Existence of Orbital Order and its Fluctuation in Superconducting $\mathrm{Ba}\mathbf{(}{\mathrm{Fe}}_{1\mathbf{-}x}{\mathrm{Co}}_x{\mathbf{)}}_2{\mathrm{As}}_2$ Single Crystals Revealed by X-ray Absorption Spectroscopy

We performed temperature dependent x-ray linear dichroism (XLD) experiments on an iron pnictide system, $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ with $x=0.00$, 0.05, 0.08, and 0.10 to experimentally verify the existence of orbital ordering (OO). Substantial XLD was observed in polarization dependent x-ray absorption spectra of Fe $L$ edges. By exploiting the difference in the temperature dependent behaviors, OO, and structure contributions to XLD could be clearly separated. The observed OO signal indicates different occupation numbers for $d_{yz}$ and $d_{zx}$ orbitals and supports the existence of ferro-OO. The results are also consistent with the theoretical prediction. Moreover, we find substantial OO signal well above the structural and magnetic transition temperatures, which suggests the existence of strong OO fluctuations up to high temperatures.

Figure 1

(a) Fe $L_{3,2}$ edge XAS spectra from ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ with two different polarizations $E\parallel x$ (blue, inverted triangle) and $E\parallel y$ (red, triangle) at 30 K. The lower curve is the XLD spectra multiplied by 10 for a different compound (black, solid line). The inset shows the experimental geometry and axes information.

Figure 2

Total XLD (solid black lines) and OO contribution (dashed red) at various temperatures for (a) $x=0.00$ and (b) $x=0.05$ compounds, respectively. Extracted structure (blue line) and OO (red line) contributions to XLD for (c) $x=0.00$ and (d) $x=0.05$ compounds. Overlaid OO contributions at various temperatures for (e) $x=0.00$ and (f) $x=0.05$ compounds.

Figure 3

(a)–(d), OO contribution to the XLD signal for $x=0.00$, 0.05, 0.08, and 0.10 compounds.

Figure 4

(a) and (b) Temperature dependent XLD magnitude for total (black, square), OO (red, inverted triangle), and structure (blue, triangle) contributions for $x=0.00$ and $x=0.05$ compounds. (c) and (d) Temperature dependence of total XDL magnitudes for $x=0.08$ and $x=0.10$ compounds. (e) Phase diagram of OO fluctuation. $T_{S^{*}}$ ($T_{OO}$) are indicated with blue downward (red upward) arrows in pannels (a) and (b). Open star indicates OO fluctuation temperature determined by Ref. [27]