Strong Coupling of the Iron-Quadrupole and Anion-Dipole Polarizations in $\mathrm{Ba}{({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)}_2{\mathrm{As}}_2$

We use a quantitative convergent beam electron diffraction based method to image the valence electron density distribution in $\mathrm{Ba}{({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)}_2{\mathrm{As}}_2$. We show a remarkable increase in both the charge quadrupole of the Fe cations and the charge dipole of the arsenic anions upon Co doping from $x=0$ ($T_c=0\mathrm{K}$) to $x=0.1$ ($T_c=22.5\mathrm{K}$). Our data suggest that an unexpected electronic correlation effect, namely strong coupling of Fe orbital fluctuation and anion electronic polarization, is present in iron-based superconductors.

Figure 1

Measurement of the low-order electron structure factors using CBED. (a) Experimental energy-filtered CBED pattern of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ showing the 110 systematical row (reflection of $\overline{2}\overline{2}0$, $\overline{1}\overline{1}0$, 000, 110, and 220) at room temperature. (b) Calculated pattern using the dynamical Bloch wave method. (c) Line scans of the intensity profile from the experimental pattern (open circle) and calculated one (solid line) after the structure factor refinement.

Figure 2

Valence electron density map in $\mathrm{Ba}{({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)}_2{\mathrm{As}}_2$ for (a) $x=0$ and (b) $x=0.1$ as well as the two-dimensional map in the (100) plane for (c) $x=0$ and (d) $x=0.1$. The isovalues of difference charge density on the isosurface are $0.1e/{\AA }^3$ (red) and $-0.1e/{\AA }^3$ (blue), respectively. The color legend indicates the magnitude of the charge density and the contour plot has an interval of $0.05e/{\AA }^3$. The red line denotes the shortest As-As distance between the FeAs layers. (e) The radius dependence of the out-of-plane dipole moment inside the sphere centered at the As anion (black solid and dashed lines) and inside the sphere centered at the middle point of the next-nearest Fe-Fe bond illustrated as the white dashed circle in (c) and (d) (red solid and dashed lines). (f) The radius dependence of the quadrupole moments inside the sphere centered at the Fe anion.

Figure 3

Co concentration dependence of Fe $L_{2,3}$ edges EELS for $\mathrm{Ba}{({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)}_2{\mathrm{As}}_2$ for $x=0$, 0.04, 0.06, and 0.08. Inset: the measured $L_3/L_2$ white line ratio (circles) changes with $6+x$, the count of $3d$ electrons assuming ${\mathrm{Co}}^{3+}$, considerably more than the benchmark (line, see the text), indicating that Co substitution introduces charge carriers.