Superconducting energy gap and c-axis plasma frequency of (Nd,Sm)O0.82F0.18FeAs superconductors from infrared ellipsometry
A. Dubroka, K. W. Kim, M. Roessle, V.K. Malik, R. H. Liu, G. Wu, X. H. Chen, C. Bernhard
aa r X i v : . [ c ond - m a t . s up r- c on ] M a y ??? Superconducting energy gap and c -axis plasma frequency of (Nd,Sm)O . F . FeAssuperconductors from infrared ellipsometry
A. Dubroka, K. W. Kim, M. R¨ossle, V.K. Malik, R. H. Liu, G. Wu, X. H. Chen, and C. Bernhard ∗ University of Fribourg, Department of Physics and Fribourg Center for Nanomaterials,Chemin du Musee 3, CH-1700 Fribourg, Switzerland Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics,University of Science and Technology of China, Hefei, Anhui 230026, China (Dated: October 25, 2018)We present ellipsometric measurements of the far-infrared dielectric response of polycrystallinesamples of the new pnictide superconductor R O . F . FeAs ( R =Nd and Sm). We find evidencethat the electronic properties are strongly anisotropic such that the optical spectra are dominated bythe weakly conducting c -axis response similar as in the cuprate high-temperature superconductors(HTSC). Accordingly, we obtain an upper limit of the c -axis superconducting plasma frequency of ω SCpl ,c ≤
260 cm − which corresponds to a lower limit of the c -axis magnetic penetration depth of λ c ≥ µ m and an anisotropy of λ c /λ ab ≥
30 as compared to λ ab = 185 nm from muon spin rotation[A. Drew et al. , cond-mat/0805.1042]. Also in analogy to the cuprate HTSC, our spectra exhibit thesignatures of a gap-like suppression of the conductivity in the superconducting state with a largegap magnitude of 2∆ ≈
300 cm − (37 meV) and a ratio of 2∆ /k B T c ≈ PACS numbers: 74.70.-b, 78.30.-j, 74.25.Gz
The recent observation of superconductivity (SC) withcritical temperatures, T c , up to 55 K in the layeredtetragonal pnictide R O − x F x FeAs with R = La, Nd, Pr,Gd, and Sm marks the first discovery of a non copper-oxide-based layered high T c superconductor (HTSC)[1, 2, 3]. It raises the question whether a common pairingmechanism is responsible for HTSC in both the cupratesand the pnictides. Similar like the cuprates, the pnictideshave a layered structure that is comprised of alternat-ing FeAs and LaO sheets with Fe arranged on a squarelattice [1]. Theoretical calculations predict a quasi two-dimensional electronic structure with metallic FeAs lay-ers and LaO layers that mainly act as blocking layers andas charge reservoir upon chemical substitution [4, 5, 6].Also in analogy to the cuprates, SC emerges upon dopingaway from a magnetic mother compound, the maximal T c occurring just as magnetism disappears [7, 8, 9, 10].There are also some clear differences with respect to thecuprates. Band structure calculations suggest that thepnictides are multiband superconductors with up to fiveFeAs-related bands crossing the Fermi-level [4, 5, 6, 11] asopposed to the cuprates which, due a strong Jahn-Tellerdistortion, have only one relevant Cu(3 d x − y )O band.Furthermore, in these pnictides the highest T c values areachieved upon electron doping and not for hole doping[12] as in the cuprates [13].Further progress in assessing the differences and sim-ilarities of these cuprate and pnictide superconduc-tors requires experimental information especially abouttheir electromagnetic properties. The research into thecuprate HTSC has shown that infrared spectroscopy canplay an important role since it provides fairly direct andreliable information about the electronic properties in the normal state as well as in the SC state [14, 15].Even measurements on polycrystalline samples yieldedfirst important information. In particular, it was estab-lished that thanks to the very large electronic anisotropyof the cuprates, the pronounced features of the reflectiv-ity spectra are representative of the