Novel Superconducting Characteristics and Unusual Normal-State Properties in Iron-based Pnictide Superconductors: Fe-NMR and As-NQR/NMR studies in REFeAsO (RE = La, Pr, Nd) and BaKFeAs
We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO (RE=La,Pr,Nd) and BaKFeAs( 38 K) by means of Fe-NMR and As-NQR/NMR. In the superconducting state of LaFeAsO ( 28 K), the spin component of the Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin-lattice relaxation rates in LaFeAsO and BaKFeAs exhibit a -like dependence without a coherence peak just below , indicating that an unconventional superconducting state is commonly realized in these Fe-based pnictide compounds. All these events below are consistently argued in terms of an extended s-wave pairing with a sign reversal of the order parameter among Fermi surfaces. In the normal state, decreases remarkably upon cooling for both the Fe and As sites of LaFeAsO. In contrast, it gradually increases upon cooling in BaKFeAs. Despite the similarity between the superconducting properties of these compounds, a crucial difference was observed in their normal-state properties depending on whether electrons or holes are doped into the FeAs layers. These results may provide some hint to address a possible mechanism of Fe-based pnictide superconductors.
keywords:superconductivity, iron-based pnictide, LaFeAsO, (Ba,K)FeAs, NMR, NQR 74.70.-b,74.20.Rp,76.60.-k
The discovery of superconductivity (SC) in the iron (Fe)-based oxypnictide LaFeAsOF, reaching a superconducting transition temperature = 26 K, has attracted considerable interest in the fields of condensed-matter physics and material science Kamihara2008 . Shortly after this discovery, it was reported that of LaFeAsOF increases up to 43 K upon the application of pressure Takahashi , and the replacement of the La site by other rare earth (RE) elements significantly increases up to more than 50 K Ren1 ; Kito ; Ren2 ; GdFeAsO . These findings have provided a new material base for searching high- SC. The structure of mother materials contains an alternate stacking of REO and FeAs layers along the c-axis where the Fe atoms of the FeAs layer are located in a fourfold coordination forming a FeAs tetrahedron. The mother material LaFeAsO is a semimetal with a stripe antiferromagnetic (AFM) order with or Cruz . The substitution of fluorine for oxygen and/or oxygen deficiencies at the LaO layer yield a novel SC Kamihara2008 ; Ren1 ; Kito ; Ren2 ; GdFeAsO . In particular, a very sharp superconducting transition in resistance under for NdFeAsO ensures a homogeneous electronic state even in an oxygen-deficient sample Takeshita . Remarkably, Lee et al. found that increases to the maximum value of 54 K when the FeAs tetrahedron is transformed into a regular one C.H.Lee .
Another family of FeAs-based superconductors without oxygens has been reported in the ternary compound BaKFeAs with 38 K Rotter . In this compound, layers consisting of edge-sharing FeAs tetrahedra are separated by Ba(K) layers. Moreover, SC was also reported in -FeSe with 8 K Hsu . This compound is composed of stacking layers of FeSe, resembling the FeAs layers in LaFeAsOF, but containing neither any Ba(K) atoms nor LaO sheets. The present experimental facts suggest that systematic studies of the local electronic state at the Fe site are quite important to elucidate the origin of SC in the iron-based compounds.
