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Spin excitations in iron oxypnictide superconductor system
Physica C 470 (2010) S284–S287
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Physica C journal homepage: www.elsevier.com/locate/physc
Spin excitations in iron oxypnictide superconductor system Shin-ichi Shamoto a,b,*, Motoyuki Ishikado a,b, Shuichi Wakimoto a,b,c, Katsuaki Kodama a,b, Ryoichi Kajimoto b,c, Masatoshi Arai b,c, Tatsuo Fukuda a,b, Hiroki Nakamura b,d, Masahiko Machida b,d, Hiroshi Eisaki b,e a
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan JST-TRIP, Chiyoda, Tokyo 102-0075, Japan J-PARC Center, Tokai, Ibaraki 319-1195, Japan d CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015, Japan e Nanoelectronic Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan b c
a r t i c l e
i n f o
Article history: Accepted 17 November 2009 Available online 26 November 2009 Keywords: Inelastic neutron scattering LaFeAsO1xFx Spin excitation Magnetic rod
a b s t r a c t The spin excitations in the LaFeAsO1xFx system have been studied by inelastic neutron scattering measurements with powder samples. In the parent compound, the spin excitation was observed as a magnetic rod at (p, p, l) in the downfolded tetragonal Brillouin zone. It persisted even in the tetragonal phase at T = 280 K. In the superconducting compounds with x = 0.057 and 0.082, the spin excitations developed below the superconducting transition temperatures up to the same order of magnitude as that in the parent compound, and they were peaked at about 11 meV. The spin excitation, however, almost disappeared in an overdoped compound with x = 0.158, which exhibited only low temperature superconductivity below 7 K. These results indicate that the present superconductivity intimately correlates with the spin fluctuation possibly in relation to the nesting condition between the Fermi surfaces at C and M points. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction In the iron oxypnictide superconductor system, LaFeAsO1xFx, discovered by Hosono group [1], there is a spin density wave phase in the parent compound, LaFeAsO, in the vicinity of superconducting phase as shown in Fig. 1 [2]. The ordered magnetic moment at iron site observed by neutron diffraction measurement is about 0.36 lB, which is much smaller than about 2 lB estimated by the first-principles band calculations [3,4]. It is very unusual that the calculated magnetic moment is much larger than the experimental value. This calculated magnetic moment closely correlated to the arsenic z-position in the crystal structure. The observed arsenic z-position can be reproduced in the calculations only by using the large magnetic moment. Correspondingly, a phonon dispersion with iron and arsenic atoms at about 30 meV observed in a superconducting crystal PrFeAsO1y at room temperature by inelastic X-ray scattering at BL35XU in Spring-8 was reproduced by assuming a magnetic order with about 2 lB at iron site [5], suggesting spin fluctuation with large magnetic moment in a finite energy region. Three electron volt splitting in 3s binding energy is observed in a superconducting sample, CeFeAsO0.89F0.1, by Fe 3s core-level
* Corresponding author. Address: Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan. E-mail address: [email protected] (S. Shamoto). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.11.132
spectrum [6]. This splitting is attributed to the magnetic moment with about 1 lB at Fe site. On the other hand, ordered magnetic moment at Fe site in superconducting samples has not been detected by Moessbauer spectroscopy [7]. In addition, NMR studies also suggest that there is no correlation between spin fluctuation and the superconductivity [8]. It should be noted that the measuring time scale of Fe 3s core-level spectrum is about 1015 s, which is much faster than the other two probes, again suggesting the spin fluctuation in a finite energy region. Here, inelastic neutron scattering experiments have been carried out in LaFeAsO1xFx system to study the spin excitations depending on the fluorine concentration from the parent compound to the overdoped compound. 2. Experimental procedures Powder samples of LaFeAsO1xFx with x = 0, 0.057, 0.082, and 0.158 have been synthesized by solid state reaction starting with nominal compositions of x = 0, 0.05, 0.10, and 0.20, respectively. The x values in the synthesized samples were determined by secondary ion microprobe mass spectrometry measurements. Powder X-ray diffraction data show that our samples contain only single 1111 phase with a space group of P4/nmm, demonstrating the high quality of samples. Based on the Meissner signal by SQUID measurement, superconducting transition temperatures in LaFeAsO1xFx with x = 0, 0.057, 0.082, and 0.158 were estimated
S.-i. Shamoto et al. / Physica C 470 (2010) S284–S287
Fig. 1. Phase diagram of LaFeAsO1xFx system. Closed circles are samples measured by inelastic neutron scattering.
