Oxygen deficiency in the iron-based HTSCGdFeAsO 1Ã¢Â�Â�� seems to create a parallelogram shaped Fe2+-ion/oxygen deficiency

pattern in the Fe2O2 plane in c-direction. These two-dimensional nano structures form superconducting current channels which

are separated by h = 0.828nm. The doping distance in direct ion of the super-current shows a strong correlation to the transition

temperature

Huber, F.

Leschinski, P.

Röser, H.P

von Schönermark, M.

English

Institute of Transport Research:Publications

Acta Astronautica 64 (2009) 1011–1013www.elsevier.com/locate/actaastroACADEMY TRANSACTIONS NOTEOxygen deficiency structure in iron-based high temperaturesuperconductor GdFeAsO1−H.P. Roesera,∗, P. Leschinskia, F.M. Huberb, M.F. von Schoenermarka,A.S. Nikoghosyanc, M. TobermandaInstitute of Space Systems, Universitaet Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, GermanybSteinbeis Transferzentrum Raumfahrt, Roetestr. 15, 71126 Gaeufelden, GermanycDepartment of Microwave and Telecommunication, Yerevan State University, Alex Manoogian 1, Yerevan, 375025, ArmeniadNASA Dryden Flight Research Center, P.O. Box 273, Edwards, CA 93523, USAReceived 21 September 2008; accepted 3 November 2008Available online 9 January 2009AbstractOxygen deficiency in the iron-based HTSC GdFeAsO 1− seems to create a parallelogram shaped Fe2+-ion/oxygen deficiencypattern in the Fe2O2 plane in c-direction. These two-dimensional nanostructures form superconducting current channels whichare separated by h = 0.828nm. The doping distance in direction of the super-current shows a strong correlation to the transitiontemperature.© 2008 Elsevier Ltd. All rights reserved.Keywords: Iron-based high temperature superconductor; Superconducting unit area; Superconducting carrier density1. IntroductionVery recently, a new family of high temperature su-perconductors (HTSC) – consisting of fluorine-dopediron-based layered LnO1−FFeAs with lanthanideelements Ln = La, Gd, Ce, Pr, Nd, Sm – have beendiscovered ([1–4] and references therein) with criticaltransition temperatures Tc between 26 and 54K. Thesesuperconductors have a tetragonal layered structure anda two-dimensional superconducting plane.Several research groups [2,5] have succeeded in syn-thesising iron-based HTSCs with oxygen deficiencyinstead of F-doping, e.g. GdFeAsO1−. This material∗ Corresponding author. Tel.: +4971168562375;fax: +4971168563596.E-mail address: roeser@irs.uni-stuttgart.de (H.P. Roeser).0094-5765/$ - see front matter © 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.actaastro.2008.11.010has been well studied showing a transition temperatureabove 50K at an optimum deficiency level of = 0.15.In this paper, we will show that the correlation betweenthe spacing (x) of Fe2+-ion/oxygen deficiency positionsin the Fe2O2 plane and Tc, as described by Eq. (1) forcuprates and F-doped iron-based HTSCs [3,6,7], appliesalso to GdFeAsO1− (GAFO) for n = 1.(2x)2 · n−2/3 · 2Meff · kTc = h2 (1)2. Electronic and geometrical structureThe crystal unit cell structure of GAFO consists of2 · [GdFeAsO] and has a tetragonal layered structurewith the space group P4/nmm (Fig. 1). The atomsGd3++Fe2+ provide five electrons to As3−+O2−,creating a metallic behaviour with a uniform poten-tial pattern throughout the crystal. Superconductivity1012 H.P. Roeser et al. / Acta Astronautica 64 (2009) 1011 –1013Fig. 1. (a) Superconducting Fe2O2 plane of GdFeAsO1− showing the oxygen deficiency distribution and the superconducting current channels.