Solid State Communications 152 (2012) 644–648

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Solid State Communications

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Relationship between crystal structure and superconductivity iniron-based superconductorsC.H. Lee a,b,∗, K. Kihou a,b, A. Iyo a,b, H. Kito a,b, P.M. Shirage a, H. Eisaki a,ba National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japanb Transformative Research-Project on Iron Pnictides (TRIP), JST, Chiyoda, Tokyo 102-0075, Japan

a r t i c l e i n f o

Article history:Accepted 8 December 2011by H. HosonoAvailable online 14 December 2011

Keywords:A. PnictidesA. Fe-based superconductorsC. Crystal structure analysisE. Powder neutron diffraction

a b s t r a c t

We studied the relationship between crystal structure and superconductivity in iron-based superconduc-tors. The superconducting phase diagram of LnFeAsO1−y (Ln = rare-earth) is established as a function ofthe oxygen deficient content which is determined by Rietveld refinement. The relationship between Tcand the Fe–(Pn,Ch)–Fe bond angle (Pn= pnictogen, Ch= chalcogen) indicates that Tc attains a maximumvalue when Fe(Pn, Ch)4-tetrahedrons form a regular shape. A higher Tc value could be attainedwith sam-ples containing regular Fe(Pn,Ch)-tetrahedrons, an Fe–(Pn,Ch) bond length that is longer than the Fe–Asbond, and an intermediate (Fe plane)–(Fe plane) distance of 9 Å–15 Å.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The recent discovery of superconductivity in LaFeAsO1−xFx atthe superconducting temperature of Tc = 26 K has triggeredan energetic search for new superconductors [1]. The subsequentfinding of the high Tc value of 55 K in SmFeAsO1−xFx [2]demonstrates the potential of Fe-based superconductors as beyondthe conventional BCS superconductors. The wide variety ofcompounds is also an advantage in finding new superconductorswith high Tc .

The crystal structure of Fe-based superconductors characteris-tically consists of two-dimensional stacking layers (Fig. 1). Com-monly, they consist of FePn- or FeCh-layers (Pn = pnictogen,Ch = chalcogen) that conduct the superconducting current. The Featom is surrounded by four Pn or Ch atoms in Fe(Pn, Ch)-layers,forming a Fe(Pn, Ch)4-tetrahedron. The shape of a Fe(Pn, Ch)4-tetrahedron can be defined with two kinds of Fe-(Pn, Ch)-Fe bondangle α and β (inset of Fig. 5). A regular Fe(Pn, Ch)4-tetrahedronhas α = β = 109.47°. Various types of stacking layers can be in-duced between the Fe(Pn,Ch)-layers, which leads to the variety ofFe-based superconductors.

Fe-based superconductors can be categorized into severalgroups. The highest Tc yet achieved is for the so-called 1111-system, which has LnFeAsO (Ln = rare-earth) as the parent com-pound with two types of stacking layers LnO and FeAs (Fig. 1(a)).

∗ Correspondence to: National Institute of Advanced Industrial Science andTechnology (AIST), Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan.Tel.: +81 29 861 5268; fax: +81 29 861 5340.

E-mail address: c.lee@aist.go.jp (C.H. Lee).

0038-1098/$ – see front matter© 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2011.12.012

Charges are transferred from LnO to FeAs layers by substitution orintroduction of defect of oxygen atoms [1–4]. Non-doped LnFeAsOcompounds exhibit an antiferromagnetic phase transition accom-panied by a structural phase transition from tetragonal to or-thorhombic crystal structure at low temperature. As carriers aredoped, the antiferromagnetic long-range order disappears withsubsequent appearance of the superconducting phase.

In the so-called 122-system with chemical formula of AFe2As2(A = Ca, Sr, Ba), holes and electrons are doped by substitutionof the A site by alkali metals and of the Fe sites by Co or Niatoms, respectively (Fig. 1(b)). The maximum Tc is achieved for(Ba, K)Fe2As2, which has Tc = 38 K [5]. The so-called 111-system with chemical formula of LFeAs (L = alkali metal) ex-hibits a maximum Tc of 23 K for NaFeAs (Fig. 1(c)) [6,7]. The11-system compounds, Fe(Se,Te) (Tc = 14 K), exhibit the sim-plest crystal structure with no stacking layer between the Fe(Se,Te)-layers (Fig. 1(d)) [8–10]. Characteristically, they do not haveAs atoms unlike other Fe-based superconductors. The longestc-axis is achieved in perovskite-type compounds with perovskitestructure layers stacking between FeAs-layers. An example of thesecompounds is shown in Fig. 1(e), which depicts the crystal struc-ture of a 42622-system with chemical formula of A4X2O6Fe2As2(X = Al, Sc, V, Cr). The maximum Tc for those compounds is 43 Kfor Ca4(Mg, Ti)3OyFe2As2 [11].

