Raman scattering study of spin-density-wave order and electron-phonon coupling in Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$

We report Raman scattering measurements on iron-pnictide superconductor Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals with varying cobalt $x$ content. The electronic Raman continuum shows a strong spectral weight redistribution upon entering the magnetic phase induced by the opening of the spin-density-wave (SDW) gap. It displays two spectral features that weaken with doping, which are assigned to two SDW-induced electronic transitions. Raman symmetry arguments are discussed to identify the origin of these electronic transitions in terms of orbital ordering in the magnetic phase. Our data do not seem consistent with an orbital ordering scenario and advocate for a more conventional band-folding picture with two types of electronic transitions in the SDW state: a high-energy transition between two anticrossed SDW bands and a lower-energy transition involving a folded band that does not anticross in the SDW state. The latter transition could be linked to the presence of Dirac cones in the electronic dispersion of the magnetic state. The spectra in the SDW state also show significant coupling between the arsenide optical phonon and the electronic continuum. The symmetry dependence of the arsenide phonon intensity indicates a strong in-plane anisotropy of the dielectric susceptibility in the magnetic state.

Figure 1

Different crystal cells used to describe Ba-122, with 1Fe/cell (red), paramagnetic tetragonal (green), magnetic orthorhombic (black), and their projection in the iron atom plane. Associated first Brillouin zones and their projection in the ($k_x,k_y$) plane. Different configurations of incident and scattered light polarizations called $\left(x^{\prime }{y}^{\prime }\right)$ for crossed polarizations along Fe-As bonds, $\left(xy\right)$ for crossed polarizations along Fe-Fe bonds, and $\left(LL\right)$ for circular polarizations.

Figure 2

Temperature dependence of Raman response for the undoped compound BaFe${}_2$As${}_2$ in the $\left(x^{\prime }{y}^{\prime }\right)$ configuration, showing a spectral weight transfer from low to high energy across the magnetostructural transition.

Figure 3

Raman response for $x$ $=$ 0, 0.02, and 0.045, and for indicated configurations, at high temperature, just above the magnetic transition, just below and at low temperature (red, orange, green, and blue curves, respectively). It shows a spectral weight loss at low energy across the magnetic transition in all symmetries which strongly weakens with doping.

Figure 4

Subtraction between Raman responses below ($T\sim 30$ K) and above the magnetic transition ($T=150$, 120, and 70 K for $x=0$, 0.02, and 0.045) for indicated configurations and for $x=0$, 0.02, and 0.045. The thinner lines for $\left(x^{\prime }{y}^{\prime }\right)$ configuration are the subtraction with higher temperature references ($T$ $=$ 230, 200, and 140 K for $x=0$, 0.02, and 0.045). The gray dashed lines indicate roughly the onset of depletion and the peak position in $\left(x^{\prime }{y}^{\prime }\right)$ configuration for $x=0$. The arrows indicate the low-energy steplike feature.

Figure 5

(a) Low-temperature Raman response, compared to the high-temperature one, in the $\left(x^{\prime }{y}^{\prime }\right)$ configuration for the parent compound Ba-122 showing two spectral features at ${\Delta }_{\mathrm{SDW}}$ and ${\Delta }_{\mathrm{SDW}}^{\prime }$. Insert: Anticrossing of a hole and an electron band inducing the opening of a SDW gap ${\Delta }_{\mathrm{SDW}}$ and associated Raman response calculated in the case of perfect nesting.[32, 33] For simplicity constant Raman vertices along the hole and electron Fermi surfaces and a small phenomenological broadening $\gamma =0.05{\Delta }_{\mathrm{SDW}}$ were taken. We note that in our notation ${\Delta }_{\mathrm{SDW}}$ is a two-particle gap. In the case of perfect nesting, this gap is exactly twice the single particle gap, as extracted by ARPES experiments. (b) Illustration of two anticrossings between one electron band and two hole bands. (c) Illustration of two anticrossed bands and an additional hole band, which does not interact with the others. (d) Illustration of a Dirac cone.

Figure 6

(a) Raman response temperature dependence in the $\left(x^{\prime }{y}^{\prime }\right)$ configuration zoomed on the As phonon mode energy at around 180 cm${}^{-1}$ for $x$ $=$ 0, 0.02, and 0.045. Spectra were translated for clarity. The gray dashed line is at 180 cm${}^{-1}$. (b) Raman response at low temperature ($T\sim 30$ K) in the $\left(x^{\prime }{y}^{\prime }\right)$ and $\left(LL\right)$ configurations for the same dopings.

Figure 7

(a) Raman response at low temperature ($T=23/30$ K) for $x=0$, 0.02, 0.03, and 0.045 dopings in the $\left(x^{\prime }{y}^{\prime }\right)$ configuration and their associated fit with a Fano line shape (see text). The spectra were translated vertically for clarity. (b) As phonon frequency (full circles) and width (empty circles) as a function of doping.