to be 0, 25, 29, and 7 K, respectively, as shown in Fig. 1. By using neutron diffraction, we confirmed that all samples except for the parent compound exhibit no magnetic ordering down to 4 K. The overdoped sample (x = 0.158) exhibits filamentary superconductivity with about 10% volume fraction at 5 K, suggesting the highly degraded superconductivity. Details of syntheses and characterizations of all samples will be published elsewhere [9]. Inelastic neutron scattering experiments were performed using the triple-axis spectrometer TAS-1 at JRR-3M and the chopper spectrometer MERLIN at ISIS. Powder sample of 25 g (TAS-1) or 34 g (MERLIN) was placed in a vanadium cell or an aluminum foil and sealed in an aluminum can, and then mounted in a closed-cycle He gas refrigerator. Collimations of TAS-1 was open-800 -S-800 800 (S denotes sample) with fixed final neutron energy at Ef = 30.5 meV, leading to instrumental resolutions of 3.5 meV in energy and 0.06 Å1 in momentum transfer. Observed scattering intensities were normalized among samples by using nuclear Bragg peak intensities at (0, 0, 2). Ei = 30 meV was used at MERLIN.
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Fig. 2. Spin excitation intensity in the energy range from 7.5 to 9 meV at T = 140 K. The peak shape at 1.2 Å1 has a long tail in higher-momentum transfers, as would be expected for the magnetic excitation of a two-dimensional system.
Fig. 3. Temperature dependence of spin excitation intensity integrated in the E range from 7.5 to 9 meV and the Q range from 1.0 to 1.3 Å1. The maximum corresponds to the magnetic ordering temperature [10].
3. Results and discussion 3.1. Parent compound LaFeAsO Steeply disperse spin excitations were observed in dynamical structure factors, S(Q, E), of the parent compound LaFeAsO at 1.2 Å1 and 2.5 Å1. The intensity in the energy range from 7.5 to 9 meV peaked at T = 140 K as a function of temperature. It weakly decreased with increasing temperature, and persisted up to 280 K. The magnetic signals at 140 K after subtracting constant background from the dynamical structure factor are shown as a function of Q in Fig. 2. The peak shape at 1.2 Å1 has a long tail at higher-momentum transfers due to powder averaging over a magnetic rod at (p, p, l) in the downfolded tetragonal Brillouin zone. The solid line is a fit curve using Warren function of 2-dimensional system with Fe 3d form factor. The effective magnetic rod width j = p/n is estimated to be about 0.05 Å1 (n = 62(12) Å) at 140 K [10]. As shown in Fig. 3, the integrated intensity had a maximum at the magnetic ordering temperature, and decreased gradually with increasing temperature. It is consistent with the 2-dimensionality of spin excitation. The Fermi surfaces have cylindrical shapes [11]. Because of the strong nesting condition from hole-like Fermi surfaces at C point to electron-like Fermi surfaces at M point as shown in Fig. 4, Lindhard response function calculated from band structure has a sharp peak at the nesting wave vector (p, p, l) [12,13]. The downfolded Brillouin zone corresponds to a unit cell with two iron atoms in the square lattice. Based on the itinerant electron picture, non-interacting spin susceptibility v0(q, x) may be enhanced by Coulomb interaction tensor U as described by the random phase approximation as follows [14]:
vðq; xÞ ¼
v0 ðq; xÞ 1 U v0 ðq; xÞ
ð1Þ
Fig. 4. Schematic Fermi surfaces of LaFeAsO. Third Fermi surface at C point is not shown. Downfolded tetragonal Brillouin zone corresponds to a unit cell with two Fe atoms, while the unit cell of unfolded zone includes one Fe atom. The wave vector of observed spin excitation corresponds to the scattering vector from C to M points.