A remarkable feature in Fe-based superconductors is the strongcorrelation between crystal structure and superconductivity. Thefact that superconductivity can also be induced by either theapplication of pressure or substitution of As by P atoms withoutcarrier doping [12–16] indicates that crystal structure can be akey factor for the appearance of superconductivity. In the 1111-system, Tc depends strongly on rare-earth atoms [4,17,18], which

C.H. Lee et al. / Solid State Communications 152 (2012) 644–648 645

(a) LnFeAsO(Ln = rare-earth).

(b) AFe2As2 (A = Ca,Sr, Ba).

(c) LFeAs (L = Li, Na). (d) Fe(Se, Te). (e) A4X2O6Fe2As2(A = Ca, Sr) (X = Mg,Al, Sc, Ti, V, Cr).

Fig. 1. Crystal structures of iron-based superconductors. (a) LnFeAsO, (b) AFe2As2 , (c) LFeAs, (d) Fe(Se,Te), and (e) A4X2O6Fe2As2 .

is quite different from the situation for LnBa2Cu3O7−y cuprates,which exhibit a constant Tc of about 90 K except Pr compounds.Decreasing the size of rare-earth ions from La to Nd results in anincrease in Tc with amaximum around Nd and Smwhere Tc = 56 K.On the heavy rare-earth side, Tc decreases with further decreasingtheir ionic size. To explain this phenomenon, we have proposedthat the shape of the FeAs4-tetrahedrons is essential in Fe-basedsuperconductors [19]. Themaximumvalue of Tc would be obtainedwhen the FeAs4-tetrahedrons form a regular shape.

In the present study, therefore, we focus our attention on theimportance of crystal structure for superconductivity. We sum-marize the relationship between crystal structure and supercon-ductivity in Fe-based superconductors and propose a strategy forattaining higher Tc .

2. Experimental procedure

Polycrystalline samples of LnFeAsO1−y were prepared by thehigh-pressure method using a cubic-anvil high-pressure appara-tus. Samples were synthesized at 1050–1150 °C under a pressureof 2.0–5.5 GPa for 2 h in a BN crucible. Oxygen deficiency was in-duced by controlling the ratio of Fe and Fe2O3 as startingmaterials.Details of the synthesis method are given in Ref. [17]. The amountof samples used for neutron scattering measurements was about0.3 g for each composition.

Powder X-ray diffraction measurements were performed atroom temperature using Cu Kα radiation (RIGAKU Ultima IV) toconfirm the purity and lattice parameters of obtained samples.Their Tc was determined using a SQUID magnetometer (QuantumDesign MPMS) under a magnetic field of 5 Oe after zero-fieldcooling from a temperature sufficiently above Tc .

Neutron scattering measurements were performed by thepowder diffractometer HERMES of the Institute for MaterialsResearch, TohokuUniversity, which is installed at the JRR-3 reactorof JAEA at Tokai. Incident neutrons were monochromated usingthe (331) reflection of a Ge monochromator. The sequences ofhorizontal collimators were 12’-blank-S-22’ where S denotes thesample position. Diffraction patterns were collected over the 2θrange of 3°–153° at constant steps of 0.1° using a multidetector.Powder samples were placed in a vanadium can. A closed-cyclecryostat was used to cool the samples to T = 10 K. The data wereanalyzed by the Rietveldmethod using the Rietan program [20] forthe refinement of crystallographic structures.

3. Results and discussion

3.1. Superconducting phase diagram

The oxygen content of the samples synthesized for the presentneutron scattering measurements was determined by Rietveld

Fig. 2. Lattice constant a as a function of the oxygen deficiency y for LnFeAsO1−y atroom temperature.

analysis. The actual oxygen content was larger than the nominalvalues for all samples because of the oxidation of the startingrare-earth elements during sample synthesis. Fig. 2 depicts theoxygen deficient content y vs. the lattice constant a for LnFeAsO1−yat room temperature. The lattice constant a decreases linearlywith increasing oxygen deficiency. The oxygen content of all othersamples was estimated from the obtained linear relationship andbymeasuring the lattice constant a using X-ray diffraction becauseof the limitation on beam time of neutron scattering. The reductionof the lattice constant a is also observed with increasing atomicnumber of rare-earths owing to the contraction of their ionic radii.

