The influence of spin-phonon coupling on antiferromagnetic spin fluctuations in FeSe under pressure: the First-principles calculations with van der Waals corrections
aa r X i v : . [ c ond - m a t . s up r- c on ] S e p The influence of spin-phonon coupling on antiferromagnetic spin fluctuations in FeSeunder pressure: the First-principles calculations with van der Waals corrections
Qian-Qian Ye, Kai Liu, ∗ and Zhong-Yi Lu † Department of Physics, Renmin University of China, Beijing 100872, China (Dated: May 14, 2018)The electronic structures, lattice dynamics, and magnetic properties of crystal β -FeSe underhydrostatic pressure have been studied by using the first-principles electronic structure calculationswith van der Waals (vdW) corrections. With applied pressures, the energy bands around the Fermienergy level consisting mainly of Fe-3 d orbitals show obvious energy shifts and occupation variations,and meanwhile the frequencies of all optical phonon modes increase. Among these phonon modes, the A g mode, which relates to the Se height from the Fe-Fe plane, shows a clear frequency jump in therange between 5 and 6 GPa. This is also the pressure range within which the highest superconductingtransition temperature T c of FeSe is reached in experiments. In comparison with the other phononmodes, the zero-point vibration of the A g mode induces the strongest fluctuation of local magneticmoment on Fe under a pressure from 0 to 9 GPa, and the induced fluctuation reaches the maximumaround 5 GPa. These results suggest that the effect of phonon via spin-phonon coupling need to beconsidered when exploring the superconducting mechanism in iron-based superconductors. PACS numbers: 74.70.Xa, 74.25.-q, 71.15.Mb, 63.20.kk
I. INTRODUCTION
With the simplest crystal structure among the iron-based superconductors ever found,
PbO-type β -FeSehas attracted tremendous attention both experimentallyand theoretically as an archetype system to explore theunconventional superconductivity mechanism in the iron-based superconductors. The superconducting transitiontemperature T c of FeSe is found to be 8 K at an ambientpressure, and extremely sensitive to external pressureswhile it can grow to the maximum of ∼
37 K around6 − On the other hand, the nuclear magneticresonance (NMR) measurement has found strongly en-hanced antiferromagnetic (AFM) spin fluctuations near T c and that both T c and spin fluctuations are raised bypressures, suggesting a close correlation between the spinfluctuations and the superconducting mechanism in theiron-based superconductors. With applied pressures, the crystal structure of β -FeSe shows notable changes. Its volume undergoes ashigh as 20% reduction and the interlayer spacing showslarge decreases.
In contrast, the height of Se fromthe Fe-Fe plane first decreases and then increases withpressure. By summarizing the T c s of FeSe under pres-sures and the T c s of various iron (and nickel)-based su-perconductors, a striking correlation between the T c andthe height of anion ( i.e. Se in FeSe) is revealed.
More-over, Moon and Choi have found that the magnetic in-teractions and magnetic order are very sensitive to theheight of chalcogen species from Fe-Fe plane by study-ing the FeTe system with fixed height Z T e using thedensity-functional calculations. This is also reflected inthe experiments that the nonsuperconducting FeTe bulksamples become superconducting in the FeTe thin filmsunder tensile stress. These observations indicate thatthe crystal structures and magnetic properties, both ofwhich link with T c in iron chalcogenide superconductors, are obviously correlated and can be tuned by an appliedpressure.A direct consequence of substantial changes in thecrystal structure under pressure is that the lattice dy-namics would be influenced. However, within thestandard McMillan-Eliashberg framework, the electron-phonon coupling calculations without spin-polarizationgive too low values for the transition temperature T c of FeSe. When the spin polarization effects are in-cluded, the calculated electron-phonon coupling valuein the checkerboard AFM N´eel structure shows abouta twofold increase, but still cannot account for the ex-perimentally observed T c of FeSe. It is now commonlyaccepted that FeSe is not a conventional electron-phononsuperconductor, but the spin-fluctuation mediated par-ing yields the unconventional superconductivity. Nevertheless, a clear iron isotope effect on T c of FeSe wasobserved in experimental measurement, and the mag-netic properties were found to be very sensitive to thelattice parameters of FeSe x Te − x from the density func-tional calculations, thus we are curious about what rolethe lattice vibrations play in the spin fluctuations (via thespin-phonon coupling effect) of FeSe. More importantly,how the role of the lattice vibrations will change alongwith pressure, especially around the pressure with thehighest T c of FeSe, has never been studied.As FeSe has Se-Fe -Se layers composed of edge-sharingtetrahedra with an Fe center, the van der Waals (vdW)interaction plays an important role in the interlayerbonding. When a pressure is applied, the interlayer dis-tance of FeSe shows much larger reduction compared withthe in-plane lattice constants. In order to precisely de-scribe the lattice dynamics of FeSe under pressure incalculations, the vdW interactions between FeSe layersneed to be accurately accounted for. Since the con-ventional density functionals are unable to describe cor-rectly the vdW interactions, which arise from nonlocallong-range electron correlations, both nonlocal cor-relation functional and a semi-empirical dispersionpotential method have been proposed to include thedispersion interactions. Nowadays, the density functionaltheory (DFT) problem for vdW interaction has become avery active field and theoretical studies have been carriedout on various relevant molecules and materials.