where
v0 ðq; xÞ ¼
X k
f ðek Þ f ðekþq Þ ek ekþq x id
ð2Þ
The observed magnetic excitation can be compared with the imaginary part of calculated dynamical spin susceptibility. The observed width, j 0.05 Å1, is much narrower than the calculated width of 0.3 Å1. This enhancement can be attributed to the electron correlation effects [13]. On the other hand, the spin excitation can also be explained by the localized spin pictures such as J1a–J1b–J2–Jc model [15,16]. Double stripe magnetic structure, however, is realized in Fe1.068Te with a monoclinic crystal structure of b = 89.2° [17], suggesting an importance of long-range magnetic interactions as often observed in an itinerant electron system [18].
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3.2. Superconducting compounds LaFeAsO1xFx In LaFeAsO1xFx system, the spin density wave phase coexists with the superconducting phase at x = 0.04, according to NMR result [8]. In an electron doped system, BaFe2xCoxAs2, the coexistence also observed in BaFe1.92Co0.08As2 by neutron scattering [19]. From the phase boundary, the superconducting transition temperature sharply increases as a function of in-plane a-axis lattice parameter [20], suggesting the first order phase transition. The spin excitations in the LaFeAsO1xFx superconducting compounds (x = 0.057 and 0.082) were observed in the same Q regions (1.2 Å1 and 2.5 Å1) as the spin density wave in the parent compound as shown in Fig. 5 [21]. The peak intensities at 1.2 Å1 were not less than those at 2.5 Å1, suggesting their magnetic origin. These peaks disappeared at high temperatures such as about 220 K. According to our preliminary results, they developed below about 30 K and peaked at about 11 meV. The onset temperature and the peak energy roughly correspond to the superconducting transition temperatures and 4.7 kBTc, respectively. This result does not contradict with the resonance peak picture [22]. The resonance energy of 14 meV reported on Ba0.6K0.4Fe2As2 (Tc = 38 K) corresponds to 4.3 kBTc [22]. Underdoped superconductor BaFe1.92Co0.08As2 (Tc = 11 K) also shows resonance-like peak at 4.5 meV, corresponding to 4.7 kBTc [18]. The Q-integrated dynamical spin susceptibility v00 (x) at 11 meV for the superconducting samples is comparable to that of the parent compound as shown in Fig. 5. Based on the peak intensity, the effective magnetic moment is estimated to be about 0.4 lB under an assumption that the maximum spin excitation energy reaches at 200 meV as observed in CaFe2As2 [23]. This value is roughly consistent with Fe 3s core-level spectrum [6]. The spin excitation, however, almost disappeared in the overdoped compound with x = 0.158 [21]. Because there is a sum rule in the total weight of q-integrated dynamical structure factor S(x), the disappearance of spin excitation suggests that spin fluctuation disappears in the overdoped compound at least at low energy, regardless of the resonance effect. In contrast with this result, NMR measurements in LaFeAsO1xFx system by Ishida group show strong suppression of 1/T1T with doping, more than one order of magnitude just above the superconducting transition temperatures [8]. 1/T1T, however, measures low energy part of the dynamical spin susceptibility. In addition, our spin excitations are mainly observed in the superconducting states. It should also be noted that observed 1/T1T merges at room temperature. The origin of spin excitation disappearance in the overdoped compound would be attributed to the nesting condition between the Fermi surfaces at C and M points. One possibility is that hole-like Fermi surface vanished at C point as reported in Ba(Fe0.85Co0.15)2As2 [24]. Another possibility is that nesting condition became insufficient between Fermi surfaces at C and M points. Anyway, these
Fig. 5. Imaginary part of dynamical spin susceptibility v00 (x) at x = 11 meV as a function of x in LaFeAsO1xFx. Open circle shows v00 (x) of the parent compound measured at T = 140 K, while closed circle data are measured at 4 K [21].