Fig. 3 shows the superconducting phase diagramof LnFeAsO1−y.All samples exhibit superconductivity above y ∼ 0.04 but thedoping dependence of Tc is different. For LaFeAsO1−y, Tc exhibits aflat top at around y = 0.10 and then decreases with increasing y asis usually observed in the overdoped region of a superconductingphase diagram. In contrast, overdoped-like behavior of Tc is notobserved for Ln = Pr,Nd, and Tb samples. For PrFeAsO1−y, Tcexhibits an approximately flat top over the whole doping range.For NdFeAsO1−y and TbFeAsO1−y, Tc keeps increase until y ∼ 0.3.The doping level does not appear to reach the overdoped regionfor Ln = Pr,Nd, and Tb samples. Further oxygen deficiency causesthe samples to decompose. An apparent difference can also beobserved around the boundary between the non-superconductingand superconducting phases. For Ln = La, Pr, and Nd samples, Tcincreases quickly at the boundary, whereas for Ln = Tb samples,Tc increases only gradually over the whole doping range. Thoseresults show that Ln = La samples exhibit slightly overdoped-likebehavior but turn into underdoped-like behavior with increasingatomic number of rare-earths. The present behavior could berelated with the sensitive small electron Fermi surface to theposition of As atoms, which has mainly dx2−y2 orbital charactertouching barely the Fermi energy [21]. The dx2−y2 band can be

646 C.H. Lee et al. / Solid State Communications 152 (2012) 644–648

Fig. 3. Tc as a function of the oxygen deficiency y for LnFeAsO1−y and half of thefluorine-doping content x for LaFeAsO1−xFx . Solid circles and open squares indicatedata for LnFeAsO1−y and LaFeAsO1−xFx , respectively. Data of LaFeAsO1−xFx is resultsreported in a literature [22]. The solid lines are guide to the eye.

pushed up with increasing atomic number of rare-earths andvarying the position of As atoms, which appears to be consistentwith the change from slightly electron overdoped-like behavior forLn = La samples to underdoped-like behavior for Ln = Tb samples.These results may support the argument that the dx2−y2 band playan important role in the appearance of superconductivity.

The open squares in Fig. 3(a) show the Tc of fluorine dopedLaFeAsO1−xFx reported in the literature [22]. Half values of x areplotted because carriers induced by a fluorine doping should beas half as those induced by an oxygen deficiency. However, thedependence of Tc on carrier doping is stronger in fluorine-dopedsamples than in oxygen-deficient samples, which suggests that theconcentration of doped carriers is lower for oxygen-deficient sam-ples than for fluorine-doped samples. The discrepancy betweenfluorine-doped and oxygen-deficient samples was also reportedpreviously [19,23]. This could be because an electron is capturedaround an oxygen vacant site that is surrounded by La3+ ions foroxygen-deficient samples.

3.2. Bond angle dependence of Tc

Fig. 4 shows Tc as a function of the As–Fe–As bond angle α forthe present obtained data for LnFeAsO1−y samples. The bond angleα tends to decrease with increasing the concentration of carrierdoping, which is a consequence of shrinkage of the lattice constantawith keeping Fe–As bond length at a constant value. As shown, Tcdoes not simply depend only on the shape of FeAs4-tetrahedrons.For Ln = Pr and Nd samples, Tc increases with varying the bond

Fig. 4. Tc vs. bond angle α for LnFeAsO1−y at room temperature. The solid lines areguide to the eye.

Fig. 5. Maximum Tc for each system vs. bond angle α. Our results as well as datafrom the literature [5–7,11,24–63] are plotted. The bond angles of LnFeAsO1−y aremeasured at T = 12 K. The vertical dashed line indicates the bond angle of a regulartetrahedron (α = 109.47°).

angle α toward the value of regular tetrahedron α = 109.47°.On the other hand, for Ln = Tb samples, Tc increases althoughthe bond angle α move away from the value of 109.47°. ForLn = La samples, Tc first increases then decreases with decreasingthe bond angle α. These are because Tc depends not only on theshape of FeAs4-tetrahedrons but also on carrier concentration. Therelationship between the shape of FeAs4-tetrahedrons and Tc canbe derived only when optimum doped samples are compared. TheLn = Nd sample at optimum doped level exhibits the highestTc , which has the closest shape of FeAs4-tetrahedrons to a regularformation in LnFeAsO1−y samples.

