Abstract
Iron arsenide superconductors based on the material LaFeAsO_{1−x}F_{x} are characterized by a twodimensional Fermi surface (FS) consisting of hole and electron pockets yielding structural and antiferromagnetic transitions at x=0. Electron doping by substituting O^{2−} with F^{−} suppresses these transitions and gives rise to superconductivity with a maximum T_{c} of 26 K at x=0.1. However, the overdoped region cannot be accessed due to the poor solubility of F^{−} above x=0.2. Here we overcome this problem by doping LaFeAsO with hydrogen. We report the phase diagram of LaFeAsO_{1−x}H_{x} (x<0.53) and, in addition to the conventional superconducting dome seen in LaFeAsO_{1−x}F_{x}, we find a second dome in the range 0.21<x<0.53, with a maximum T_{c} of 36 K at x=0.3. Density functional theory calculations reveal that the three Fe 3d bands (xy, yz and zx) become degenerate at x=0.36, whereas the FS nesting is weakened monotonically with x. These results imply that the band degeneracy has an important role to induce high T_{c}.
Introduction
Since the discovery of superconductivity in LaFeAsO_{1−x}F_{x} with T_{c}=26 K in early 2008 (ref. 1), various types of iron pnictides containing square lattices of Fe^{2+} have been investigated^{2,3,4}. That maximum was raised to 55 K in Ln1111type LnFeAsO_{1−x}F_{x} (Ln denotes lanthanide)^{5}. The compound of LaFeAsO_{1−x}F_{x} is paramagnetic metal with tetragonal symmetry at room temperature and undergoes a tetragonal–orthorhombic transition around 150 K accompanied by a paraantiferromagnetic (AFM) transition^{6,7}. Superconductivity emerges when the transitions are suppressed by carrier doping via element substitution or pressure application. To explain the emergence of superconductivity near the AFM phase, a spin fluctuation model resulting from Fermi surface (FS) nesting between hole and electron pockets was proposed based on density functional theory (DFT) calculations^{8,9}. This model explains the suppression of superconductivity in LaFeAsO_{1−x}F_{x} upon electron doping to the filling level of hole pockets (x=0.2) and the striking difference in the maximum T_{c} between LnFeAsO_{1−x}F_{x} (26–55 K) and LaFePO (4 K) or between La1111(26 K) and Sm1111(55 K)^{10}.
However, the phase diagrams reported so far for LnFeAsO systems are rather incomplete. For instance, the suppression of T_{c} in overdoping region had not been confirmed for any Ln1111types (except La). This situation primarily comes from the low solubility limit of fluorine in LnFeAsO_{1−x}F_{x} (x<0.15–0.20). Recently, we reported the syntheses of (Ce, Sm)FeAsO_{1−x}H_{x} (0<x<0.5) by using the high solubility limit of hydrogen and obtained a complete superconducting dome ranging 0.05<x ≤0.4~0.5 with optimum T_{c} of 47 K for the Cesystem or 56 K for the Smsystem, agreeing well with that the previous data of each fluorinedoped sample in x<0.15 (refs 11,12). The position and occupancy of hydrogen substituting the oxygen sites were verified by neutron powder diffraction measurement and the charge state of hydrogen was examined by DFT calculations^{12}. The neutron powder diffraction measurement on CeFeAsO_{1−x}D_{x} revealed that hydrogen species exclusively substitute the oxygen sites in the CeO layer, and DFT calculations indicated that the hydrogen 1s band is located at −3 to −6 eV, which is close to level of the oxygen 2p band and the charge state of the hydrogen is −1. These results substantiate the idea that hydrogen exclusively substituting the O^{2–} sites occurs as H^{−}, supplying electrons to the FeAs layer, the same as fluorine does (O^{2–}=H^{−}+e^{−}).