results suggest that the present superconductivity intimately correlates with the spin fluctuation in relation to the nesting condition between the Fermi surfaces at C and M points. 3.3. Comparison with a borocarbide superconductor We would like to compare the present superconductor with a borocarbide superconductor. In the case of YNi2B2C with Tc = 14.2 K, a phonon peak developed at 2D 4.3 meV 3.5 kBTc below Tc from a soft phonon mode spread in a wide energy range [25], similarly to the resonant spin excitation observed in Ba0.6K0.4Fe2As2 [22]. The soft phonon mode in YNi2B2C can be interpreted like LuNi2B2C [26] as a Kohn anomaly due to strong nesting on Fermi surface [27]. On the other hand, the observed spin excitations in iron pnictide superconductors can also be interpreted as the result of strong nesting on Fermi surfaces. Borocarbide and iron pnictide superconductors exhibit similar enhancements below Tc on phonon and spin excitation, respectively. This may correspond simply to the sign change of superconducting gaps. 4. Summary In the parent compound, LaFeAsO, the spin excitation observed as a magnetic rod at (p, p, l) persisted in the tetragonal phase at T = 280 K. The spin excitations in the superconducting compounds with x = 0.057 and 0.082 increased below the superconducting transition temperatures up to the same order of magnitude as that in the parent compound, and they were peaked at about 11 meV. The spin excitation, however, almost disappeared in an overdoped compound with x = 0.158, which exhibited only low temperature superconductivity below 7 K. These results indicate that the present superconductivity intimately correlates with the spin fluctuation possibly in relation to the nesting condition between the Fermi surfaces at C and M points. The present iron pnictide superconductor is also contrasted with a borocarbide superconductor. Acknowledgements This work was supported by Grant-in-Aids for Specially Promoted Research (17001001) from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) and JST, Transformative Research-Project on Iron Pnictides (TRIP). Inelastic neutron scattering experiment was partially conducted under UKJapan collaboration. References [1] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [2] Clarina de la Cruz, Q. Huang, J.W. Lynn, Jiying Li, et al., Nature 453 (2008) 899. [3] S. Ishibashi, K. Terakura, H. Hosono, J. Phys. Soc. Jpn. 77 (2008) 053709. [4] I.I. Mazin, M.D. Johannes, Nat. Phys. 5 (2008) 141. [5] T. Fukuda, A.Q.R. Baron, H. Nakamura, M. Machida, et al., in preparation. [6] F. Bondino et al., Phys. Rev. Lett. 101 (2008) 267001. [7] S. Kitao, Y. Kobayashi, S. Higashitaniguchi, et al., J. Phys. Soc. Jpn. 77 (Suppl. C) (2008) 121. [8] Y. Nakai et al., J. Phys. Soc. Jpn. 77 (2008) 073701. [9] M. Ishikado, et al., in preparation. [10] M. Ishikado, R. Kajimoto, S. Shamoto, M. Arai, et al., J. Phys. Soc. Jpn. 78 (2009) 043705. [11] D.J. Singh, M.H. Du, Phys. Rev. Lett. 100 (2008) 237003. [12] J. Dong et al., Europhys. Lett. 83 (2008) 27006. [13] I.I. Mazin, D.J. Singh, M.D. Johannes, M.H. Du, Phys. Rev. Lett. 101 (2008) 057003. [14] T.A. Maier et al., Phys. Rev. B 79 (2009) 134520. [15] R.A. Ewings et al., Phys. Rev. B 78 (2008) 220501(R). [16] Jun Zha, D.T. Adroja, Dao-Xin Yao, R. Bewly, Shiliang Li, X.F. Wang, G. Wu, X.H. Chen, Jiangping Hu, Pengcheng Dai, Nat. Phys. 5 (2009) 555. [17] S. Li, C. de la Cruz, Q. Huang, Y. Chen, J.W. Lynn, J. Hu, Y.-L. Huang, F.-C. Hsu, K.W. Yeh, M.-K. Wu, P. Dai, Phys. Rev. B 79 (2009) 054503. [18] M.D. Johannes, I.I. Mazin, arXiv:0904.3857.
S.-i. Shamoto et al. / Physica C 470 (2010) S284–S287 [19] A.D. Christianson, et al., arXiv:0904.0767. [20] P.M. Shirage, K. Miyazawa, M. Ishikado, et al., Physica C 469 (9–12) (2009) 355. [21] S. Wakimoto, K. Kodama, M. Ishikado, et al., arXiv:0906.2453. [22] A.D. Christianson et al., Nature 456 (2008) 930. [23] Jun Zhao et al., Nat. Phys. 5 (2009) 555.