(b) Illustration to determine the current carrying periodicity x by the parallelogram shaped HTSC unit area.is achieved by doping using 2F1−-ions at O2−-ionsites or through oxygen deficiency. The electronic ar-rangement in the unit cell with a missing O-atom isGd3++Fe2++As3− creating a periodic potential disor-der with two free electrons in this unit cell. This issimilar to YBa2Cu3O7− with two free electrons atthe oxygen deficiency position [6] and a super-currentflow in the CuO2 plane. For the F-doped Fe-basedHTSCs it has been suggested that the super-currentflows in c-direction [3]. We will assume the same situ-ation for the oxygen deficiency case. This is supportedby electronic structure calculations showing the sameresults for fluorine doping and oxygen deficiency [4].Assuming a regular oxygen deficiency distribution inthe Fe2O2 plane, the doping  can be transformedinto distances x and g for the missing O-atoms. Usingthe same nomenclature as in previous papers [3,6,7],()−1 is the doping density and  represents the HTSCunit area ASC with a doped element at each corner.Fig. 1 shows crystals sliced through the diagonal planein c-direction. The optimum doping = ()−1 = 0.15leads to = 6.67 ≈ 6.5 because the Fe2O2 unit areacontains two O-atoms (Fig. 1b) and therefore the Fe2O2unit area can be split into two halves and the HTSCunit area is made of integrals of 12 Fe2O2 unit areas.Because of the fact that the Fe2O2 unit area is rectan-gular with an area of A = a√2 · c, the super-current isanisotropic and probably only flows in a straight linefrom Fe–O to Fe–O and within an angle . This resultsin ASC having the form of a parallelogram withASC = x · h =  · a√2 · c (2)Within the Fe2O2 superconducting plane the doping dis-tances x and g are given by Pythagoras formulax2 = z21 · c2 + z22 · (a/√2)2 (3)g2 = z23 · c2 + z24 · (a/√2)2 (4)The superconducting unit area can also be calculated byASC = (z1 + z3) · c · (z2 + z4) · (a/√2)− z1 · z2 · c · (a/√2) − z3 · z4 · c · (a/√2) (5)as illustrated in Fig. 1b leading toz1 · z4 + z2 · z3 = 2 ·  (6)with zi ∈ N. The requirements that(a) the super-current flows along two neighbouringdoped unit cells where the closest doped half Fe2O2unit cell must lay within the angle range  and(b) no super-current flows in the Fe–Fe direction withinthe angle range 24H.P. Roeser et al. / Acta Astronautica 64 (2009) 1011 –1013 1013Table 1Structural data of superconducting GdFeAsO1− with an deficiency value of  = 0.15.Tc (K) Crystal structure (nm) Atomic doping HTSC unit area (2x)2×10−18 (m2)Exp. 52.9 ± 0.6 a = 0.389  = 0.15 z1(c) = 4; z2(a/√2) = 5 52.5c = 0.838 x = 3.62nmCalc. 52.9 Tetragonal ASC = 6.5 · Fe2O2 z3(c) = 1; z4(a/√2) = 2g = 1.00nm; h = 0.828nmlead to the following inequalities:(z1 · c)/(z2 · a/√2)> c/a√2 → 2z1 > z2 (7)(z3 · c)/(z4 · a/√2)c/a√2 → 2z3 z4 (8)For GAFO, Eq. (6) results in 2 · = 13 with the con-sequence that z  0 and only a few combinations ofz  12 are possible. A calculation with a simple com-puter program using Eq. (6) and inequalities (7) and(8) leads to a one-to-one correspondence with z1 = 4,z2 = 5, z3 = 1 and z4 = 2 as illustrated in Fig. 1a and b.The above results show that GAFO works with a super-conducting unit area of ASC = 6.5 Fe2O2 and the super-current flows in current channels as illustrated in Fig. 1with a periodicity distance x given by Eq. (3) resultingto x = 3.62nm. The parallel current channels are sepa-rated