When comparing the superconducting dome of LaFeAsO_{1−x}F_{x} with (Ce, Sm)FeAsO_{1−x}H_{x}, it is found that the dome width is twice as narrow as that of (Ce, Sm)FeAsO_{1−x}H_{x} and the optimum T_{c} of LaFeAsO_{1−x}F_{x} is much lower than that of (Ce, Sm)FeAsO_{1−x}H_{x}. Moreover, the temperature dependence of resistivity in the normal conducting state indicates that the (Ce, Sm)FeAsO_{1−x}H_{x} behave nonFermi liquid, that is, ρ(T)~T, whereas LaFeAsO_{1−x}F_{x} obeys Fermi liquid, that is, ρ(T)~T^{2}. These differences remind us the idea that the electron doping via fluorine substitution in LaFeAsO_{1−x}F_{x} is not enough to draw out the genuine physical property of LaFeAsO.
In this Article, we study the LaFeAsO system, the prototype material for the Ln1111 system, and examine its superconducting properties by using H^{−} in place of F^{−} for electron doping. We report the existence over a wider x range of another T_{c} dome with higher T_{c} in addition to the dome reported so far by F^{−} substitution. Not only are there differences in maximum T_{c} and shape between these two domes, but also the second dome with resistivity characterized by a linear temperature dependence corresponds to that observed in other Ln1111 systems (except La) with higher T_{c}. Based on DFT calculations of the crystal structures of these doped samples determined at 20 K, we discuss the origin for the superconductivity.
Results
Twodome structure
In Fig. 1a,b, we show the temperature dependence of electrical resistivity for LaFeAsO_{1−x}H_{x}. At x=0.01 and 0.04, a kink in resistivity due to structural or magnetic transitions was seen around 150 K (refs 6,7). As x is increased, the transitions are suppressed and the onset T_{c} appears for x ≥ 0.04, and zero resistivity is attained for x ≥ 0.08. The onset T_{c}, determined from the intersection of the two extrapolated lines in Fig. 1c,d attains a maximum of 29 K at x=0.08 and decreases to 18 K at x=0.21, forming the first T_{c} (x) dome. For 0.08≤ x ≤0.21, the temperature dependence of resistivity ρ(T) in the normal state obeys a T^{2}law, indicating that the system is a strongly correlated metal in Fermi liquid theory^{13}. The T_{c} (x) and temperature dependence of ρ above T_{c} agree well with those in LaFeAsO_{1−x}F_{x} (ref. 1). Further electron doping (x > 0.21) continuously enhances T_{c} to 36 K around x=0.36 for which ρ(T) exhibits Tlinear dependence. Figure 1e,f shows the temperature dependence of volume magnetic susceptibility χ for samples with different x. Because of the presence of metal iron impurities, each sample has a positive offset. The diamagnetism due to superconductivity is clear to see for x >0.04. Shielding volume fraction exceeds 40% at 2 K in 0.08≤ x ≤0.46, and then decreases to 20% at x=0.53, forming the second T_{c} dome in the composition range 0.21<x<0.53. This dome is newly found by the present study.
Pressure effect
Figure 2a–d shows the changes in ρ(T) for samples with x=0.08, 0.21, 0.30 and 0.46 under applied pressures (P) up to 3 GPa. The onset T_{c} increases largely with P for x=0.08, 0.21 and 0.30, whereas the T_{c} for x=0.46 slightly decreases from 33 K to 32 K at P=2.7 GPa. The maximum T_{c} obtained at x=0.30 under P=2.6 GPa is 46 K, which is distinctly higher than the maximum T_{c} (43 K) in the LaFeAsO_{1−x}F_{x} under high pressure^{14}. The T_{c} valley around x=0.21 under ambient pressure disappears, resulting in the onedome structure as observed in other Ln1111 series. Figure 2e summarizes the T_{s} and T_{c} under ambient pressure in the LaFeAsO_{1−x}H_{x} and LaFeAsO_{1−x}F_{x} (ref. 15) along with T_{c} at P=3 GPa of LaFeAsO_{1−x}H_{x}. Two superconducting domes are evident and each has maximum T_{c} around x=0.08 and 0.36. The first dome is located adjacent to the orthorhombic and AFM phase and is almost the same as previously reported for LaFeAsO_{1−x}F_{x}, whereas the second dome appears adjacent to the first dome. At P=3 GPa, the two domes merge into a wider dome having a closed shape and a range similar to those in CeFeAsO_{1−x}H_{x} with maximum T_{c}=47 K (ref. 12). This unification of the two domes on applying high pressure may be understood as lattice compression; the reduction of the aaxis (~1% under 3 GPa) in LaFeAsO_{1−x}F_{x} is assumed to bring it close to a LaFeAsO_{1−x}H_{x} lattice^{16}. Then, a 1%reduction of aaxis for LaFeAsO_{1−x}H_{x} draws its lattice close to that of CeFeAsO_{1−x}H_{x} under an ambient pressure^{12}.
