In-plane electronic anisotropy resulted from ordered magnetic moment in iron-based superconductors

S.-F. Wu,1,* W.-L. Zhang,1,† V. K. Thorsmølle,1 G. F. Chen,2 G. T. Tan,3 P. C. Dai,4 Y. G. Shi,2 C. Q. Jin,2 T. Shibauchi,5 S. Kasahara,6 Y. Matsuda,6 A. S. Sefat,7 H. Ding,2 P. Richard,8 and G. Blumberg 1,9,‡ 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA. 2Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, Beijing 100875, China 4Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA 5Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan 6Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan 7Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 8Institut quantique, Université de Sherbrooke, 2500 Boulevard de l’Université, Sherbrooke, Québec J1K 2R1, Canada 9National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia

(Received 5 December 2017; revised 30 June 2020; accepted 7 July 2020; published 24 July 2020) We study the in-plane electronic anisotropy in the parent compounds of several families of Fe-based superconductors (BaFe 2 As 2 , EuFe 2 As 2 , NaFeAs, LiFeAs, FeSe, and LaFeAsO) by polarization-resolved Raman scattering. We measure intensity of the fully symmetric c-axis vibration of As atom mode in the XY scattering geometry and notice that the mode's intensity is significantly enhanced below the magnetostructural transition only for compounds showing magnetic ordering. In particular, we find that the intensity ratio of this As phonon in the XY vs. X X scattering geometries is proportional to the square of the ordered magnetic moment. We relate this As phonon intensity enhancement below the Néel temperature in iron pnictides to in-plane electronic anisotropy induced by the collinear spin-density wave order. The lattice, orbital, and magnetic degrees of freedom are strongly coupled in the Fe-based superconductors. This is best evidenced by the observation, in most parent compounds, of a magnetic transition from paramagnetic to collinear antiferromagnetic (AFM), occurring at a temperature T N slightly below the temperature T S at which a structural transition from tetragonal to orthorhombic phase occurs. The interplay between these degrees of freedom is complex and led to a chicken-egg problem for which there is still no consensual view [1,2]. The electronic structure is directly affected by an electronic band folding accompanied by the formation of a collinear spin-density wave (SDW) gap [3][4][5][6]. As a result, a significant electronic anisotropy was found for properties measured along the two planar orthogonal Fe-Fe directions (Fig. 1) below the magnetostructural transition, notably in electrical transport [7], optical conductivity [8,9], thermopower [10] density-of-states (DOS) imaging [11], and quasiparticle band dispersions [12]. Raman scattering offers a unique way to study the electronic anisotropy below the magnetostructural transition of the iron-based superconductors [6,13]. For example, one can study the interband transitions along the two planar orthogonal Fe-Fe directions (Fig. 1) in a detwinned sample [6] or investigate the As fully symmetric phonon in a twinned sample [14].
In relation to this study, it has been noticed that the Raman coupling vertex to the As fully symmetric phonon: the c-axis vibration of As atom, which modulates the Fe-As-Fe bond angle of the Fe-As tetrahedra (Fig. 1), -is forbidden for XY scattering geometry in the tetragonal phase, whereas the coupling becomes finite in the orthorhombic phase. However, because orthorhombicity of the lattice constants δ for all studied materials is weak, the emerging As mode's intensity due to geometrical lattice anisotropy is expected to be small. Surprisingly, a significant intensity of the As phonon in the nearly forbidden XY scattering geometry has been observed for Ba(Fe 1−x Au x ) 2 As 2 below T N , in contrast to the weak signals at temperatures between T S and T N [14]. Similar results were reported for Ba(Fe 1−x Co x ) 2 As 2 [15]. In addition, the temperature dependence of integrated As phonon intensity was reported to be proportional to square of the magnetic moment M(T ) 2 below T N [14]. The origin of this anomalous intensity enhancement was related to the in-plane electronic anisotropy induced by the collinear SDW order (b) Schematic diagram of the magnetic structure. Red arrows: Fe local moments forming collinear AFM order. Blue arrows: c-axes vibrations of the fully symmetric As phonon mode. [14]. Furthermore, the Fano model analysis of data revealed that temperature dependence of the Raman vertex amplitude is proportional to magnitude of the magnetic order parameter M(T ) [14]. While previous Raman study established the intimate link between the As phonon intensity, the electronic anisotropy and the magnetic order parameter by studying the temperature and doping dependence of the As phonon in the 122 system [14], a detailed study of this relation among different families of iron-based superconductors where the ordered magnetic moment varies is still lacking.
In this paper, we employ polarization resolved Raman scattering spectroscopy to study the in-plane electronic anisotropy for typical 122, 111, 1111, and 11 families of Fe-based superconductors. For all compounds showing magnetic ordering, we observe a strong intensity for the fully symmetric As mode appearing below T N in the nearly forbidden XY scattering channel as a result of significantly enhanced anisotropy of the in-plane electronic polarizability, while no such enhancement is found for compounds without magnetically ordered state. We also find that the ratio of the As phonon intensity in the XY vs. X X scattering geometries, I XY /I X X , is proportional to the square of the magnetic ordered moment M 2 . This conclusion is consistent with previous study for Ba(Fe 1−x Au x ) 2 As 2 alloys [14]. Because the geometrical lattice anisotropy δ = (a − b)/(a + b) below T S is relatively small, we conclude that the intensity enhancement of the As phonon in the magnetic phase originates from the collinear SDW order-induced inplane electronic anisotropy.