Polycrystalline samples of LaFeAsO, PrFeAsO, NdFeAsO, and BaKFeAs were synthesized via the high-pressure synthesis technique described elsewhere Kito . Although the real oxygen content of the samples may be greater than the nominal (intended) values due to the oxidation of the starting RE elements, powder X-ray diffraction measurements indicate that these samples are almost entirely composed of a single phase. The s for all samples were determined by susceptibility measurement, which indicated a marked decrease due to the onset of SC below 20 K, 28 K, 28 K, 22 K, 46 K, and 53 K for LaFeAsO, Fe-enriched LaFeAsO, LaFeAsO, LaFeAsO, PrFeAsO, and NdFeAsO, respectively. Note that the lattice parameters = 4.0226 Å and = 8.7065 Å of Fe-enriched LaFeAsO are very close to those of LaFeAsO ( = 4.0220 Å and = 8.7110 Å), indicating that the physical properties of both samples are compatible. of LaFeAsO is lower than that of LaFeAsO because the former is in an overdoped regime. This result is corroborated by the fact that the lattice parameters of LaFeAsO are smaller than those of LaFeAsO ( 28 K). The samples were moderately crushed into powder for the NQR/NMR measurements. Fe-NMR and As-NQR/NMR measurements were performed by using the phase coherent pulsed NMR/NQR spectrometer in the temperature () range between 4 K and 280 K. was measured using the saturation recovery method.
3 Results and discussion
3.1 Fe-NMR study of LaFeAsO
Figure 1(a) shows the Fe-NMR spectra for LaFeAsO obtained by a sweeping frequency () at a magnetic field 11.97 T at 30 K. For parallel to the -plane, a single NMR spectrum is observed with a very narrow linewidth with 20 kHz. This result indicates that the FeAs layers of this sample are rather homogeneous irrespective of the oxygen deficiency in the LaO layer. For parallel to the c-axis, respective asymmetric peaks are observed in the spectra, corresponding to the crystal directions with and , where is the angle between the field and the c-axis. Anisotropic Knight shifts, defined as a shift from (), are % and % at 30 K for and , respectively.
Figures 1(b) and (c) show the dependences of the Fe-NMR spectra at = 6.309 T and 11.97 T parallel to the -plane() with 24 K and 20 K, respectively. The dependence of for parallel to the -plane is shown in Fig. 2(a). The Knight shift comprises the -independent orbital contribution and the -dependent spin contribution, denoted as and , respectively. Note that it increases upon cooling, exhibiting a dependence opposite to those of the As and F sites Grafe ; Ahilan ; ImaiJPSJ . This is because the hyperfine-coupling constant at the Fe site is negative, originating from the inner core-polarization. In this compound, note that , where is the on-site negative term dominated by the inner core polarization, and is the transferred positive one from the neighbor Fe sites through direct Fe-Fe and/or indirect Fe-As-Fe bondings. A transferred hyperfine-coupling constant at the As site consists of two contributions in the isotropic term of a transferred hyperfine field () and the anisotropic one of a pseudo-dipole field () Kitagawa , both of which are induced by neighboring Fe- spin polarization. From a plot of versus with as an implicit parameter, is estimated to be % Terasaki using the orbital shift at the As site reported in literature ImaiJPSJ . Eventually, a spin component of the Knight shift , as shown in Fig. 2(b), decreases to almost zero well below . This result suggests the possible existence of an isotropic gap in a very-low-temperature regime, providing firm evidence of spin-singlet Cooper pairing through the direct measurement of the local spin susceptibility by means of the Fe-Knight shift .
The nuclear spin-lattice relaxation rate at the Fe site was determined from a single exponential recovery curve of Fe nuclear magnetization as follows:
where and are the respective nuclear magnetizations for the thermal equilibrium condition and at time after the saturation pulse. In fact, as shown in Fig. 3, was uniquely determined from a single exponential function of in the entire range, revealing that the electronic state of the present sample is homogeneous. We have confirmed that is isotropic regardless of the crystal direction.
Figure 4 shows the dependences of at 6.309 and 11.97 T in the range of 480 K and 30240 K, respectively. In the SC state, Fe-NMR exhibits a -like dependence without a coherence peak just below 24 K at = 6.309 T. Note that any deviation from the dependence was not observed even at well below . Here, it should be noted that in most d-wave superconductors with a line-node gap, such as copper oxides high- superconductors, tends to exhibit a linear dependence at low temperatures, probing the residual density of states (RDOS) at the Fermi level in association with an impurity effect.