Lanthanide cation substitution effect
Here we consider the relation between the two domes of the Lasystem and the domes of the other Ln1111 systems. To compare the temperature dependence of resistivity of LaFeAsO_{1−x}H_{x} with that of other Ln1111 systems, we performed powerlaw fitting, ρ=ρ_{0}+AT^{n} (ρ_{0}: residual resistivity) in the temperature range above T_{c} to 150 K (Supplementary Fig. S1). Figure 3a shows the relation between the exponents n and x for LnFeAsO_{1−x}H_{x} (Ln=La, Ce, Sm and Gd; The sample preparation and temperature dependence of electrical resistivity and volume magnetic susceptibility for newly found GdFeAsO_{1−x}H_{x} are summarized in Supplementary Fig. S2 and in the Supplementary Methods.). Fermi liquidlike behaviour, n=2, is observed only in lowx LaFeAsO_{1−x}H_{x}, whereas nonFermi liquid behaviuor, n<2, is observed for highx LaFeAsO_{1−x}H_{x} and for the entire range of x in the other systems. Figure 3b shows the plot of T_{c} versus exponent n for the same systems. As n approaches unit for each system, T_{c} becomes a maximum, indicating that this feature of the second dome in LaFeAsO_{1−x}H_{x} is commonly seen for domes in other Ln1111; that is, the first dome is unique to La1111, whereas the second is universally to all four systems. Figure 3c–f shows the xvariation in T_{c} for all four systems. The optimal x in the T_{c} dome continuously shifts to lower x when comparing Ln=La through to Gd.
Discussion
We have found an unusual twodome structure in T_{c} for the LaFeAsO_{1−x}H_{x} system, the higher T_{c} dome being associated with a universal structure of LnFeAsO_{1−x}H_{x} systems generally. To understand these dome structures, we calculated the electronic state of these materials using the crystal structures determined at 20 K. The electron doping via substitution of O^{2–} sites with H^{−} ion was modelled in virtual crystal approximation assuming hydrogen acts as a quasifluorine ion supplying an electron to the FeAs layer^{12}, that is, the oxygen (Z=8) sites were substituted for virtual atoms which have a fractional nuclear charge (Z=8+x), where x is hydrogen fraction. Figure 4a–d shows the twodimensional crosssections of FS for the various doping levels. These compositions, x=0.08, 0.21, 0.36 and 0.40, correspond to the top of first dome, T_{c} valley, the top of the second dome and overdoping region, respectively. At x=0.08, the size of an outer d_{xy} (x, y and z coordination is given by the Fe square lattice) or inner d_{yz,zx} hole pockets at the Γ point is close to that of two electron pockets at the M point, indicating that nesting in the (π π) direction between the hole and the electron pockets is strong. As x increases, the nesting monotonically weakens because the hole pockets are gradually reduced but the electron pockets are expanded. It is pointed out that as the pnictogen height, h_{Pn}, from the Fe plane increases, the d_{xy} hole pocket is enlarged; nesting then becomes better^{10}. In the present case, although h_{As} increases with x as shown in Fig. 4e, the size of the d_{xy} hole pocket remains almost unchanged irrespective of x. This result may be understood by considering that expansion of d_{xy} hole pocket by structural modification is cancelled by reduction due to the upshift of Fermi level (E_{F}) by electron doping.
Nesting between hole and electron pockets is the most important glue in the spin fluctuation model^{8,9}. The decrease in T_{c} from x=0.08 through 0.21 may be understood as a reduction in spin fluctuations due to weakening of the nesting in a similar manner to LaFeAsO_{1−x}F_{x}. It is, however, difficult to understand by the FS nesting that the experimental findings that T_{c} (x) increases over a wider dome range of 0.21<x<0.53 and optimizes at 36 K around x=0.36.