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[24] Y. Sekiba, T. Sato, K. Nakayama, K. Terashima, et al., New J. Phys. 11 (2009) 025020. [25] H. Kawano, H. Yoshizawa, H. Takeya, K. Kadowaki, Phys. Rev. Lett. 77 (1996) 4628. [26] P. Dervenagas et al., Phys. Rev. B 52 (1995) R9839. [27] M. Ichioka, K. Machida, J. Phys. Soc. Jpn. 72 (2003) 2064.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Spin excitations in iron oxypnictide superconductor system Shin-ichi Shamoto a,b,*, Motoyuki Ishikado a,b, Shuichi Wakimoto a,b,c, Katsuaki Kodama a,b, Ryoichi Kajimoto b,c, Masatoshi Arai b,c, Tatsuo Fukuda a,b, Hiroki Nakamura b,d, Masahiko Machida b,d, Hiroshi Eisaki b,e a
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan JST-TRIP, Chiyoda, Tokyo 102-0075, Japan J-PARC Center, Tokai, Ibaraki 319-1195, Japan d CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015, Japan e Nanoelectronic Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan b c
a r t i c l e
i n f o
Article history: Accepted 17 November 2009 Available online 26 November 2009 Keywords: Inelastic neutron scattering LaFeAsO1xFx Spin excitation Magnetic rod
a b s t r a c t The spin excitations in the LaFeAsO1xFx system have been studied by inelastic neutron scattering measurements with powder samples. In the parent compound, the spin excitation was observed as a magnetic rod at (p, p, l) in the downfolded tetragonal Brillouin zone. It persisted even in the tetragonal phase at T = 280 K. In the superconducting compounds with x = 0.057 and 0.082, the spin excitations developed below the superconducting transition temperatures up to the same order of magnitude as that in the parent compound, and they were peaked at about 11 meV. The spin excitation, however, almost disappeared in an overdoped compound with x = 0.158, which exhibited only low temperature superconductivity below 7 K. These results indicate that the present superconductivity intimately correlates with the spin fluctuation possibly in relation to the nesting condition between the Fermi surfaces at C and M points. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction In the iron oxypnictide superconductor system, LaFeAsO1xFx, discovered by Hosono group [1], there is a spin density wave phase in the parent compound, LaFeAsO, in the vicinity of superconducting phase as shown in Fig. 1 [2]. The ordered magnetic moment at iron site observed by neutron diffraction measurement is about 0.36 lB, which is much smaller than about 2 lB estimated by the first-principles band calculations [3,4]. It is very unusual that the calculated magnetic moment is much larger than the experimental value. This calculated magnetic moment closely correlated to the arsenic z-position in the crystal structure. The observed arsenic z-position can be reproduced in the calculations only by using the large magnetic moment. Correspondingly, a phonon dispersion with iron and arsenic atoms at about 30 meV observed in a superconducting crystal PrFeAsO1y at room temperature by inelastic X-ray scattering at BL35XU in Spring-8 was reproduced by assuming a magnetic order with about 2 lB at iron site [5], suggesting spin fluctuation with large magnetic moment in a finite energy region. Three electron volt splitting in 3s binding energy is observed in a superconducting sample, CeFeAsO0.89F0.1, by Fe 3s core-level
* Corresponding author. Address: Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan. E-mail address: [email protected] (S. Shamoto). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.11.132
spectrum [6]. This splitting is attributed to the magnetic moment with about 1 lB at Fe site. On the other hand, ordered magnetic moment at Fe site in superconducting samples has not been detected by Moessbauer spectroscopy [7]. In addition, NMR studies also suggest that there is no correlation between spin fluctuation and the superconductivity [8]. It should be noted that the measuring time scale of Fe 3s core-level spectrum is about 1015 s, which is much faster than the other two probes, again suggesting the spin fluctuation in a finite energy region. Here, inelastic neutron scattering experiments have been carried out in LaFeAsO1xFx system to study the spin excitations depending on the fluorine concentration from the parent compound to the overdoped compound. 2. Experimental procedures Powder samples of LaFeAsO1xFx with x = 0, 0.057, 0.082, and 0.158 have been synthesized by solid state reaction starting with nominal compositions of x = 0, 0.05, 0.10, and 0.20, respectively. The x values in the synthesized samples were determined by secondary ion microprobe mass spectrometry measurements. Powder X-ray diffraction data show that our samples contain only single 1111 phase with a space group of P4/nmm, demonstrating the high quality of samples. Based on the Meissner signal by SQUID measurement, superconducting transition temperatures in LaFeAsO1xFx with x = 0, 0.057, 0.082, and 0.158 were estimated
S.-i. Shamoto et al. / Physica C 470 (2010) S284–S287
Fig. 1. Phase diagram of LaFeAsO1xFx system. Closed circles are samples measured by inelastic neutron scattering.
