − T c versus T /T c for Sr122P along with thosefor Ba122P with T c =30 K [8] and BaK122 with T c =38 K[4]. Inset shows the H dependence of ( T T ) − / ( T T ) − T c at T ∼ . T c . Dotted and Solid curves are simulations on the as-sumption of (c) DOS for simple nodal gap with RDOS (modelA) and (d) DOS for multigap composed of a small nodal gapwith RDOS and full gaps (model B). In Sr122P, the model Bis appropriate (see the text). N is given by N res N = s ( T T ) − T → ( T T ) − T = T c . Using this relation, it is deduced that N res /N is approx-imately 0.72 when H = 14 T. Although the 1 /T T doesnot exhibit a constant at low temperatures when H < T ∼ . T c , the N res /N sare as large as 0.56 and 0.66 in H =1 T and 2.9 T, re-spectively, being much larger than N res /N ∼ H ∼ N res /N =0 forfully gapped SC in BaK122[4]. The H dependence ofRDOS in this compound is discussed by specific heatmeasurements later. The solid curves in Figs. 4(a) and4(b) are simulations when we assume two possible SC-gap models: (A) single nodal gap of ∆( φ ) = ∆ sin(2 φ )with N res /N (denoted as model A), which was tenta-tively assumed for Ba122P[8], and (B) multigap withthe fully gapped s ± -wave state in some bands[4] andgapless in other bands under H (model B), which re-produce the T dependence of 1 /T in the gapless SCstate. The simulations based on the respective modelsA and B for Sr122P(Ba122P[8]) are shown by the dot-ted curves with parameters of 2∆ ∼ k B T c (6 k B T c )and N res /N =0.72(0.34) and by the solid curves withparameters of 2∆ L ∼ k B T c (6 k B T c ) for bands withfull gaps and a smearing factor of DOS η = 0 . L assumed in BaK122[4] besides the gapless band with N res /N =0.72(0.34). The assumed DOS for the model Aand B are indicated in Figs. 4(c) and 4(d), respectively. BaFe (As P ) ( T J.S.Kim et al. C / T ( m J / K / m o l ) H ( T )SrFe (As P ) T= 1.8 K T 0
FIG. 5: Field dependence of specific heat C ( T ) /T at 1.8 Kand the γ ( ≡ lim T → C ( T ) /T ) estimated from the T depen-dence of C ( T ) /T above 1.8 K[20]. The solid curves are afitting with the function of H α ( α ∼ . C ( T ) /T at T → (As . P . ) [10]. To reveal the origin of the RDOS, we present the fielddependence of the specific heat C ( T ) /T at 1.8 K and theresidual γ ( ≡ lim T → C ( T ) /T ) extrapolated to T = 0 Kby fitting with C ( T ) /T = γ + βT + δT in Fig. 5[20].The result reveals that γ is proportional to ∼ H . for0 < H <
14 T, indicating that the low-energy quasi-particle excitation is dominated by the nodal gap. Thesignificant difference from the H . dependence expectedin the d -wave line node gap state suggests the multi-band effect with the unequal sizes of gaps[24], in addi-tion to the Doppler shift of the quasiparticle energy inthe vortex state, as seen in Ba122P [8, 9, 11, 23]. Using γ n ≡ C ( T c ) /T c ∼
28 mJ/ (mol K ) at T c , the fractionof RDOS was estimated to be ∼
60% of N in the ap-plication of H =14 T, which is roughly consistent with the result obtained by the P-NMR experiment. Evenwhen H = 0 without vortices, the residual γ that derivesfrom the impurity scattering remains ∼ )at T =0 K [20], corresponding to γ/γ n ∼ P-NMR linewidths, the low-energyquasiparticle DOS in the nodal gap is sensitively inducedeven by very small amount of impurity scattering. Thisbehavior is in contrast with the case of BaK122 ( T c = 38K) characterized by a fully gaped SC state, where the ap-plication of field of H = 6 ∼
12 T does not induce suchlow-energy quasiparticle excitation [4, 25]. It is thereforelikely that the presence of RDOS is inherent in the 122iron-pnictides in which a lattice contraction takes placeby either the chemical substitution of P for As or the ap-plication of pressure. The results are consistently arguedwith the multigap feature that possess a large gap-sizeratio ∆ L / ∆ S of a large gap (∆ L ) to a small gap (∆ S ).Here, we remind the well-established cases of the multi-band SC with a large gap-size ratio ∆ L / ∆ S ∼
3, whichwas demonstrated in MgB [26] and NbSe [27]. Even inthese conventional s-wave superconductors, low-lying ex-citations are induced due to the delocalization of quasi-particles within the vortices at significantly low fields at ∼ H c /
10. The rapid increase in N res /N at low H inthese compounds is a consequence of the small magni-tude of the second gap and the associated small conden-sation energy. Likewise, in Sr122P, it might be expectedthat the large fractional RDOS is promptly induced byfields sufficiently smaller than H c ∼
