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on “ Quadrupole Effects of Layered Iron Pnictide Superconductor Ba(Fe_0.9Co_0.1)₂As₂”
J. Phys. Soc. Jpn. 80 (2011) 073702

Spin or Orbital
Origin of Large Elastic Anomalies in Iron-Based Superconductor

by Masahito Yoshizawa (Graduate School of Engineering, Iwate University)
Published July 14, 2011

Iron-based superconductors, like high-Tc cuprates, have a high critical temperature T_sc. It is expected that these superconductors will have promising possible applications in the future. Further, there has been considerable global interest in the mechanism of superconductivity in these superconductors. Among the derived structures in iron-based compounds with different structures, the 122-system BaFe₂As₂ shows stripe magnetic order with a structural change from tetragonal to orthorhombic. The order disappears and the superconductivity is exhibited when Fe is replaced with Co. It has been proposed that the mechanism of superconductivity depends on spin and orbitals [1-4]. The superconductivity would be mediated by the fluctuation in adjacent order parameters. Elastic constant is a suitable probe for investigating neighboring structural instability.

By examining the correlation between the magnitude of elastic anomaly and T_sc, it could be inferred whether the elastic anomaly is related to the emergence of superconductivity. If the elastic anomaly disappears rapidly along with the collapse of the adjacent order, it can be concluded that the correlation between the two is weak. Goto et al. reported that, in the case of Ba(Fe_0.9Co_0.1)₂As₂ in the over-doped region, C₆₆ exhibits a softening of 21 % at T_sc from room temperature, as shown in Fig. 1 [5]. Such a large elastic anomaly in the region where the adjacent order collapsed indicates the strong effect of the order parameter that triggers structural instability on the emergence of superconductivity.

Fig. 1: Temperature dependence of the elastic constant C66 of Ba(Fe0.9Co0.1)2As2 (made by using the figure taken from ref. [5]).

What is the order parameter of the phase adjacent to the superconducting phase? Large elastic anomalies are often observed in a 4f electron system with a bilinear coupling between quadrupole operator O and elastic strain ε; this bilinear coupling is represented as Oε [6]. Initially, the origin of the elastic anomalies in iron-based superconductors was considered to be because of the nematic order in these superconductors [7]. Because of time-reversal symmetry, a bilinear coupling between the elastic strain and a single spin is not possible. Therefore, spin nematic order of a pair of spins has been considered. Nematicity is one of the interesting topics in solid-state physics. Bilinear coupling between nematic order and elastic strain is possible. The spin-orbit interaction because of nematic order deforms the crystal. Small lattice distortion in this compound can be reasonably attributed to the weak spin-orbit coupling. An investigation to determine whether the large elastic anomalies have been caused by the nematic order will be conducted.

Since the symmetry of the d orbitals in Fe is the same as that of the strain, they can cause the elastic anomaly. Figure 2(a) shows the schematic illustration of Fe 3d electron with intermediate spin state S = 1 [8]. The equivalence of the x and y axes in tetragonal symmetry leads to the degeneration of the d_zx’ and d_y’z orbitals. This degeneracy is lifted by ε_xy or ε_xx-ε_yy elastic strain, and results in anomalies in the corresponding C₆₆ or (C₁₁-C₁₂)/2. In the case of the low spin state, the spin in the d_yz/d_zx state activated thermally from d_xy behaves in the same manner as in the intermediate state. This is the Jahn-Teller effect, which is based on the localized image of d electron. The Curie-Weiss behavior of the elastic constant (fitting curve in Fig.1) has been considered to support the localized picture of the d electron.

Fig. 2: (a) Schematic illustration of a ground state d6 configuration of Fe ion with an intermediate spin state of S = 1 and low-spin state [8]. (b) Effect of band on the crystal deformation. Four M points in square lattice do not become equivalent by the strain εxy, which makes the band consisting of dyz/dzx and dx2-dy2 degeneracy lifted [4].

The A15 compound V₃Si and Laves-phase compound CeRu₂ are well known superconductors that exhibit substantial elastic anomalies [9,10]. These anomalies are ascribed to the large density of states at Fermi energy. Actual 3d-orbitals form bands in iron-based superconductor. The degeneracy of d_y’z orbital and of d_zx’ orbital are lifted in the momentum space, except in the case of Γ-point. The bands located above the Fermi energy at Γ-point form hole Fermi surfaces and electron pockets at the zone boundary. As shown in Fig 2(b), four M-points do not becomes equivalent under ε_xy. This formation of bands of the 3d orbitals may cause an elastic anomaly. The band nesting along [π/a, π/a, 0] direction, which is a characteristic feature in iron-based superconductors, may cause the C₆₆ softening. It is suggested that ferro-quadrupole order with C₆₆ softening occurs by two-orbiton process that is initiated by antiferro-quadrupolar fluctuation caused by interband nesting [11].

The origin of the large elastic anomalies found in iron-based superconductors is still not understood completely. More detailed analysis and discussion of the results of Goto et al. are required to fully understand the mechanism of superconductivity in iron-based materials.

References

• [1] I. I. Mazin et al.: Phys. Rev. Lett. 101 (2008) 057003.
• [2] H. Kontani and S. Onari, Phys. Rev. Lett. 104 (2010) 157001.
• [3] K. Kuroki et al.: Phys. Rev. Lett. 101 (2008) 087004.
• [4] Y. Yanagi et al.: Phys. Rev. B 81 (2010) 054518.
• [5] T. Goto et al.: J. Phys. Soc. Jpn. 80 (2011) 073702.
• [6] B. Lüthi: Physical Acoustics in the Solid State (Springer-Verlag, 2004).
• [7] R. M. Fernandes et al.: Phys. Rev. Lett. 105 (2010)157003.
• [8] F. Krüger et al.: Phys. Rev. B 79 (2009) 054504.
• [9] L. R. Testerdi and T. B. Bateman: Phys. Rev. 154 (1967) 402.
• [10] M. Yoshizawa et al.: J. Phys. Soc. Jpn. 66 (1997) 2355.
• [11] H. Kontani et al.: arXiv:1103.3360v2.
Note The above article should be referred as “M. Yoshizawa: JPSJ Online—News and Comments [July 14, 2011]” when citing.



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