weakly conducting c -axis response. The metallic ab -plane component merelygives rise to a moderate increase of the overall magnitudeof the conductivity with respect to the one of c -axis com-ponent [14, 15, 16, 17, 18, 19]. This interpretation hasbeen confirmed by direct measurements of the in-planeand c -axis response on single crystals [15, 17]. Accord-ingly, measurements on polycrystals can provide reliableinformation, for example on the eigenfrequency of the c -axis phonon modes, the upper limit of the c -axis plasmafrequency of the SC condensate, ω SCpl , and the magnitudeof the SC energy gap, ∆ [14, 15, 16, 17, 18, 19].Concerning the optical properties of the pnictides,so far only few reports have been reported on theundoped mother compound [20] and superconductingLaO . F . FeAs [21, 22] which did not detail the impactof SC on the dielectric function.In this letter we present ellipsometric measurementsof the far-infrared dielectric response of polycrystallinesamples of R O . F . FeAs with R = Nd and Sm and T c = 52(2) and 45(3) K, respectively. In the first place,our data reveal that the electronic properties are stronglyanisotropic, similar to the cuprate HTSC. From our datawe thus obtain an upper limit of the c -axis SC plasmafrequency of ω SCpl ,c ≤
260 cm − and a magnetic penetra-tion depth of λ c ≥ µ m, compared with the in-planevalues of λ ab = 185 nm and ω SCpl ,ab ≈ − frommuon spin rotation measurements [23, 24]. In addition, SmOFFA d c [ m c m ] T [K]NdOFFA
FIG. 1: Temperature dependent resistivity of the polycrys-talline NdO . F . FeAs and SmO . F . FeAs samples. our data show that the magnitude of the SC energy gapis 2∆ = 300 cm − with a ratio of 2∆ /k B T c ≈ . F . FeAs (NdOFFA) and SmO . F . FeAs(SmOFFA) have been synthesized by conventional solidstate reaction methods as described in Refs. [2, 7]. Stan-dard powder x-ray diffraction patterns were measuredwhere all peaks could be indexed to the tetragonalZrCuSiAs-type structure. dc resistivity (see Fig. 1) andmagnetisation measurements were made to determine themidpoint (10% to 90% width) of the resistive and dia-magnetic transitions T c (∆ T c ) of 52(3) K for NdOFFAof 45(3) for SmOFFA. The samples were polished usingdiamond suspension to obtain flat and shiny surfaces.While the surfaces were certainly not perfectly mirror-like, the material had a high density and did not giverise to significant depolarisation effects as confirmed byUV ellipsometry measurements.The infrared ellipsometry measurements in the range45 to 640 cm − (5 - 80 meV) were performed with ahome-built setup attached to a Bruker 113V Fast-Fourierspectrometer as described in Ref. [25]. The angle of inci-dence of the polarised light was 80 ◦ . Ellipsometry enablesone to directly measure the complex dielectric function,˜ ǫ ( ω ) = ǫ ( ω ) + i ǫ ( ω ), and the related optical conductiv-ity ˜ σ ( ω ) = − i ωǫ (˜ ǫ ( ω ) − σ ( ω ), and Fig. 2(c) the corresponding realpart of the dielectric function, ǫ ( ω ), while Figs. 2(b)and 2(d) detail the SC induced changes. The inset ofFig. 2(a) shows the calculated reflectivity spectra whichagree well with previously reported ones [20, 22]. It is im-mediately evident from our data that the electronic part of the optical response is extremely weak. The most pro-nounced features are indeed due to the infrared-activephonon modes which give rise to pronounced, narrowpeaks near 102, 257, 270 and 440 cm − . The electronicpart of σ ( ω ) has a surprisingly small magnitude of lessthan 100 Ω − cm − and there is only a very weak sig-nature of an inductive response in ǫ ( ω ), which becomesnegative only below 300 cm − . We note that very similaroptical data have been obtained on four correspondingsamples which contained Sm and La instead of Nd.This weakly conducting behaviour needs to be rec-onciled with the metallic dc transport with ρ dc =0 .