3.2 As-NQR study of LaFeAsO
Here, we review the As-NQR results for LaFeAsO ( K) at MHz and zero field Mukuda . In the As-NQR measurements at , the recovery curve of As nuclear magnetization with 3/2 is also expressed by a single exponential function as follows:
As shown in Fig. 5, was almost fitted by a single exponential function in the SC state and the normal state, ensuring that is uniquely determined over the entire range.
Figure 4 shows the dependence of As-NQR for LaFeAsO with = 28 K. In the SC state, at the As site exhibits a -like dependence without a coherence peak just below 28 K, resembling the Fe-NMR result. Considering that Fe-NMR measured in the SC mixed state under 6.309 T exhibits a dependence similar to that of As-NQR , it would be expected that the presence of vortex cores would not affect the quasiparticle excitations in the SC state considerably. This implies that the measurements can clarify the SC gap structure although it has been measured under . Therefore, the -like behavior with no coherence peak gives firm evidence for an unconventional superconducting nature inherent to the Fe-pnictide superconductors. In d-wave superconductors, which also exhibit -like behavior with no coherence peak, a -like behavior was observed at low temperatures, indicating the presence of the RDOS at the Fermi level. This event is well understood in terms of the impurity scattering effect in a unitarity limit in unconventional superconductors with a line-node gap, such as d-wave superconductors. This is not the case in the Fe-based superconductors. When noting that similar results have been reported in the As-NMR studies on F-substituted LaFeAs(OF) Grafe ; Nakai and PrFeAs(OF) Matano , and the Se-NMR study on FeSe Kotegawa and considering that these materials are far from a clean system, a d-wave model is not suitable for understanding these unconventional behaviors in Fe-based pnictide superconductors.
3.3 As-NMR study of BaKFeAs
Figure 6 shows the typical As-NMR spectra for the oriented powder of BaKFeAs with = 38 K at 37.5 MHz. The sharp central peak observed around 5.1 T originates from the central transition () in the As-NMR spectrum. The satellite peaks () around 4.7 and 5.5 T originate from the first-order perturbation effect of the nuclear quadrupole interaction (NQI), allowing us to estimate the nuclear quadrupole frequency 5(2) MHz to be larger than 2.2 MHz for the mother compound BaFeAs Fukazawa .
Next, we deal with the SC characteristics probed by the measurement. The recovery curve of As nuclear magnetization () for the As-NMR measurement is expressed by a theoretical curve as follows:
Figures 7(a) and (b) show in the SC state and the normal state, respectively.
Figure 8 shows the dependence of As-NMR for BaKFeAs at 5.1 T along with the data of LaFeAsO. We note that the present data on BaKFeAs are consistent with the result reported by another group FukazawaSC . In the SC state, decreases sharply below 37 K upon cooling without a coherence peak just below , strongly suggesting an unconventional SC nature. Furthermore, the seems to be close to a dependence well below . However, we note that the dependence of cannot be exactly reproduced by any simple SC gap model, either with line nodes or without nodes, which may relate to the characteristics of the multiband SC state observed in BaKFeAsARPES .
These unconventional features of below were commonly observed in most FeAs-based superconductors Mukuda ; Terasaki ; Grafe ; Nakai ; Matano ; Kotegawa ; FukazawaSC . In contrast, a fully-gapped SC state was observed in experiments such as ARPES ARPES and magnetic penetration depth Penetrationdepth . To reconcile these issues, was theoretically calculated on the basis of a nodeless extended -wave pairing model with a sign reversal of the order parameter between the hole and electron Fermi surfaces Mazin ; Kuroki . In the framework of either a two-band model, where the unitary scattering due to impurities is assumed NMRtheory , or a five-band model in a rather clean limit NMRtheory2 , the experiments are well reproduced by such calculations. In fact, the results of s for Fe and As in the SC state are consistent with the latter model. This may be because the intrinsic behavior of is measured for a highly homogeneous sample, which is guaranteed by the very sharp NMR linewidth. In this context, our results are consistently argued in terms of the extended s-wave pairing with a sign reversal of the order parameter among Fermi surfaces. Further, it would be desirable to measure at temperatures lower than 4 K and to systematically examine an impurity effect in these compounds.