to be 0, 25, 29, and 7 K, respectively, as shown in Fig. 1. By using neutron diffraction, we confirmed that all samples except for the parent compound exhibit no magnetic ordering down to 4 K. The overdoped sample (x = 0.158) exhibits filamentary superconductivity with about 10% volume fraction at 5 K, suggesting the highly degraded superconductivity. Details of syntheses and characterizations of all samples will be published elsewhere [9]. Inelastic neutron scattering experiments were performed using the triple-axis spectrometer TAS-1 at JRR-3M and the chopper spectrometer MERLIN at ISIS. Powder sample of 25 g (TAS-1) or 34 g (MERLIN) was placed in a vanadium cell or an aluminum foil and sealed in an aluminum can, and then mounted in a closed-cycle He gas refrigerator. Collimations of TAS-1 was open-800 -S-800 800 (S denotes sample) with fixed final neutron energy at Ef = 30.5 meV, leading to instrumental resolutions of 3.5 meV in energy and 0.06 Å1 in momentum transfer. Observed scattering intensities were normalized among samples by using nuclear Bragg peak intensities at (0, 0, 2). Ei = 30 meV was used at MERLIN.
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Fig. 2. Spin excitation intensity in the energy range from 7.5 to 9 meV at T = 140 K. The peak shape at 1.2 Å1 has a long tail in higher-momentum transfers, as would be expected for the magnetic excitation of a two-dimensional system.
Fig. 3. Temperature dependence of spin excitation intensity integrated in the E range from 7.5 to 9 meV and the Q range from 1.0 to 1.3 Å1. The maximum corresponds to the magnetic ordering temperature [10].
3. Results and discussion 3.1. Parent compound LaFeAsO Steeply disperse spin excitations were observed in dynamical structure factors, S(Q, E), of the parent compound LaFeAsO at 1.2 Å1 and 2.5 Å1. The intensity in the energy range from 7.5 to 9 meV peaked at T = 140 K as a function of temperature. It weakly decreased with increasing temperature, and persisted up to 280 K. The magnetic signals at 140 K after subtracting constant background from the dynamical structure factor are shown as a function of Q in Fig. 2. The peak shape at 1.2 Å1 has a long tail at higher-momentum transfers due to powder averaging over a magnetic rod at (p, p, l) in the downfolded tetragonal Brillouin zone. The solid line is a fit curve using Warren function of 2-dimensional system with Fe 3d form factor. The effective magnetic rod width j = p/n is estimated to be about 0.05 Å1 (n = 62(12) Å) at 140 K [10]. As shown in Fig. 3, the integrated intensity had a maximum at the magnetic ordering temperature, and decreased gradually with increasing temperature. It is consistent with the 2-dimensionality of spin excitation. The Fermi surfaces have cylindrical shapes [11]. Because of the strong nesting condition from hole-like Fermi surfaces at C point to electron-like Fermi surfaces at M point as shown in Fig. 4, Lindhard response function calculated from band structure has a sharp peak at the nesting wave vector (p, p, l) [12,13]. The downfolded Brillouin zone corresponds to a unit cell with two iron atoms in the square lattice. Based on the itinerant electron picture, non-interacting spin susceptibility v0(q, x) may be enhanced by Coulomb interaction tensor U as described by the random phase approximation as follows [14]:
vðq; xÞ ¼
v0 ðq; xÞ 1 U v0 ðq; xÞ
ð1Þ
Fig. 4. Schematic Fermi surfaces of LaFeAsO. Third Fermi surface at C point is not shown. Downfolded tetragonal Brillouin zone corresponds to a unit cell with two Fe atoms, while the unit cell of unfolded zone includes one Fe atom. The wave vector of observed spin excitation corresponds to the scattering vector from C to M points.