70 T[28]. It canbe attributed to that the presence of a small gap withnodes causes the quasiparticles within the vortices to bemore significantly delocalized than in conventional fully-gapped superconductors. In this context, it is a multi-gap effect with a gap-size ratio of different bands beingsignificantly large to induce the large contribution forthe gapless low-lying quasiparticle excitations in the SCstate for Sr122P. Under these situations, we claim thatthe model B (Fig. 4(d)), which deals with the multigapsystem, is appropriate for Sr122P, although both modelsseem to be able to reproduce the experimental results.Such multiband scenario gives a reasonable explanationfor the fact that T c = 26 K of Sr122P is still relativelyhigh irrespective of the gapless SC state in some of themultiple bands, which may be characteristic for P-doped122 compounds.Finally, in order to shed light on an origin of thesmall gap with nodes, we compare the SC characteris-tics and the lattice parameters for Sr122P, Ba122P andBaK122 in Table I. The fully-gapped s ± -wave state inBaK122 is characterized by the largest c -axis length andthe highest h P n , whereas the gapless SC state in Sr122Pis by the lowest h P n and the reduction of c -axis length,which is more significant than in others. Actually, theresidual DOS was more prominent in Sr122P than inBa122P[8, 10, 11, 20], as seen via both the NMR andthe specific heat measurements, implying that the por-tion of the Fermi surfaces with RDOS becomes large ingoing from Ba122P to Sr122P. According to the band-structure calculation for Ba122P, the orbital characterof one of the hole sheets is very sensitive to h P n whenAs is substituted by P in 122 compounds, and pointedout that 3D nodal structures appear in a largely-warpedhole FS having a strong Z /XZ/Y Z orbital characterin Ba122P[16], which was supported experimentally byARPES[17]. Since more prominent 3D feature in elec-tronic structure may be anticipated in Sr122P than inBa122P, as corroborated by the normal-state propertiesdiscussed above, it is possible that the origin of a nodal-structure in some of the multiple bands is ascribed tothe largely-warped Fermi surface. In particular, the im-portant point on the scenario is that the fully-gapped s ± -wave state in the other quasi-2D bands keeps T c still highthrough the interband scattering between quasi-2D elec-tron and hole FSs within the k x - k y plane in associationwith the multiband SC nature[16]. In other context, themonotonous decrease of the maximum T c from BaK122,Ba122P, Sr122P, to Ca122P is probably due to the de-crease of the total SC condensation energy for the fully-gapped s ± -wave state due to the worse nesting propertiesin some of the multiple bands. Another possible scenariofor a nodal gap structure is the closed nodal loops locatedat the flat parts of the electron Fermi surface, which wasproposed in Ba122P by Yamashita et al. [12]. To revealthe strong material dependence of SC-gap structure inFe-based superconductors, the further systematic stud-ies on 122 compounds are desired to focus on the rela-tion between the local structure of Fe P n layer and thegap structure.In summary, the P-NMR and specific heat measure-ments on single crystallines SrFe (As . P . ) (Sr122P)have revealed an unconventional gapless SC with nodes,which is accounted for by the multiband feature with thegap-size ratio of different bands being significantly large.The normal-state property is dominated by the devel-opment of antiferromagnetic correlations pointing to thecloseness to an antiferromagnetic quantum critical pointfor x =0.35. However, the comparison between the other122 compounds reveals the reduction of AFM correla-tions in Sr122P, implying the worse nesting property insome of multiple bands due to three-dimensional feature,which is suggested in Ba122P by the band-calculationand ARPES results[16, 17]: The three-dimensionality ap-pears in the largely warped hole Fermi surface, whereasthe other quasi-two dimensional electron and hole Fermisurfaces within the k x - k y plane is not significantly mod-ified. If we assume the nodal gap on the largely warpedhole Fermi surface, this scenario gives a reasonable ex-planation for relatively high T c regardless of the gaplessfeature in this compound, where the interband scatteringwithin the quasi 2D bands stabilizes the fully-gapped s ± - wave state. The present results in association with themultiband nature will develop an insight into the strongmaterial dependence of SC-gap structure in Fe-based su-perconductors. We thank K. Kuroki, S. Kawasaki, T. Yoshida, and K. 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