3.4 Normal-state properties of LaFeAsO and BaKFeAs
Next, we address the normal-state properties of LaFeAsO and BaKFeAs through the results. As shown in Fig. 9, at the Fe site for LaFeAsO gradually decreases upon cooling down to , resembling the behavior of measured by NQR at the As site. Actually, at the Fe site is well scaled to at the As site down to 60 K with a ratio of . It has been theoretically proposed that the multiple spin-fluctuation modes with Q = (, 0) and (0,) originating from the nesting across the disconnected Fermi surfaces would mediate the extended s-wave pairing with a sign reversal of the order parameter. However, in our simple analyses of results Terasaki , we could only state that the spin fluctuations at finite wave vectors are more significant than the ferromagnetic spin fluctuation mode in this compound. Nevertheless, it is noteworthy that the s for both the Fe and As sites decrease upon cooling, indicating a decrease in the low-energy spectral weight of spin fluctuations over the entire space from room temperature. In contrast, in the case of the copper-oxide superconductors, s of Cu and O exhibit a different dependence due to the difference in the -dependence of and the development of AFM spin fluctuations around Takigawa . The suppression of spin fluctuations over the entire space upon cooling below room temperature was observed in FeAs-based superconductors, which has never been observed for other strongly correlated superconductors where an AFM interaction plays a vital role in mediating the Cooper pairing.
Figure 10 shows the dependence of in the normal state of BaKFeAs, along with the results of As-NQR for the electron-doped LaFeAsO and As-NMR s for the undoped BaFeAs Fukazawa and the electron-doped Ba(FeCo)As Ning . It gradually increases upon cooling down to = 37 K, in contrast to a significant decrease in the case of LaFeAsO. However, it should be noted that in the electron-doped Ba(FeCo)As gradually decreases upon cooling and remains almost constant down to K below 100 K Ning . It is remarkable that the dependence of in the hole-doped BaKFeAs is significantly different from those in the electron-doped compounds such as Ba(FeCo)As and LaFeAsO; nevertheless, the SC characteristics possess common features in these compounds. Recently, on the basis of the fluctuation exchange approximation (FLEX) on an effective five-band Hubbard model, Ikeda found that with decreasing temperatures, is enhanced in undoped and hole-doped systems. On the other hand, in electron-doped systems, it decreases significantly upon cooling, exhibiting a pseudogap behavior that originates from the band structure effect, that is, the existence of a high density of states just below the Fermi level. The effect becomes more remarkable with electron-doping. This qualitatively explains the NMR results. Such a pseudogap behavior exists even without electron correlation in the present band structure. Currently, the mechanism responsible for a pairing glue causing a possible extended s-wave pairing remains unknown.
3.5 As-NQR studies of REFeAsO (RE = La, Pr, Nd)
Figure 11 shows the As-NQR spectra just above their s for LaFeAsO ( 20 K), LaFeAsO ( 28 K), LaFeAsO() ( 22 K), PrFeAsO ( 46 K), and NdFeAsO ( 53 K). A As-NQR frequency () is obtained from the frequency at the peak of their As NQR spectra. Figure 12 shows a plot of versus for REFeAsO (RE = La, Pr, Nd). In the case of the LaFeAsO system, this plot appears to exhibit a dome-like shape, having a maximum K at 10 MHz. Note that the respective s = 46 K and 53 K of the optimally doped samples of REFeAsO (RE = Pr and Nd) become larger than K of LaFeAsO as increases from 10 MHz in LaFeAsO to 12 MHz in PrFeAsO and NdFeAsO. This correlation between and suggests an intimate relationship between the maximum value of and an optimum local structure, as revealed in literature C.H.Lee .