Figure 4f–i shows band structures near E_{F} for sample composition x=0.08, 0.21, 0.36 and 0.40. As the unit cell contains two irons, there are ten bands around the E_{F} derived from bonding and antibonding of 3d orbitals of the two neighbouring irons that cross the E_{F} around the Γ and M points. The unoccupied bands move continuously lower with x. In particular, the bands derived from the antibonding orbital between the d_{xy} orbitals, which we shall call the 'antid_{xy} bands' hereafter, and the band derived from the degenerate d_{yz,zx} bonding orbitals are lowered in energy and cross the bondingd_{xy} band around x=0.36, forming degenerate states of Fe 3d_{xy,yz,zx} three bands near E_{F} as seen in Fig. 4j. After this triplydegenerate state is formed, the antid_{xy} band and bonding d_{yz,zx} band create a new band below E_{F} at x=0.40 by reconstruction (see inset of Fig. 4i). Note in Fig. 4e that the As–Fe–As angle of FeAs_{4} tetrahedron is far from that of regular tetrahedron (109.5°) in the optimally doped region (x=0.33−0.46). The band structures of LaFeAsO_{1−x}H_{x} (x=0.08, 0.21, 0.36 and 0.40) with only structural change are shown in Supplementary Fig. S3. Although the magnitude of the energy difference between these three bands becomes small with x, the band crossing is not caused only by the structural change, indicating that not only the change in local structure around iron but also asymmetric occupation of doped electrons in the bondingd_{yz,zx}, d_{xy} and antibondingd_{xy}, affect the band shift. As the bonding d_{yz,zx} and d_{xy} bands are almost flat along the ΓZ direction, their band crossing at x=0.36 form a shoulder in the total density of states (DOS) at E_{F} (Fig. 4m), indicating an electronic instability of the system arising from degeneration of the d_{xy} and d_{yz,zx} bands. In such a situation, structural transitions, for instance band JahnTeller distortion, may occur to reduce the energy of the system. However, in the present results, any structural transition could not be observed at least down to 20 K in samples with 0.08≤ x ≤0.40.
Table 1 summarizes the characteristics of each T_{c} dome described above. The primary question is what the origin is for the second dome, that is, the dome in the Ln1111 with higher T_{c}. The resistivity above T_{c} changes from quadratic to linear dependence as x approaches the top of the second dome region. As the nesting between hole and electron pockets monotonically is weakened with x, it is rationally considered that the contribution of FS nesting to the second T_{c} dome is not dominant. In addition, the calculated DOS shows the presence of a shoulder of the DOS (E_{F}) at x=0.36 related by the degeneracy of three bands derived from Fed_{yz,zx} and d_{xy} orbitals. Given these results, the band degeneracy appears to have an important role in emergence of the second dome. For the ironbased superconductors, there is another pairing model derived from a large softening of a shear modulus observed near the tetragonal–orthorhombic transition of parent compounds^{17,18,19}. This model tells that the Fed orbitals are possible to order when their degeneracy in Fed_{yz,zx} orbitals is removed at the structural transition and the fluctuations of this orbital ordering are shown capable of inducing superconductivity^{18,19}. If we follow the orbital fluctuation model, the second dome and Tlinear resistivity in the present system might be understood as results of electron pairing and carrier scattering by the fluctuations of the degenerated Fed_{xy,yz,zx} orbitals, respectively.