Fig. 5 shows Tc as a function of the (Pn,Ch)–Fe–(Pn,Ch) bondangle α for the present obtained data for LnFeAsO1−y samplesas well as published values for various pnictide superconductors[5–7,11,24–63]. The maximum Tc for each system and thecorresponding bond angles are plotted in the figure to clarify theirrelationship at the optimum doped level. The dependence of thebond angle α on the lanthanoid in the LnFeAsO1−y system showsthat FeAs4-tetrahedrons form a regular shape around NdFeAsO1−y.Obviously, Tc attains a maximum value when FeAs4-tetrahedronsform a regular shape. This tendency is also observed in the 1111-system of AFeAsF, which contains layers of fluorine and alkaline-earth metals. Tc is higher for Ca(Fe,Co)AsF, which contains nearlyregular-shaped FeAs4-tetrahedrons, than for Sr(Fe,Co)AsF whoseFeAs4-tetrahedrons are elongated along the ab-plane.

The same peak structure is also observed in the plot of Tc vs.anion height above the Fe(Pn,Ch)-layer [64,65]. For FeAs-basedcompounds, although anion height is determined by both the bondangle α and the Fe–As bond length, it is effectively determinedby the bond angle since the Fe–As bond length is almost constantfor all iron pnictides because of covalent bonding. Therefore, Tc vs.bond angle and Tc vs. anion height can be seen to be equivalentwhenever plots of FeAs-based compounds are compared.

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A similar relationship between bond angle and Tc is alsoobserved for 122-, 111-systems, and perovskite-type compounds.In the 122-system, (Ba, K)Fe2As2 contains almost regular FeAs4-tetrahedrons, which exhibits a relatively high Tc . On the otherhand, for (Ca, Na)Fe2As2, which exhibits a lower Tc , the FeAs4-tetrahedrons are distorted. In the 111-system, the FeAs4-tetrahe-drons are close to regular in shape for NaFeAs, which exhibitsa higher Tc than LiFeAs whose FeAs4-tetrahedrons are elongatedalong the c-axis. The perovskite-type compounds, A4X2O6Fe2As2and A4X3OyFe2As2, also follows approximately the same tendency,although the maximum Tc is achieved with slightly distortedFeAs4-tetrahedrons in Sr4V2O6Fe2As2 and Ca4(Mg, Ti)3OyFe2As2. Asimilar subtle shift in peak position toward lower bond angle α isalso observed in LFe2−ySe2.

To maximize Tc , both carrier concentration and the bond anglemust be optimized simultaneously. Nondoped BaFe2As2 containsdistorted FeAs4-tetrahedrons with a bond angle α = 111.1°. WithK doping, the bond angle α decreases monotonically and reachesthe regular-tetrahedron value of α = 109.47° in the optimumdoped composition (40% K doping), where Tc attains a maximumvalue of 38 K [66]. In (Sr,K)Fe2As2, on the other hand, for example,Tc does not attain the maximum value at the doping level wherethe FeAs4-tetrahedrons form regular tetrahedrons. It appears thatboth carrier concentration and the bond angle are coincidentallywell optimized in (Ba,K)Fe2As2 but not in (Sr,K)Fe2As2. This maybe the reason why (Ba,K)Fe2As2 exhibits the highest Tc in the 122-system.

In the 11-system, not only the bond angle but also the averagevalue of the Fe–(Se,Te) bond length depends on the Se andTe content, because the bond lengths of Fe–Te (∼2.57 Å) andFe–Se (∼2.39 Å) are quite different. Thus, the dependence of Tcon the Fe–(Se,Te) bond length should also be considered. It is,however, difficult to distinguish between the effects of bond lengthand bond angle on Tc when they are simultaneously varied. Inaddition, the local structural inhomogeneity arisen from two typesof tetrahedrons (FeSe4 and FeTe4 [67]) can also affect Tc , whichmakes the problem more complicate. Nevertheless, it still appearsthat Tc increases with varying the shape of Fe(Se, Te)4 towardregular tetrahedron except for FeSe. The low Tc for FeSe couldbe due to the appearance of the orthorhombic crystal structure,which is unfavorable for superconductivity. In fact, Tc for FeSeincreases drastically up to 37 K when the orthorhombic crystalstructure disappears with applying external pressure [68,69]. Onthe other hand, Tc for FeSe0.5Te0.5, which contains amore distortedFe(Se, Te)4 tetrahedron, increases only up to 26 K upon applyingexternal pressure [70].