is proportional to the electric field gradient (EFG) along the c-axis . Here , where is the nuclear quadrupole moment of As and is the asymmetry parameter of the EFG. The EFG is generally given by two contributions; one is a non-cubic charge distribution of orbitals at the As site and the other is the charge distribution arising from the surrounding ions around the As site, denoted by and , respectively. The former originates from the hybridization between the As- orbitals and Fe- orbitals in the FeAs layer, and the latter may have a predominant contribution relevant to the Madelung potential originating from the charge distributions of the neighboring Fe atoms and REO layers. The variation of lattice parameters through doping significantly influences , resulting in a dome-like shape in the plot of versus for LaFeAsO, as shown in Fig. 12. In fact, the lengths of the a- and c-axes in the tetragonal structure decrease with oxygen content in LaFeAsO, and it decreases upon the replacement of La with Nd in REFeAsO. Despite the reduction in the lattice volume, the neutron diffraction experiment by Lee et al. has revealed that the distance between the Fe- and As-planes becomes larger in NdFeAsO than in LaFeAsO C.H.Lee . By assuming the point charges of the surrounding ions around the As site, a simple calculation of has revealed that the becomes larger for NdFeAsO than for LaFeAsO and LaFeAsO. However, the calculated values of cannot reproduce the experiments quantitatively, indicating that the on-site contribution is also important in these compounds. Namely, the change in the distance between the Fe- and As-plane varies the charge distribution of the As- orbitals, increasing in going from non-superconducting LaFeAsO to NdFeAsO with 53 K. The variation of the hybridization between As- orbitals and Fe- orbitals induces the modification of the Fe-As layer-derived band structure as well. Here, we note that MHz for undoped BaFeAs is significantly lower than the value of 8.7 MHz for undoped LaFeAsO. The variation of lattice parameters due to the change in the crystal structure is expected to mainly influence . Interestingly, in the BaFeAs system increases with K doping, suggesting that an increase in either the carrier density or the hybridization between As- orbitals and Fe- orbitals leads to an increase in .
Therefore, the intimate relationship between and in REFeAsO suggests that the local configuration of Fe and As atoms is significantly related to the of Fe-based pnictide superconductors, that is, can be enhanced up to 50 K when the local configuration of Fe and As atoms becomes optimal. Here, it may be relevant that becomes maximum when the bonding angle between Fe-As-Fe coincides with that of a regular tetrahedron of FeAs C.H.Lee .
Fe-NMR and As-NQR/NMR studies have clarified the novel SC and normal-state characteristics of Fe-enriched LaFeAsO ( = 28 K) and BaKFeAs ( = 38 K). In the SC state of LaFeAsO ( 28 K), the spin component of the Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of a superconducting state formed by spin-singlet Cooper pairing. The measurements of the Knight shift and have revealed that an extended s-wave pairing with a sign reversal of the order parameter can be a promising candidate.
In the normal state of LaFeAsO, we have found a remarkable decrease in upon cooling for both the Fe and As sites, whereas gradually increases upon cooling down to in the case of BaKFeAs. Remarkably, the dependence of in the normal state drastically changes when going from the hole-doped compound BaKFeAs to electron-doped compounds such as Ba(FeCo)As and LaFeAsO; nevertheless, the SC characteristics are not drastically different among these compounds.
Recently, on the basis of the fluctuation exchange approximation (FLEX) on an effective five-band Hubbard model, Ikeda found that with decreasing temperatures, in an electron-doped system decreases significantly upon cooling, exhibiting a pseudogap behavior that originates from the band structure effect, that is, the existence of a high density of states just below the Fermi levelIkeda . This qualitatively explains the NMR results. Such pseudogap behavior exists even without electron correlation in the present band structure. Currently, the mechanism responsible for a pairing glue causing a possible extended s-wave pairing remains unknown. Further experiments on the dependences of and at both the Fe and As sites using a single crystal are required to understand the nature of spin fluctuations.