by h = 0.828nm (Table 1).3. DiscussionsOxygen deficiency doping with = 0.15 creates adisorder pattern with x = 3.62nm and g = 1.00nm andforms a parallelogram with a superconducting unitarea of ASC = 6.5 Fe2O2. According to Eq. (1) withone superconducting plane per unit cell (n = 1) andMeff = 2me this leads to a transition temperature ofTc (calc.) = 52.9K. This value compares well with theexperimental value of 52.9 ± 0.6K [2] and matchesthe correlation curve in [7]. This result supports thesuggestion that Fe2O2 represents the superconductingplane [3].The separation (d) of neighbouring superconductingFe2O2 planes is given by d = a√2 so that the supercon-ducting unit volume VSC = ASC · a√2 = (6.5×0.461×0.550)nm3 results in a superconducting carrier den-sity NSC with an effective mass of Meff = 2me ofNSC = (VSC)−1 = 6.07×1020 cm−3.With the correlation described by Eq. (1) and the as-sumption that 2x = DB, the resonance effect betweenthe de Broglie wavelength and the doping structurewould require a maximum (de Broglie) velocity ofthe superconducting pair of vDB ≈ 2.5×106 cms−1.This would result in a maximum current densityat T = 0K for superconducting GdFeAsO1− ofj(max) ≈ 5×108 Acm−2 according toj(max) ≈ 2NSC · e · vDB (9)It appears that the oxygen deficiency in FeAs HTSCshas the same effect for the superconducting process asin Y123, except that the HTSC unit area is not squareas for the symmetrical CuO2 cuprate unit cells, but ithas the size of a parallelogram.The quality of the correlation depends strongly onthe accuracy of the doping density . Measurementswith other rare-earth elements like Ce, La, Nd, Pr andSm have been done, but the actual deficiency value could not be determined precisely from polycrystallinesamples [5].References[1] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, Iron-basedlayered superconductor La[O1−xFx]FeAs (x = 0.05−0.12) withTc = 26K, J. Am. Chem. Soc. 130 (2008) 3296–3297.[2] J. Yang, Z.C. Li, W. Lu, W. Yi, X.L. Shen, Z.A. Ren, G.C. Che,X.L. Dong, L.L. Sun, F. Zhou, Z.X. Zhao, Superconductivityat 53.5K in GdFeAsO1−, Supercond. Sci. Technol. 21 (2008)082001.[3] H.P. Roeser, F.M. Huber, M.F. von Schoenermark, A.S.Nikoghosyan, M. Toberman, Fluorine-doped structure in iron-based high temperature superconductors, Acta Astronaut. 64(2009) 391–394.[4] E.Z. Kurmaev, R.G. Wilks, A. Moewes, N.A. Skorikov, Y.A.Izyumov, L.D. Finkelstein, R.H. Li, X.H. Chen, X-ray spectraand electronic structure of FeAs superconductors, Con-mat.arXiv: 0805.0668v2.[5] Z.A. Ren, G.C. Che, X.L. Dong, J. Yang, W. Yi, X.L.Shen, Z.C. Li, L.L. Sun, F. Zhou, Z.X. Zhao, Novel super-conductivity and phase diagram in the iron-based arsenic-oxidesReFeAsO1− (Re = rare earth metal) without doping, Cond-mat.arXiv: 0804.2582, 2008.[6] H.P. Roeser, F. Hetfleisch, F.M. Huber, M.F. von Schoenermark,M. Stepper, A. Moritz, A.S. Nikoghosyan, A link between criticaltransition temperature and the structure of superconductingYBa2Cu3O7−, Acta Astronautica. 62/12 (2008) 733–736.[7] H.P. Roeser, F. Hetfleisch, F.M. Huber, M.F. von Schoenermark,M. Stepper, A. Moritz, A.S. Nikoghosyan, Correlation betweenoxygen excess density and critical transition temperature insuperconducting Bi-2201, Bi-2212 and Bi-2213, Acta Astronaut.63 (2008) 1372–1375.

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Oxygen deficiency structure in iron-based high temperature superconductor GdFeAsO

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