where
v0 ðq; xÞ ¼
X k
f ðek Þ f ðekþq Þ ek ekþq x id
ð2Þ
The observed magnetic excitation can be compared with the imaginary part of calculated dynamical spin susceptibility. The observed width, j 0.05 Å1, is much narrower than the calculated width of 0.3 Å1. This enhancement can be attributed to the electron correlation effects [13]. On the other hand, the spin excitation can also be explained by the localized spin pictures such as J1a–J1b–J2–Jc model [15,16]. Double stripe magnetic structure, however, is realized in Fe1.068Te with a monoclinic crystal structure of b = 89.2° [17], suggesting an importance of long-range magnetic interactions as often observed in an itinerant electron system [18].
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3.2. Superconducting compounds LaFeAsO1xFx In LaFeAsO1xFx system, the spin density wave phase coexists with the superconducting phase at x = 0.04, according to NMR result [8]. In an electron doped system, BaFe2xCoxAs2, the coexistence also observed in BaFe1.92Co0.08As2 by neutron scattering [19]. From the phase boundary, the superconducting transition temperature sharply increases as a function of in-plane a-axis lattice parameter [20], suggesting the first order phase transition. The spin excitations in the LaFeAsO1xFx superconducting compounds (x = 0.057 and 0.082) were observed in the same Q regions (1.2 Å1 and 2.5 Å1) as the spin density wave in the parent compound as shown in Fig. 5 [21]. The peak intensities at 1.2 Å1 were not less than those at 2.5 Å1, suggesting their magnetic origin. These peaks disappeared at high temperatures such as about 220 K. According to our preliminary results, they developed below about 30 K and peaked at about 11 meV. The onset temperature and the peak energy roughly correspond to the superconducting transition temperatures and 4.7 kBTc, respectively. This result does not contradict with the resonance peak picture [22]. The resonance energy of 14 meV reported on Ba0.6K0.4Fe2As2 (Tc = 38 K) corresponds to 4.3 kBTc [22]. Underdoped superconductor BaFe1.92Co0.08As2 (Tc = 11 K) also shows resonance-like peak at 4.5 meV, corresponding to 4.7 kBTc [18]. The Q-integrated dynamical spin susceptibility v00 (x) at 11 meV for the superconducting samples is comparable to that of the parent compound as shown in Fig. 5. Based on the peak intensity, the effective magnetic moment is estimated to be about 0.4 lB under an assumption that the maximum spin excitation energy reaches at 200 meV as observed in CaFe2As2 [23]. This value is roughly consistent with Fe 3s core-level spectrum [6]. The spin excitation, however, almost disappeared in the overdoped compound with x = 0.158 [21]. Because there is a sum rule in the total weight of q-integrated dynamical structure factor S(x), the disappearance of spin excitation suggests that spin fluctuation disappears in the overdoped compound at least at low energy, regardless of the resonance effect. In contrast with this result, NMR measurements in LaFeAsO1xFx system by Ishida group show strong suppression of 1/T1T with doping, more than one order of magnitude just above the superconducting transition temperatures [8]. 1/T1T, however, measures low energy part of the dynamical spin susceptibility. In addition, our spin excitations are mainly observed in the superconducting states. It should also be noted that observed 1/T1T merges at room temperature. The origin of spin excitation disappearance in the overdoped compound would be attributed to the nesting condition between the Fermi surfaces at C and M points. One possibility is that hole-like Fermi surface vanished at C point as reported in Ba(Fe0.85Co0.15)2As2 [24]. Another possibility is that nesting condition became insufficient between Fermi surfaces at C and M points. Anyway, these
Fig. 5. Imaginary part of dynamical spin susceptibility v00 (x) at x = 11 meV as a function of x in LaFeAsO1xFx. Open circle shows v00 (x) of the parent compound measured at T = 140 K, while closed circle data are measured at 4 K [21].