We are grateful to N. Tamura, H. Yamashita, and H. Kinouchi for their assistance with some parts of NMR/NQR measurements. We are grateful to K. Miyazawa, P.M. Shirage, H. Kito, K. Kihou, and H. Eisaki for providing the crystals of REFeAsO and (Ba,K)FeAs, and S. Suzuki, S. Miyasaka, and S. Tajima for providing LaFeAsO. This work was supported by a Grant-in-Aid for Specially Promoted Research (20001004) and by the Global COE Program (Core Research and Engineering of Advanced Materials-Interdisciplinary Education Center for Materials Science) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
- (1) Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono: J. Am. Chem. Soc. 130, 3296 (2008).
- (2) H. Takahashi, K. Igawa, K. Arii, Y. Kamihara, M. Hirano, and H. Hosono: Nature 453, 376 (2008).
- (3) Z. A. Ren, W. Lu, J. Yang, W. Yi, X. L. Shen, Z. C. Li, G. C. Che, X. L. Dong, L. L. Sun, F. Zhou, and Z. X. Zhao: Chin. Phys. Lett. 25, 2215 (2008).
- (4) H. Kito, H. Eisaki, and A. Iyo: J. Phys. Soc. Jpn. 77, 063707 (2008).
- (5) Z. A. Ren, G. C. Che, X. L. Dong, J. Yang, W. Lu, W. Yi, X. L. Shen, Z. C. Li, L. L. Sun, F. Zhou, and Z. X. Zhao: Europhys. Lett. 83, 17002 (2008).
- (6) 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 and Z.X. Zhao: Supercond. Sci. Technol. 21, 082001 (2008).
- (7) C. de la Cruz, Q. Huang, J. W. Lynn, J. Y. Li, W. Ratcliff II, J. L. Zarestky, H. A. Mook, G. F. Chen, J. L. Luo, N. L. Wang, and P. C. Dai: Nature 453, 899 (2008).
- (8) N. Takeshita, A. Iyo, H. Eisaki, H. Kito, and T. Ito: J. Phys. Soc. Jpn. 77, 075003 (2008).
- (9) C. H. Lee, H. Eisaki, H. Kito, M. T. Fernandez-Diaz, T. Ito, K. Kihou, H. Matsushita, M. Braden, and K. Yamada: J. Phys. Soc. Jpn. 77, 083704 (2008).
- (10) M. Rotter, M. Tegel, and D. Johrendt: Phys. Rev. Lett. 101, 107006 (2008).
- (11) F.-C. Hsu, J.-Y. Luo, K.-W Yeh, T.-K. Chen, T.-W. Huang, P.M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu, D.-C. Yan, and M.-K. Wu: Proc. Natl. Acad. Sci. U.S.A. 105, 14262 (2008).
- (12) H. Mukuda, N. Terasaki, H. Kinouchi, M. Yashima, Y. Kitaoka, S. Suzuki, S. Miyasaka, S. Tajima, K. Miyazawa, P. M. Shirage, H. Kito, H. Eisaki, and A. Iyo: J. Phys. Soc. Jpn. 77, 093704 (2008).
- (13) N.Terasaki, H. Mukuda, M. Yashima, Y. Kitaoka, K. Miyazawa, P. M. Shirage, H. Kito, H. Eisaki, and A. Iyo: J. Phys. Soc. Jpn. 78, 013701 (2009).
- (14) H.-J. Grafe, D. Paar, G. Lang, N. J. Curro, G. Behr, J. Werner, J. Hamann-Berrero, C. Hess, N. Leps, R. Klingeler, and B. Bchner: Phys. Rev. Lett. 101, 047003 (2008).
- (15) K. Ahilan, F.L. Ning, T. Imai, A.S. Sefat, R. Jin, M.A. McGuire, B.C. Sales, and D. Mandrus: Phys. Rev. B 78 100501(R) (2008).
