Ru doping in iron-based pnictides: The “unfolded” dominant role of structural effects for superconductivity

We present an ab initio study of Ru substitution in two different compounds, ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ and LaFeAsO, pure and F doped. Despite the many similarities among them, Ru substitution has very different effects on these compounds. By means of an unfolding technique, which allows us to trace back the electronic states into the primitive cell of the pure compounds, we are able to disentangle the effects brought by the local structural deformations and by the impurity potential to the states at the Fermi level. Our results are compared with available experiments and show (i) satisfying agreement of the calculated electronic properties with experiments, confirming the presence of a magnetic order on a short-range scale, and (ii) Fermi surfaces strongly dependent on the internal structural parameters, more than on the impurity potential. These results enter a widely discussed field in the literature and provide a better understanding of the role of Ru in iron pnictides: although isovalent to Fe, the Ru-Fe substitution leads to changes in the band structure at the Fermi level mainly related to local structural modifications.

Figure 1

Left panels: experimental values (Refs. [4, 13, 16, 25, 26, 27, 28, 29, 30]) of the in-plane $a$ (a) and out-plane $c/2$ and $c$ (b) vectors for Ba-122 (circles), La-1111 (squares), and La1111(F) (triangles) compounds as a function of Ru concentration. Right panels: experimental values (empty symbols) of the As height (Refs. [16, 25, 29, 30]), with respect to the metallic plane, as a function of Ru concentration for Ba-122 (c) and La-1111 (d), compared with ab initio nonmagnetic (dashed lines) and AFM2-magnetic (continuous lines) calculations. In the case of La1111, results for the stripe-AFM2 F-doped compound are also shown (triangles).

Figure 2

(a) Fe-As (squares), Ru-As (triangles), and TM-As (circles) bond lengths for Ba-122 (solid lines, filled symbols) and La-1111 (dashed lines, empty symbols) as a function of Ru concentration. Right panels: Fe-As-Fe (squares), Ru-As-Ru (triangles), and TM-As-TM (circles) bond angle for Ba-122 (b) and La-1111 (c) as a function of Ru concentration.

Figure 3

Calculated local magnetic moment of Fe (filled symbols) and Ru (empty symbols) in Ba-122 (circles), La-1111 (squares), and La-1111F (triangles) as function of Ru concentration. The inset sketches the ordering of the magnetic moments on the TM sites, in the stripe (AFM2) phase and the orientation of the metallic plane as considered in our calculations.

Figure 4

Effective band structure (EBS) for Ba-122 as function of Ru concentration ($x=0.0,0.25,0.5$), unfolded on the 2-Fe bct primitive cell. Panels (a), (d), and (g) show the band structure of pure Ba-122 with highlighted the projected orbital character ($d_{yz}, d_{xz}, d_{x^2-y^2}$, respectively); here, the size of the data points is proportional to the amount of Bloch character. Panels (b) and (c) show the band structure for the fully relaxed structure (standard calculation) at $x=0.25$ and 0.5 Ru content, respectively. Panels (e) and (f) report the band structure of the Ru doped compound (at $x=0.25$ and 0.5 Ru content, respectively) in the structure of pure Ba-122. Finally, panels (h) and (i) show the band structure obtained for pure Ba-122 in the fully relaxed doped structures (at $x=0.25$ and 0.5 Ru content, respectively). The inset sketches the high-symmetry points in the pbz.

Figure 5

Fermi surface for Ba-122 as function of Ru concentration, obtained by the standard calculation at the given Ru content: $x=0.0,0.25,0.5,0.75$ [(a), (b), (c) and (d), respectively]. The color gradient represents the value of the spectral functional $A(\mathbf{k},E_F)$ calculated according to Eq. (4).

Figure 6

Effective band structure (EBS) for La-1111 and La-1111F as function of Ru concentration ($x=0.0,0.25,0.5$), unfolded on the 2-Fe primitive cell. Panels (a), (d), and (g) show the band structure of the pure La-1111 compound decorated with the orbital character ($d_{yz}, d_{xz}, d_{x^2-y^2}$, respectively); here, the size of the data points is proportional to the amount of Bloch character. Panels (b) and (c) show the band structure for the fully relaxed structure (standard calculation) of La-1111 at $x=0.25$ and 0.5 Ru content, respectively. Panels (e) and (f) report the band structure of Ru-doped La-1111 (at $x=0.25$ and 0.5 Ru content, respectively) in the structure of pure La-1111. Panels (h) and (i) show the band structure obtained for pure La-11111 in the fully relaxed doped structures (at $x=0.25$ and 0.5 Ru content, respectively). Finally, panels (j), (k), and (l) show the band structure for the fully relaxed structure (standard calculation) of F-doped La-1111 compound at $x=0.0$, 0.25, and 0.5 Ru content, respectively. The inset sketches the high-symmetry points in the pbz.

Figure 7

Size of the internal and external $d_{xz}$ and $d_{yz}$ hole pockets (i.e., the Fermi vectors $k_F$) for Ba-122 and La-1111 as function of Ru concentration in the $\mathrm{\Gamma }-X$ and $\mathrm{\Gamma }-M$ directions. Circles represent the results obtained using structures with fully relaxed internal parameters (standard structures); the lines with squares have been obtained using the structures of the pure compounds dressed with the proper amount of Ru atoms; the lines with triangles represent the result obtained with relaxed Ru-doped structures dressed entirely with Fe atoms at each TM site.

Figure 8

Atom projected DOS for Ba-122 on the Ru (a) and Fe (b) sites at different Ru content ($x=0,0.25,0.5,0.75,1$), in arbitrary units. The partial density of states corresponding to different concentrations is arbitrarily shifted on the $y$ axes to allow comparison. (c) Total DOS for Ba-122 at $x=0.5$ calculated for the fully optimized (gray filled curve), all Fe (relaxed structure dressed up with Fe atoms only, dashed line), and pure (pure structure dressed up with 50% Ru doping, continuous line) structures, and compared with the fully optimized pure $x=0$ Ba-122 case (dotted line).