The overall distribution of data for FeAs-based compoundsexhibits a peak around α = 109.47° with a half-width at half-maximum of about 5°. Characteristically, Tc seems to be sensitiveto the bond angle α at around α = 109.47°. On the other hand, ata bond angle away from α = 109.47°, Tc seems to be insensitiveto the bond angle and can be affected dominantly by other factors.In contrast, for the FeP-system, Tc seems to be insensitive to thebond angle α even at around α = 109.47°. Ca4Al2O6Fe2P2 andSr4Sc2O6Fe2P2 exhibit the same value of Tc = 17 K, but containquite different bond angles α = 109.4° and 118.3°, respectively.By comparing with isostructural FeAs-based compounds, such asA4X2O6Fe2As2, which is sensitive to the bond angle α, it is foundthat the difference can be attributed to different Fe–As (∼ 2.42 Å)and Fe–P (∼ 2.26 Å) bond lengths. The bandwidth can be broaderin FeP-based compounds because of a smaller Fe–Pn bond length,which could be responsible for the insensitivity.

The advantage of regular tetrahedrons in attaining high Tcis not only observed in pnictides. LnNi2B2C is a superconductorthat contains NiB4-tetrahedron layers [60–63]. Its Tc dependsstrongly on rare-earth atoms and has a maximum Tc = 16.6 K

Fig. 6. (Fe plane)–(Fe plane) distance dependence of Tc for samples containingapproximately regular FeAs4-tetrahedrons. The solid and dash lines are guide tothe eye.

Fig. 7. Fe–As bond length dependence of Tc for A4X2O6Fe2Pn2 containingapproximately regular FePn4-tetrahedrons.

in LuNi2B2C wherein NiB4-lattices approximately form a regulartetrahedron. Remarkably, both pnictides and LnNi2B2C exhibit asimilar dependence of Tc on bond angle, although the mechanismof superconductivity could be different between both systems.

3.3. Effect of other structural parameters on Tc

To deduce the effect of structural parameters other than bondangle on Tc , we compared samples containing approximatelythe same bond angle α. Fig. 6 shows Tc as a function of the(Fe plane)–(Fe plane) distance for samples containing regularFeAs-tetrahedrons. As shown, Tc increases with increasing the(Fe plane)–(Fe plane) distance until about 9 Å. This suggeststhat superconductivity in Fe pnictides favors two-dimensionality.However, Tc does not increasesmonotonically, but rather saturatesfor Sr4V2O6Fe2As2 and Ca4(Mg, Ti)3OyFe2As2 samples where the(Fe plane)–(Fe plane) distance is about 16 Å. To clarify thesaturation value of Tc , further studies in the intermediate region(9–15 Å) are required.

The Fe–Pn bond length dependence of Tc was deduced by com-paring Sr4V2O6Fe2As2 and Ca4Al2O6Fe2P2, which are isostructuraland contain approximately equivalent regular FePn-tetrahedronswith almost equivalent (Fe plane)–(Fe plane) distances. Fig. 7demonstrates that a longer Fe–Pn bond length is more favorablefor attaining higher Tc . It could be that a longer Fe–Pn bond lengthcauses a higher Tc and higher sensitivity of Tc to the bond angle α.

4. Conclusions

Wehave studied the relationship between crystal structure andsuperconductivity in iron-based superconductors. Carrier dopingdependence of Tc in LnFeAsO1−y depends on the rare-earth atoms.

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A slightly overdoped-like dependence was observed for Ln = Lasamples, which turned into an underdoped-like dependence withincreasing atomic number of rare-earths up to Ln = Tb. Therelationship between Tc and the (Pn, Ch)–Fe–(Pn, Ch) bond angleindicates that Tc attains a maximum value when the Fe(Pn, Ch)4-tetrahedrons form a regular shape. A longer Fe-(Pn, Ch) bondlength than the Fe–As bond and an intermediate (Fe plane)–(Feplane) distance of 9–15 Å may be advantageous for attaininghigher Tc .

Acknowledgments

We thank K. Kuroki, M. Braden, and K. Yamada for valuablediscussions. This work was supported by a Grant-in-Aid forScientific Research C (No. 22540380) from the Japan Society for thePromotion of Science.

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