- (16) T. Imai, K. Ahilan, F.L. Ning, M.A. McGuire, A.S. Sefat, R. Jin, B.C. Sales, and D. Mandrus: J. Phys. Soc. Jpn. 77 Suppl. C, 47 (2008).
- (17) K. Kitagawa, N. Katayama, K. Ohgushi, M. Yoshida, and M. Takigawa: J. Phys. Soc. Jpn. 77, 114709 (2008).
- (18) Y. Nakai, K. Ishida, Y. Kamihara, M. Hirano, and H. Hosono: J. Phys. Soc. Jpn. 77, 073701 (2008).
- (19) K. Matano, Z.A. Ren, X.L. Dong, L.L. Sun, Z.X. Zhao, and G.-Q. Zheng: Europhys. Lett. 83, 57001 (2008).
- (20) H. Kotegawa, S. Masaki, Y. Awai, H. Tou, Y. Mizuguchi, and Y. Takano: J. Phys. Soc. Jpn. 77, 113703 (2008).
- (21) H. Fukazawa, K. Hirayama, K. Kondo, T. Yamazaki, Y. Kohori, N. Takeshita, K. Miyazawa, H. Kito, H. Eisaki, and A. Iyo: J. Phys. Soc. Jpn. 77, 093706 (2008).
- (22) H. Fukazawa, T. Yamazaki, K. Kondo, Y. Kohori, N. Takeshita, P. M. Shirage, K. Kihou, K. Miyazawa, H. Kito, H. Eisaki, and A. Iyo: arXiv:0901.0177.
- (23) H. Ding, P. Richard, K. Nakayama, K. Sugawara, T. Arakane, Y. Sekiba, A. Takayama, S. Souma, T. Sato, T. Takahashi, Z. Wang, X. Dai, Z. Fang, G.F. Chen, J.L. Luo, and N.L. Wang: Europhys. Lett. 83, 47001 (2008); T. Kondo et al., Phys. Rev. Lett. 101, 147003 (2008); L. Zhao et al., Chin. Phys. Lett. 25, 4402 (2008).
- (24) K. Hashimoto, T. Shibauchi, T. Kato, K. Ikada, R. Okazaki, H. Shishido, M. Ishikado, H. Kito, A. Iyo, H. Eisaki, S. Shamoto, and Y. Matsuda: J. Phys. Soc. Jpn. 77 Suppl. C, 145 (2008) ; L. Malone et al., arXiv:0806.3908 (unpublished); C. Martin et al. arXiv:0807.0876 (unpublished).
- (25) I.I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du: Phys. Rev. Lett. 101, 057003 (2008).
- (26) K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H. Aoki: Phys. Rev. Lett. 101, 087004 (2008).
- (27) A.V. Chubukov, D. Efremov, and I. Eremin: Phys. Rev. B 78, 134512 (2008); Y. Bang, H.Y. Choi: Phys. Rev. B 78, 134523 (2008); D. Parker, O.V. Dolgov, M.M. Korshunov, A.A. Golubov, and I.I. Mazin: Phys. Rev. B 78, 134524 (2008); M.M. Parish, J. Hu, and B.A. Bernevig: Phys. Rev. B 78, 144514 (2008).
- (28) Y. Nagai, N. Hayashi, N. Nakai, H. Nakamura, M. Okumura, and M. Machida: New J. Phys. 10, 103026 (2008).
- (29) M. Takigawa, A.P. Reyes, P.C. Hammel, J.D. Thompson, R.H. Heffner, Z. Fisk, and K.C. Ott: Phys. Rev. B 43, 247 (1991).
- (30) F. Ning, K. Ahilan, T. Imai, A. S. Sefat, R. Jin, M. A. McGuire, B. C. Sales, and D. Mandrus: J. Phys. Soc. Jpn. 78, 013711 (2009).
- (31) H. Ikeda: J. Phys. Soc. Jpn. 77, 123707 (2008).