The phononic Raman scattering intensity is proportional to I ∝ |ê i · R ·ê s | 2 , whereê i andê s are the polarization unit vectors of the incoming and scattering light, respectively, and R is the Raman tensor [29]. For the D 4h point group the X X , XY , X X , and X Y polarization geometries probe A 1g + B 1g , A 2g + B 2g , A 1g + B 2g , and A 2g + B 1g symmetry excitations, respectively. In the orthorhombic phase with D 2h point group symmetry, the unit cell rotates by 45 • ; the A 1g and B 2g representations of the D 4h point group merge into the A g representation of the D 2h point group, and A 2g and B 1g (D 4h ) merge into B 1g (D 2h ). In the orthorhombic phase, the X X and XY polarization geometries probe A g + B 1g and A g symmetry excitations, respectively [14].
Before investigating the behavior of the A 1g /A g symmetry As phonon across the magnetostructural transitions, we first examine the A 1g and A g Raman tensors: where A D 2h g (orthorhombic phase) has been rotated by 45 • to keep the same XY Z axis notation as in the tetragonal phase. Here,ā andb are the diagonal elements of the A D 2h g Raman tensor in the natural coordinate system of the orthorhombic phase (before the 45 • rotation).
Accordingly, the A 1g -symmetry mode is forbidden in the XY scattering geometry in the tetragonal phase. This is the case for LiFeAs, which shows neither structural nor magnetic transition. As shown in Fig. 2(a), sharp Raman phonon peaks at 186 cm −1 and 237 cm −1 , corresponding to a A 1g (As) and a B 1g (Fe) modes, respectively, are detected in the X X scattering geometry. However, as expected for the tetragonal structure of LiFeAs, these modes have no intensity in the XY scattering geometry. Similar Raman results are reported for the tetragonal Fe 1+y Te 0.6 Se 0.4 single crystal [30].
If anisotropy develops in the orthorhombic phase, the A g anion mode may acquire a finite intensity |(ā −b )/2| 2 in the XY scattering geometry related to the anisotropy of the inplane polarizability associated to this A g anion mode, becausē a andb are the polarizability derivatives along the two Fe-Fe orthogonal directions (X and Y ) in the orthorhombic phase. Since the lattice orthorhombicity δ is small (Table I), the intensity due to geometrical anisotropy is expected to be weak. For example, for the FeSe material, which exhibits a structural phase transition at 90 K [31,32] but no long-range magnetic ordering, we observe a A g (Se) phonon at 180 cm −1 and a B 1g (Fe) phonon at 208 cm −1 for the X X polarization [ Fig. 2(b)]. Although the intensity of the A g (Se) phonon with the XY polarization is finite at 20 K [inset of Fig. 2(b)], it is only 2% of the corresponding intensity recorded for the X X polarization (Table I)   (g) A g (As) phonon intensity ratio in XY vs. X X geometries (I XY /I X X ) at 15 K as a function of the squared ordered magnetic moment/Fe [23,25]. The black line is a linear fit.
In contrast, BaFe 2 As 2 with strong magnetic ordering clearly shows the 181 cm −1 A g (As) mode [13,15,34,35] in the XY scattering geometry below T N [ Fig. 2(c)]. Similar observation is made for NaFeAs [Figs. 2(e) and 2(f)], which also encounters both a structural and a magnetic phase transition: (i) We observe only a weak intensity between T S and T N , and (ii) the 162 cm −1 A g (As) phonon mode appears in the XY spectra only below T N . LaFeAsO [36][37][38] is another system with split structural and magnetic phase transitions. In this case as well, we detect sizable intensity for the A 1 g (in-phase La and As) mode at 166 cm −1 and the A 2 g (out-of-phase La and As) mode at 209 cm −1 in the XY scattering geometry below T N [ Fig. 2(d)].
To quantify the intensity of the A g (As) phonon in the XY scattering geometry below T N in different families of Fe-based superconductors, we study the ratio between the A g (As) mode intensity in the XY and X X scattering geometries I XY /I X X . This ratio is proportional to |(ā −b )/(ā +b )| 2 , which is a direct measure of the in-plane polarizability anisotropy of the A g (As) mode. Based on Table I, the ratio I XY /I X X is significant only for compounds with long-range magnetic ordering. For example, the ratio I XY /I X X is 300% for BaFe 2 As 2 , 16% for NaFeAs and 50% for LaFeAsO, as compared to 2% for FeSe, i.e., 1-2 orders of magnitude smaller. Such behavior cannot be solely explained by weak geometrical lattice orthorhombicity δ, instead, the observation relates the mode's intensity to magnetic order parameter. This is best evident from Fig. 2(g), where we show that the I XY /I X X ratio of the A g (As) phonon intensity for different Fe-based families is proportional to the square of the magnetic moment M 2 .
In conclusion, we revealed a significant intensity enhancement of the emergent A g (As) phonon mode in the XY scattering geometry below T N only for parent compounds of Fe-based superconductors showing magnetic order. We demonstrate that the ratio of the As phonon intensity in the XY and X X scattering geometries I XY /I X X is proportional to the square of the magnetic ordered moment M 2 . We conclude that the generic A g (As) phonon intensity enhancement below T N in iron pnictides is due to the in-plane electronic anisotropy induced by the collinear SDW order: a larger ordered moment in the magnetic phase results in lager in-plane electronic anisotropy, which in turn cause larger As phonon intensity ratio I XY /I X X below T N .
We thank E. Bascones and K. Haule for discussions.