35 mΩcm and σ dc = 2800 Ω − cm − at 60 K (the Nd-OFFA sample) and also with the short in-plane magneticpenetration depth of λ ab = 185 −
235 nm and thus size-able SC plasma frequency of ω SCpl ,ab ≈ − − as obtained from muon spin rotation (in parts on thesame samples) [23, 24]. The explanation of this puzzlingbehaviour can be found in the literature on the earlier in-frared studies on polycrystalline samples of the cuprateHTSC [16, 18, 27]. Very similar trends were observedhere, that are meanwhile well understood in terms of thevery strong electronic anisotropy of the electronic trans-port parallel and perpendicular to the conducting CuO planes which are separated by various kinds of essentiallyinsulating blocking layers. Notably, it was found thatthe infrared spectra on polycrystalline samples are domi-nated by the characteristic features of the nearly insulat-ing c -axis response. The overall conductivity of the elec-tronic background was found [16] to be much lower thanthe dc conductivity as measured by transport. For exam-ple in La − x Sr x CuO [18] the dc extrapolation of σ ( ω )right above T c yields values of at most 200 Ω − cm − ,whereas transport measurements on polycrystals give dcconductivities of 10 − Ω − cm − [27]. To the con-trary, for isotropic crystalline materials like the mangan-ite perovskites, it is well known that the dc conductivityinferred from infrared data on polycrystals is systemat-ically higher than the corresponding values from trans-port measurements which are decreased by grain bound-ary effects [28]. The previous works on polycrystalline[18, 19] and single crystalline samples [15, 17] of thecuprate HTSC have also shown that many aspects ofthe far-infrared c -axis dielectric function can be reliablydeduced from measurements on polycrystalline samples.This includes besides the infrared active phonon modes,the magnitude of the SC energy gap, and the upper limitof the plasma frequency of the c -axis SC condensate [14].Returning to the pnictide superconductors, our in-frared data thus highlight a very strong anisotropy ofthe electronic responses parallel and perpendicular to theFeAs layers. Furthermore, they enable us to extract im-portant information about the c -axis response of thesenew superconductors. As outlined below, we can obtainthe magnitude of the SC energy gap and also a reliablelower limit of the anisotropy of the SC magnetic pene- ( K ) - ( K ) [ - c m - ] wavenumber [cm -1 ] ~ 300 cm -1 NdOFFA wavenumber [cm -1 ] (b) NdOFFA SC ~2 [ - c m - ]
40K 10K (a) * R [cm -1 ]
10K 55K wavenumber [cm -1 ]
300 K10 K180 K40 K55 K100 K (c)
SmOFFA
NdOFFA ( c m - ) T [K]
NdOFFA pl,c =260 cm -1 SmOFFA wavenumber [cm -1 ] NdOFFA (d) -30-20-1001020 SC pl,c =250 cm -1 SC SmOFFA S W [ m c m - ] T [K]NdOFFA
FIG. 2: Temperature dependence of the infrared dielectric response of the (Nd,Sm)O . F . FeAs superconductors. (a) Repre-sentative spectra of the real part of the conductivity, σ ( ω ). The arrow marks the onset of the SC induced gap-like suppression.The inset shows calculated reflectivity spectra. (b) Difference between the conductivity in the normal and the SC state interms of σ (10 K) − σ (55 K). The shaded area indicates the missing spectral weight due to the SC condensate. The insetdetails the temperature dependence of the integral of σ ( ω ) between 45 and 300 cm − (SW). (c) Corresponding spectra of thereal part of the dielectric function, ǫ ( ω ). The inset details the temperature evolution of ǫ (50 cm − ). (d) Difference spectra ǫ (10 K) − ǫ ( T c ) [solid lines] showing the SC induced change of ǫ ( ω ). Dotted lines show fits with the function − ( ω SCpl ,c /ω ) . tration depth of λ c /λ ab ≥ σ ( ω ) below the onset frequency of ω ∗ SC ≈