However, the DFT calculations with vdW-interactioncorrections have rarely been applied to the iron-basedsuperconductors.
We have studied the electronic structures, lattice dy-namics, and magnetic properties of FeSe under pressureusing DFT calculations with vdW corrections. The varia-tions of band structures and the phonon frequencies from0 to 9 GPa, as well as the effect of zero-point vibrationsof phonon modes on the local magnetic moment fluctua-tions and band structures have been investigated.
II. COMPUTATIONAL DETAILS
The first-principles electronic structure calculationswere carried out with the Vienna ab-initio simulationpackage, which makes use of the projector aug-mented wave (PAW) method. The exchange-correlationfunctionals were represented by the generalized gradi-ent approximation (GGA) of Perdew-Burke-Ernzerhof(PBE) type. In order to describe the vdW interactionsnot included in the conventional density functional, ourcalculations adopted the DFT-D2 method with semi-empirical dispersion energy adding to the Kohn-ShamDFT energy. The energy cutoff for the plane waves wasset to 350 eV. The 1 × × × ×
12 K-point mesh. The Fermi-level was broadened by the Gaussian smearing methodwith a width of 0.05 eV. Both the cell parameters and theinternal atomic positions were allowed to relax. The sys-tem under hydrostatic pressures in a range of 0 − The atoms were allowed to relax until the forces weresmaller than 0.01 eV/˚A. After the equilibrium structureswere obtained, the frequencies and displacement patternsof the phonon modes were calculated using the dynam-ical matrix method. The atomic displacements due tothe zero-point vibrations of phonon modes were obtainedaccording to the method of Ref. 38. In the present case,the atoms were displaced to the vibrational state with apotential energy of ¯ hω s / s ,while its normal-mode coordinates can reach two maximaalong two opposite directions.There is another issue in the calculations need to benoted, i.e. the magnetic order that we choose in thisstudy. Unlike other iron pnictides such as LaOFeAs and BaFe As , no any long-range magnetic order has been found for β -FeSe in experiment. However, thestrong AFM spin fluctuations were observed for the un-doped FeSe. Theoretically it is very difficult to directlysimulate such a paramagnetic phase by using DFT cal-culations. Considering that the checkerboard-AFM N´eelorder and the paramagnetic phase share the followingimportant features: (1) local moments around Fe atoms,(2) zero net magnetic moments in a unit cell, and (3)the same space symmetry, the checkerboard-AFM N´eelstate can be thus feasible to properly model the para-magnetic phase in many aspects.
