Angle-resolved photoemission study of the role of nesting and orbital orderings in the antiferromagnetic phase of BaFe${}_2$As${}_2$

We present a detailed comparison of the electronic structure of BaFe${}_2$As${}_2$ in its paramagnetic and antiferromagnetic (AFM) phases through angle-resolved photoemission studies. Using different experimental geometries, we resolve the full elliptic shape of the electron pockets, including parts with $d_{\mathit{xy}}$ symmetry along its major axis that are usually missing. This allows us to precisely define how the hole and electron pockets are nested and how the different orbitals evolve at the transition. We conclude that the imperfect nesting between hole and electron pockets explains rather well the formation of gaps and residual metallic droplets in the AFM phase, provided the relative parity of the different bands is taken into account. Beyond this nesting picture, we observe shifts and splittings of numerous bands at the transition. We show that the splittings are surface sensitive and probably not a reliable signature of the magnetic order. On the other hand, the shifts indicate a significant redistribution of the orbital occupations at the transition, especially within the $d_{\mathit{xz}}/d_{\mathit{yz}}$ system, which we discuss.

Figure 1

(a) FS measured in the PM state at $T=150$ K with $\hslash \omega =34$ eV photons, obtained by integration of the spectral intensity in a 10 meV window around $E_F$. The direction of the light polarization, $\mathbf{A}$, is indicated on the map for each measurement. The plane of light incidence is $\mathit{xz}$ and the analyzer slits are fixed along $k_y$. (b)–(e) Energy-momentum intensity plots along (b) $k_x$ through $Z$, (c) $k_y$ through $X$, (d) $k_y$ through $Y$, and (e) $k_x$ through $Y$. Black lines indicate dispersions determined experimentally. $X$ and $Y$ are equivalent points in the BZ, but are given different names here for clarity.

Figure 2

(a) Sketch of the 3D AFM and PM BZ. (b), (c) Dispersions measured at $k_z=1$ in the PM phase for hole and electron bands, along the major (b) and minor axis (c). Red lines sketch the dispersion expected after interaction between the electron and hole bands. (d) Sketch of the PM FS (thick solid lines) with parts translated with ${\mathbf{q}}_{\text{AF}}$ as dashed lines. Thin red dashed lines indicate the AFM BZ boundaries. The structurally folded electron pockets are omitted except on the left corner. (e) Sketch of the BZ in the $\mathit{xz}$ plane. Thick lines indicate hole and electron pockets.

Figure 3

(a) FS in the AFM state at $T=20$ K and with the same conditions as in Fig. 1. (b) Energy-momentum intensity plot of the even electron band along $k_y$ through $X$, as well as second derivative (SD) image with respect to energy (center) and k (lowest). (c), (d) Energy-momentum intensity plots and SD images with respect to $k$ of the shallow electron band along $k_y$ through $Y$ in two different surface conditions. (e) SD along $k_x$ through $Z$ in the odd geometry. (f) SD through a droplet near the $Z$ point in the $k_x$ direction.

Figure 4

(a) Sketch of the electron ellipse in the PM phase (thick line) and in the AFM phase (dotted line). Colors indicate the orbital character. (b), (c) Dispersion in the PM phase (open symbols) and the AFM phase (closed symbols) along the ellipse major axis (b) and minor axis (c). Thick lines indicate the dispersions calculated in the PM phase and renormalized by a factor of 3.[29] (d) Spectra at $k_F$ at 150 K (thin lines) and 20 K (thick lines) for different cuts of the ellipse identified by their with respect to the ellipse major axis.