Finally, we consider why the twodome structure is only found in LaFeAsO_{1−x}H_{x} and not (CeGd)FeAsO_{1−x}H_{x}. The degeneracy of three bands derived from Fe3d_{yz,zx} and d_{xy} orbitals is realized when energy splitting between the 3d_{yz,zx} and d_{xy} bands mainly derived from distortion of FeAs_{4} tetrahedron is cancelled out by asymmetric occupation of doped electrons in the these three bands. The magnitude of the energy difference between these three bands becomes small on going from La ion to Ce–Gd ions in LnFeAsO because the As–Fe–As angle of FeAs_{4} tetrahedron continuously approach to the angle (109.5°) of a regular tetrahedron as the lanthanide ion is changed from La (114°) to Gd (110°)^{20}. In particular, this deviation in the Lasystem is rather large compared with the other system. Therefore, the threefold degeneracy in (CeGd)FeAsO_{1−x}H_{x} on electron doping is expected to occur in lower x than that (x=0.35) in LaFeAsO_{1−x}H_{x}. As a consequence, we think that the second dome primarily originating from the band degeneracy is separated from the first dome from FS nesting. The present discussion on orbital fluctuation model is based on DFT calculations. Further effort is required to confirm the validity of this idea on decisive experimental evidences such as angularresolved photoemission and elastic shear modulus measurements using the single crystals.
Methods
Synthesis, structural and chemical analyses of LaFeAsO_{1−x}H_{x}
As reported previously, LaFeAsO_{1−x}H_{x} was synthesized by solidstate reactions using starting materials La_{2}O_{3}, LaAs, LaH_{2}, FeAs and Fe_{2}As under high pressure^{11}. The phase purity and structural parameters at room temperature were determined by powder Xray diffraction measurements with MoKα1 radiation. The structure parameters at low temperatures were determined by synchrotron Xray diffraction measurements at 20 K using the BL02B2 beamline in the SPring8, Japan. Hydrogen content in the synthesized samples was evaluated by thermogravimetric mass spectroscopy, and the chemical composition with the exception of hydrogen was determined with a wavelengthdispersivetype electronprobe microanalyzer.
Electric and magnetic measurement
Resistivity and magnetic susceptibility at ambient pressure were measured using a physical property measurement system with a vibrating sample magnetometer attachment. Electrical resistivity measurements under high pressure were performed by the dc fourprobe method. Pressures were applied at room temperature and maintained using a pistoncylinder device. A liquid pressuretransmitting medium (Daphne oil 7373) was used to maintain hydrostatic conditions.
Density functional theory calculations
The electronic structure for LaFeAsO_{1−x}H_{x} was derived from nonspinpolarized DFT calculations using the WIEN2K code^{22} using the generalized gradient approximation Perdew–Burke–Ernzerhof functional^{23} and the fullpotential linearized augmented plane wave plus localized orbitals method. To ensure convergence, the linearized augmented plane wave basis set was defined by the cutoff R_{MT}K_{MAX}=9.0 (R_{MT}: the smallest atomic sphere radius in the unit cell), with a mesh sampling of 15×15×9 k points in the Brillouin zone.
Additional information
How to cite this article: Iimura, S et al. Twodome structure in electrondoped iron arsenide superconductors. Nat. Commun. 3:943 doi: 10.1038/ncomms1913 (2012).
Change history
20 December 2013
The original version of this Article contained a typographical error in the spelling of the author Satoru Matsuishi, which was incorrectly given as Satoru Matuishi. This has now been corrected in both the PDF and HTML versions of the Article.
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Acknowledgements
We thank Professor H. Fukuyama of Tokyo university of Science for discussions. This research was supported by the Japan Society for the Promotion of Science (JSPS) through the FIRST program, initiated by the CSTP. The synchrotron radiation experiments were performed at the BL02B2 of SPring8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI; proposal no. 2011A1142).
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H.H. and S.M. planned the research. S.I., T.H. and Y.M. performed the highpressure synthesis. S.I. performed measurement. H.S. and S.W.K. carried out highpressure resistivity measurement. S.I., J.E.K. and M.T. performed Synchrotron Xray diffraction measurements. S.I. and S.M. performed DFT calculations. H.H. and S.I. and S.M. discussed the results and wrote the manuscript.
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Supplementary Figures S1S3 and Supplementary Methods (PDF 1127 kb)
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Iimura, S., Matsuishi, S., Sato, H. et al. Twodome structure in electrondoped iron arsenide superconductors. Nat Commun 3, 943 (2012). https://doi.org/10.1038/ncomms1913
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DOI: https://doi.org/10.1038/ncomms1913
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