Especially, for therecently grown FeSe monolayer on SrTiO with signa-tures of T c above 50 K by transport measurement, theobserved shape of Fermi surface in angle-resolved pho-toemission spectroscopy (ARPES) experiments canbe reproduced in the DFT calculations by the AFM N´eelorder of FeSe monolayer either without substrate or onSrTiO substrate. In Table I, our calculated lattice pa-rameters for bulk FeSe in nonmagnetic and AFM N´eelstates with or without vdW interactions are comparedwith the experimental results. As listed in the table, thecalculated structure parameters in the AFM N´eel orderwith vdW interaction show the best overall agreementwith the experimental measurement and also yieldthe better results than the previous calculations by us-ing PBE and hybrid functionals. More importantly, thelattice constant along the stacking direction which wouldchange most under pressure is well reproduced. So wechoose the AFM N´eel order to simulate the paramagneticphase of FeSe in the following studies.Regarding the vdW correction to the conventionalDFT functionals, the more accurate vdW-optB86bfunctional, which includes the nonlocal vdW interac-tion in the exchange and correlation functionals, wasalso adopted in the studies of FeSe at ambient pressurein order to examine the influence of different vdW ap-proaches. Consistent results of the vdW-optB86b func-tional and the DFT-D2 method were obtained for the lat- TABLE I. The calculated fully-relaxed lattice parameters forbulk FeSe in nonmagnetic and AFM N´eel states with or with-out vdW interactions are listed along with the experimentalresults. a (˚A) b (˚A) c (˚A) Z Se (˚A)NMNo-vdW 3.679 3.679 5.999 1.385vdW 3.632 3.632 5.382 1.397N´eelNo-vdW 3.710 3.710 6.305 1.437vdW 3.654 3.654 5.471 1.436Expt.(7K) G Z R X A M (d) (e) Fe Se x y z
FIG. 1. (Color online) Electronic band structures of FeSe inAFM N´eel state under (a)0, (b)5, and (c)6 GPa pressures.The Fermi energy is set to zero. Panels (d) and (e) are thetetragonal cell and the corresponding Brillouin zone, respec-tively. tice parameters and the interlayer bonding energy ( ∼ ). These are in accordance with the previouscalculations. III. RESULTS AND ANALYSIS
Applying pressure on bulk FeSe results in dramaticchanges in its electronic band structures. The energyband near the Fermi level at Γ point (labeled by orangeline) is occupied at zero pressure [Fig. 1(a)] and it be-comes unoccupied at 5 and 6 GPa [Fig. 1(b)(c)]. Basedon the analysis of band-decomposed charge density, it isconfirmed that this band consists of the d x − y orbital ofFe at 0 and 5 GPa and changes into the d xz / d yz orbitalat 6 GPa. Around M point, the unoccupied energy bandnear Fermi level (in red color) at 0 and 5 GPa becomesoccupied at 6 GPa. After the same analysis on chargedensity, it is ascertained that this band originates fromthe d x − y orbital of Fe at zero pressure and becomes F r e qu e n c y ( T H z ) F r e qu e n c y ( c m - ) Pressure(GPa) v1 v2 v3 v4 v5 v6
FIG. 2. (Color online) Calculated phonon frequencies at Bril-louin zone center for FeSe in AFM N´eel order under pres-sures from 0 to 9 GPa. Hollow triangles at 0 GPa labelthe corresponding experimental data from Raman scatteringmeasurements. the d xz / d yz orbital at 5 and 6 GPa. The hole pock-ets around Γ point and the electron pockets around M point are consistent with previous ARPES experiment. In addition to the Γ and M points, our calculated bandstructures also show some obvious changes around the Z and A points. Around Z point, the occupied energyband (labeled by orange line) consisting of Fe d z orbitalat low pressures becomes unoccupied one with feature ofFe d x − y orbital at 6 GPa. The changes around A pointare similar as that around M point. In one word, the oc-cupations of energy bands around the Fermi level whichoriginate from the d xz / d yz and d x − y orbitals of Fe arevery sensitive to pressure. From the analysis on densityof states (DOS), contribution from Se atom around theFermi level is minor. In a recent study combined ARPESexperiment and DFT calculations on FeTe . Se . , the contributions from various Fe 3 d and Te/Se p or-bitals to the bands around Fermi level maily come fromthe d xz / d yz and d x − y orbitals. In our calculations, theapplied pressure makes the crystal lattice constants ofFeSe decrease, especially resulting in the collapse of sep-aration between FeSe layers from 5.47 ˚A at 0 GPa to 4.99˚A at 6 GPa. This would lead to corresponding changesin electronic properties such as the band structures andorbital occupations.Not only the electronic band structures show largevariations with pressure, but also the lattice dynamicsdemonstrate obvious changes. As shown in Fig. 2, all ofthe optical phonon frequencies of FeSe at Brillouin zonecenter increase with pressure. They are labeled in thesequence of energy. The modes v2, v3, and v6 are alldoubly degenerate in-plane vibrations. Among all opti-cal phonons, the frequency of mode v5 has a clear sharpjump from 5 to 6 GPa. The hollow triangles in the fig-ure are experimental results of Raman scattering at zeropressure and temperature 7 K, which are in the same (d) v3(E u ) Fe Se (c) v2(E g ) v1(A ) v6(E g ) (a) (b) (f) v4(B ) v5(A ) (e) x y z FIG. 3. (Color online) Atomic displacement patterns formodes (a)v1 ( A u ), (b)v2 ( E g ), (c)v3 ( E u ), (d)v4 ( B g ), (e)v5( A g ), and (f)v6 ( E g ) at 6 GPa pressure with correspondingsymmetries in the parentheses. color as the corresponding calculated values. By compar-ison between experimental and calculated results, thereis about 5% deviation for the frequencies of modes v4 andv5, which ascertains our theoretical approach using theAFM N´eel state. The frequencies calculated using fullyrelaxed structure in nonmagnetic state with vdW interac-tion show much worse agreement ( ∼