results suggest that the present superconductivity intimately correlates with the spin fluctuation in relation to the nesting condition between the Fermi surfaces at C and M points. 3.3. Comparison with a borocarbide superconductor We would like to compare the present superconductor with a borocarbide superconductor. In the case of YNi2B2C with Tc = 14.2 K, a phonon peak developed at 2D 4.3 meV 3.5 kBTc below Tc from a soft phonon mode spread in a wide energy range [25], similarly to the resonant spin excitation observed in Ba0.6K0.4Fe2As2 [22]. The soft phonon mode in YNi2B2C can be interpreted like LuNi2B2C [26] as a Kohn anomaly due to strong nesting on Fermi surface [27]. On the other hand, the observed spin excitations in iron pnictide superconductors can also be interpreted as the result of strong nesting on Fermi surfaces. Borocarbide and iron pnictide superconductors exhibit similar enhancements below Tc on phonon and spin excitation, respectively. This may correspond simply to the sign change of superconducting gaps. 4. Summary In the parent compound, LaFeAsO, the spin excitation observed as a magnetic rod at (p, p, l) persisted in the tetragonal phase at T = 280 K. The spin excitations in the superconducting compounds with x = 0.057 and 0.082 increased below the superconducting transition temperatures up to the same order of magnitude as that in the parent compound, and they were peaked at about 11 meV. The spin excitation, however, almost disappeared in an overdoped compound with x = 0.158, which exhibited only low temperature superconductivity below 7 K. These results indicate that the present superconductivity intimately correlates with the spin fluctuation possibly in relation to the nesting condition between the Fermi surfaces at C and M points. The present iron pnictide superconductor is also contrasted with a borocarbide superconductor. Acknowledgements This work was supported by Grant-in-Aids for Specially Promoted Research (17001001) from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) and JST, Transformative Research-Project on Iron Pnictides (TRIP). Inelastic neutron scattering experiment was partially conducted under UKJapan collaboration. References [1] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [2] Clarina de la Cruz, Q. Huang, J.W. Lynn, Jiying Li, et al., Nature 453 (2008) 899. [3] S. Ishibashi, K. Terakura, H. Hosono, J. Phys. Soc. Jpn. 77 (2008) 053709. [4] I.I. Mazin, M.D. Johannes, Nat. Phys. 5 (2008) 141. [5] T. Fukuda, A.Q.R. Baron, H. Nakamura, M. Machida, et al., in preparation. [6] F. Bondino et al., Phys. Rev. Lett. 101 (2008) 267001. [7] S. Kitao, Y. Kobayashi, S. Higashitaniguchi, et al., J. Phys. Soc. Jpn. 77 (Suppl. C) (2008) 121. [8] Y. Nakai et al., J. Phys. Soc. Jpn. 77 (2008) 073701. [9] M. Ishikado, et al., in preparation. [10] M. Ishikado, R. Kajimoto, S. Shamoto, M. Arai, et al., J. Phys. Soc. Jpn. 78 (2009) 043705. [11] D.J. Singh, M.H. Du, Phys. Rev. Lett. 100 (2008) 237003. [12] J. Dong et al., Europhys. Lett. 83 (2008) 27006. [13] I.I. Mazin, D.J. Singh, M.D. Johannes, M.H. Du, Phys. Rev. Lett. 101 (2008) 057003. [14] T.A. Maier et al., Phys. Rev. B 79 (2009) 134520. [15] R.A. Ewings et al., Phys. Rev. B 78 (2008) 220501(R). [16] Jun Zha, D.T. Adroja, Dao-Xin Yao, R. Bewly, Shiliang Li, X.F. Wang, G. Wu, X.H. Chen, Jiangping Hu, Pengcheng Dai, Nat. Phys. 5 (2009) 555. [17] S. Li, C. de la Cruz, Q. Huang, Y. Chen, J.W. Lynn, J. Hu, Y.-L. Huang, F.-C. Hsu, K.W. Yeh, M.-K. Wu, P. Dai, Phys. Rev. B 79 (2009) 054503. [18] M.D. Johannes, I.I. Mazin, arXiv:0904.3857.
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