300 cm − which is detailed in Fig. 2(b). Previous similar stud-ies on the cuprate HTSC have shown that this onsetfrequency (in the relevant so-called dirty limit of theweakly conducting c -axis response) approximately scalesas twice the maximum value of the SC gap energy, i.e., ω ∗ SC ≈
2∆ [14, 29, 30, 31]. Accordingly, we estimate∆ ≈
19 meV and 2∆ /k B T c ≈ − which develops an asymmetric shape be-low T c [see Figs. 2(a) and 2(b)]. This shape change givesrise to the wavy structure in the conductivity differencespectrum in Fig. 2(b). Such behaviour might be takenas evidence that this phonon mode strongly couples tothe electronic background. However, it appears that thepeak frequency of the phonon mode does not exhibit anyanomalous behaviour. Furthermore, we remark that sim-ilar anomalous shapes of phonon modes were previouslyobserved on polycrystalline cuprate HTSC samples [19]that were not confirmed by subsequent measurements onsingle crystals [15].As already mentioned above, our optical data also al-low us to access another important parameter of the SCibliography 4state which are the c -axis components of the plasma fre-quency of the SC condensate, ω SCpl ,c and the related mag-netic penetration depth, λ c . These values can be derivedfrom our data in two independent ways (since ellipsom-etry measures σ ( ω ) and ǫ ( ω ) independently). Firstly,one can obtain them from the so-called missing area dueto the gap-like suppression in the regular part of σ ( ω ).As shown in Fig. 2(b) by the shaded area for the mea-sured frequency range of 45 −
300 cm − , this amounts to1570 Ω − cm − or ω SCpl ,c = 245 cm − . These values arelikely even somewhat higher due to a contribution fromthe frequency range below 45 cm − . As an example, thedotted line shows an straight extrapolation which wouldyield a value of 1940 Ω − cm − or ω SCpl ,c = 270 cm − . Sec-ondly, the plasma frequency of the SC condensate can bedetermined from the inductive response in ǫ ( ω ) where aSC induced contribution is apparent in the temperatureevolution of ǫ (50 cm − ), see the inset of Fig. 2(c). Asshown in Fig. 2(d), reasonable fits to the low frequencyparts of the difference spectra of ǫ ( ω ) between the 10 Kand the temperature right above T c , can be obtained withthe function, − ( ω SCpl ,c /ω ) , that accounts for the inductiveresponse due to the SC condensate. For both samples weobtained a similar value of ω SCpl ,c = 250 −
260 cm − whichtranslates into a spectral weight of the SC condensate of ≈ − cm − . We note, that the determination of ω SCpl ,c in both cases is based on the assumption that theregular part of the dielectric function does not changebetween 10 and 55 K. Due to a possible narrowing ofthe regular part below T c , our analysis may well give aslightly overestimated value of ω SCpl ,c which neverthelessprovides a reliable upper boundary. Accordingly, we canderive from our data a lower limit of the magnetic pene-tration depth in the c -axis direction of λ c ≥ µ m. Withthe in-plane values of λ ab ≈ −
235 nm as obtainedfrom recent muon-spin-rotation measurements (that werein parts performed on the same samples) [23, 24] thisyields an anisotropy of λ c /λ ab ≥
30. It is interesting tonote that rather similar values have been obtained forweakly underdoped to optimally doped La − x Sr x CuO single crystals [33].In summary, we reported infrared opticalmeasurements of polycrystalline samples of the(Nd,Sm)O . F . FeAs superconductors. We out-lined that the optical spectra provide evidence for astrong electronic anisotropy and a very weakly conduct-ing c -axis response, similar like in the cuprate HTSC.We deduced important parameters like a lower limit forthe c -axis magnetic penetration of λ c ≥ µ m and ananisotropy of λ c /λ ab ≥
30 compared to λ ab = 185 nmfrom muon spin rotation [24]. We also determined thegap magnitude of 2∆ ≈
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