30% deviation) withexperiment. In a recent Raman-scattering measurementon Fe-based superconductor K . Fe . Se under atmo-spheric pressure, an anomalous hardening was observedfor the A g mode at T c , indicating a particular type ofconnection between phonons and superconductivity. Inour calculations, both the frequency (194.5 cm − ) andthe symmetry ( A g , shown below) of mode v5 for FeSeare similar to the 180 cm − A g mode in K . Fe . Se . Some experiments on FeSe have shown that depending onthe specific methods to apply pressure, a maximum T c of37 K can be reached under pressures approximately 6 − The anomalous freuqnecy jump of the phononmode v5 around the similar pressure range indicates somerelationship between this mode and the superconductiv-ity of FeSe.In order to identify the characteristics of each phononmode, we plot the atomic displacement patterns at 6GPa in Fig. 3. The displacement arrows are in the same scale among all panels. For the phonon mode v1,the atoms show the same displacement directions for thesame atomic species and the opposite movements for dif-ferent species. It is an Infrared active A u mode. Modesv2, v3 and v6 are all doubly degenerate in-plane vibra-tions, while modes v2 and v6 are Raman active and modev3 is Infrared active. Both modes v4 and v5 are out-of-plane vibrations. The mode v4 consists of the oppositevertical motions of Fe atoms in the same plane, while themode v5 involves the coherent motions of Se atoms rela-tive to their adjacent Fe-Fe planes. The atomic displace-ment patterns are consistent with previous studies. InRef. 7, the authors found that the anion height relativeto the Fe-Fe plane is a key factor influencing the T c ofiron-based superconductors. Among all phonon modes ofFeSe, atomic displacements in modes v1 and v5 changethe Se height mostly. However, in mode v1, the Se atomsabove and below the Fe-Fe plane show opposite heightchanges relative to the Fe-Fe plane and break the originalspacial symmetry of FeSe. Meanwhile, the displacementsof Se atoms in the A g mode v5 control precisely theSe height from Fe-Fe plane and keep the same symme-try as that before moving. In a recent time- and angle-resolved photoemission experiments on EuFe As , themodulations of electron and hole dynamics due to the A g phonon was observed. Using femtosecond optical pulses,Kim et. al. have also detected the transient magnetic or-dering in BaFe As quasi-adiabatically follows the latticevibrations of A g mode with a frequency of 5.5 THz. Due to the sharp increase of phonon frequency for the A g mode v5 of FeSe at 6 GPa (Fig. 2), it is very temptingto deduce that the A g phonon mode plays an importantrole in the T c increase of FeSe with pressure.Due to the sharp frequency increase of phonon mode v5from 5 to 6 GPa, zero-point vibrations of optical phononswere simulated in order to study their influence on thespin in FeSe. The FeSe system was set to the vibra-tional state with zero-point energy of ¯ h w s /2 in a speci-fied phonon mode s , while the normal-mode coordinatecould reach maxima along two opposite directions. Sothere are two displacement patterns for each mode ateach pressure. We plot the difference of local magneticmoment on Fe between the two displacement patterns ofeach mode at various pressures (Fig. 4), namely |△ M | = | M + − M − | , with M + being the local magnetic momenton Fe for one displacement and M − the other. From Fig.4, | △ M | caused by the zero-point vibration of mode v5has much bigger values than all other phonon modes from0 to 9 GPa and it reaches maximum value at 5 GPa. Forzero-point vibrations induced by other phonon modes, | △ M | are not zero only around 6 GPa. So it can beconcluded that all phonon modes enhance the AFM fluc-tuations around 6 GPa. This is in accordance with theexperimental observations that application of pressure onFeSe enhances AFM spin fluctuations. As the pressureincrease, the occupations of energy bands around Fermilevel consisting of Fe d orbitals demonstrate large varia-tions (Fig. 1). The sensitive occupations of these Fe d M Pressure(GPa) v1 v2 v3 v4 v5 v6
FIG. 4. (Color online) Changes of local magnetic momentfluctuations on Fe due to zero-point vibrations of differentoptical phonon modes versus pressure. orbitals to lattice vibrations are responsible for the lo-cal magnetic moment fluctuations. In addition, the localmagnetic moment M on Fe in FeSe at equilibrium struc-ture gets smaller and smaller with increasing pressure,which can be learned that the pressure suppresses theAFM state. This also agrees with the viewpoint that su-perconductivity is induced by doping charge carriers intothe parent compound to suppress the AFM state in boththe cuprate and the iron-based superconduc-tors. Because of the anomalous frequency increase ofphonon mode v5 (Fig. 2) and the enhanced spin fluc-tuations around 5 − A g mode are very small (about0.03 ˚A), the effect on the electronic band structure isobvious. Fig. 5 is the corresponding band structureswhen Se moves (a) away from and (b) close to the Fe-Fe plane at 6 GPa. At Γ point, the band around Fermilevel labeled by orange line is occupied when Se movesaway from the Fe-Fe plane [Fig. 5(a)] and becomes un-occupied when Se moves close [Fig. 5(b)]. Throughanalysis from the band-decomposed charge density, thisband consists of the Fe d x − y orbital in Fig. 5(a) andchanges into the d xz / d yz orbital in Fig. 5(b). Around M point, the energy band represented by red line showsopposite change to that at Γ point. After the same anal-ysis, it is confirmed that the band around M point comesfrom the d x − y and d xz / d yz orbitals of Fe in Fig. 5(a)and Fig. 5(b), respectively. However, the band changearound the A point is a little different from M point.For A point, the energy band (in red color) shifts downwith decreased energy when Se moves close to the Fe-Feplane. The three-dimensional views can be seen moreclearly from the shape changes of Fermi surfaces as plot-ted adjacent to the corresponding band structures. Smallchanges of crystal structure due to zero-point vibration FIG. 5. (Color online) Electronic band structures and Fermisurfaces of FeSe in AFM N´eel state as a result of zero-pointvibration of the A g mode at 6 GPa. The Fermi energy is setto zero. Panels (a) and (b) correspond to movements of atomSe far away from and close to the Fe-Fe plane, respectively.The high symmetry points in Brillouin zone are the same asthat in Fig. 1(e). alone could not affect the energy band so much unlesssome other physical mechanism is included in this pro-cess. Nonmagnetic calculations have been performed toascertain our speculations. Only in spin-polarized calcu-lations, the zero-point vibrations have great impact onthe energy bands. The dramatic changes of band struc-tures and Fermi surfaces due to the zero-point vibrationsof A g mode in AFM N´eel state at 6 GPa further supportthat spin-phonon coupling plays a key role in FeSe underpressure. IV. DISCUSSION AND SUMMARY
Our above calculations show that the zero-point vibra-tion of the A g mode of FeSe, which relates with the Seheight from the Fe-Fe plane, induces large fluctuations oflocal magnetic moment on Fe and the spin fluctuationscaused by spin-phonon coupling are further enhanced un-der pressure. In recent experiments by means of magne-tization and neutron power diffraction, a clear isotope ef-fect on T c is observed for bulk FeSe, which highlights therole of the lattice in the paring mechanism. In a Raman-scattering measurement on K . Fe . Se , an anomaly at T c in the 180 cm − A g mode is observed, which indi-cates a rather specific type of electron-phonon coupling. For the recently grown monolayer FeSe on SrTiO sub-strate showing signatures of T c above 50 K, the screen-ing due to the SrTiO ferroelectric phonons on Cooperparing in monolayer FeSe is proposed to significantly en-hance the energy scale of Cooper paring and even changethe paring symmetry. From first-principles studies onFeSe and KFe Se , the estimates of T c based on spin-resolved coupling values show around a twofold increasethan that from non-spin-resolved configurations. Theseexperimental and theoretical studies all suggest that theeffect of phonon could not be completely ignored in theparing mechanism of FeSe.Not only in iron chalcogenides, there are also evidencesof phonon effects on the unconventional superconduc-tivity in iron pnictides and cuprates. On the exper-imental side, for SmFeAsO − x F x and Ba − x K x Fe As systems, the iron isotope substitution shows the sameeffect on T c and the spin-density wave transition tem-perature T SDW , suggesting that strong magnon-phononcoupling exists. Using ultrashort and intense opticalpulses probe, ultrafast transient spin-density-wave or-der develops in the normal state of BaFe As and isdriven by coherent lattice vibrations even without break-ing the crystal symmetry, which attests a pronouncedspin-phonon coupling in pnictides. From ARPES probeof the electron dynamics in three different families ofcopper oxide superconductors, which share a commonthread of spin-fluctuation mediated pairing as iron-basedsuperconductors, it is found that an abrupt change ofelectron velocity at 50-80 meV can not be explained byany known process other than the coupling to phonon isincluded. On the theoretical side, Yildirim finds strongcoupling of the on-site Fe-magnetic moment with the As-As bonding in iron-pnictide superconductors from first-principles calculations. For computational studies ondoped LaFeAsO, the coupling magnetism with vibrationsis also found to induce anharmonicities and an electron-phonon interaction much larger than in the paramagneticstate.
From these studies, the spin-phonon couplingis evidently ubiquitous in iron-based superconductors.The spin-fluctuation mediated pairing is common iniron-based superconductors and other unconventional su-perconducting materials.
Regarding the nature of themagnetism in iron-based superconductors, there are ba-sically two contradictive views. The one is based onitinerant electron picture, in which the Fermi surfacenesting is responsible for the AFM order. On the con-trary, the other one is based on local moment interactionswhich can be described by the J - J frustrated Heisen-berg model. And it was further shown that the un-derlying driving force herein is the anion-bridged AFMsuperexchange interaction between a pair of the next-nearest-neighboring fluctuating Fe local moments embed-ded in itinerant electrons. There are now more and moreevidences in favor of the fluctuating Fe local moment pic-ture. Especially, the inelastic neutron scattering experi-ments have shown that the low-energy magnetic excita- tions can be well described by the spin waves based onthe J - J Heisenberg model.
Our calculated resultsof FeSe here show that the fluctuations of local mag-netic moment induced by the zero-point vibration of A g phonon mode are significant and are further enhancedunder pressure. Eventhough the direct electron-phononcoupling calculations both without and with spin po-larization effects cannot account for the experimentallyobserved T c of FeSe, the phonon could play an indirectrole through spin-phonon coupling. Our results suggestthe effect of phonon should be included when unravelingthe paring mechanism in iron-based superconductors.To summarize, the variation of band structures and thephonon frequencies of FeSe under 0 to 9 GPa hydrostaticpressure, as well as the effect of the zero-point vibrationson the local magnetic moment fluctuations and bandstructures, have been investigated by using DFT calcula-tions with vdW corrections. With applied pressure, theenergy bands consisting of Fe d orbitals around the Fermilevel show obvious shifts and occupation changes. At thesame time, the frequencies of all optical phonon modesat Brillouin zone center increase with pressure. Amongthese phonon modes, the A g mode related to the Seheight from Fe-Fe plane shows a clear frequency jumpfrom 5 to 6 GPa. This is around the similar pressurerange within which the highest T c is observed for FeSein experiment. Compared with other phonon modes, thezero-point vibration of the A g mode also induces thestrongest fluctuation of local magnetic moment on Fefrom 0 to 9 GPa and the fluctuation reaches maximum at5 GPa. The enhanced fluctuations of local magnetic mo-ment may be favorable to promote the T c . These resultshighlight the role of spin-phonon coupling when exploringthe superconducting mechanism of iron-based supercon-ductors. ACKNOWLEDGMENTS
We wish to thank Professor Shiwu Gao for help-ful communications. This work is supported by Na-tional Natural Science Foundation of China (Grant Nos.11004243, 11190024, and 51271197) and National Pro-gram for Basic Research of MOST of China (Grant No.2011CBA00112). Computational resources have beenprovided by the Physical Laboratory of High Perfor-mance Computing at Renmin University of China. Theatomic structures and Fermi surfaces were prepared withthe XCRYSDEN program. ∗ [email protected] † [email protected] Y. Kamihara, H. Hiramatsu, M. Hirano, R. Kawamura, H.Yanagi, T. Kamiya, and H. Hosono, J. Am. Chem. Soc. , 10012 (2006); X. H. Chen, T. Wu, G. Wu, R. H. Liu,H. Chen, D. F. Fang, Nature , 761 (2008); G. F. Chen, Z. Li, D. Wu, G. Li, W. Z. Hu, J. Dong, P. Zheng, J. L.Luo, and N. L. Wang, Phys. Rev. Lett. , 247002 (2008). M. Rotter, M. Tegel and D. Johrendt, Phys. Rev. Lett. , 107006 (2008). X. C. Wang, Q. Q. Liu, Y. X. Lv, W. B . Gao, L. X. Yang,R. C. Yu, F. Y. Li, and C. Q. 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