Nanoscale-textured superconductivity in Ru-substituted BaFe${}_2$As${}_2$: A challenge to a universal phase diagram for the pnictides

${}^{75}$As NMR experiments were performed in Ba(Fe${}_{1-}$${}_x$Ru${}_x$)${}_2$As${}_2$ for $x$ $=$ 0$\%$–80$\%$. Magnetic fractions and NMR line shapes demonstrate that Ru substitution destroys the antiferromagnetic (AF) order inhomogeneously with a magnetic moment distributed from 0.9μ${}_B$ to 0μ${}_B$. Superconductivity emerges at intermediate Ru doping and coexists with AF order only in the regions where moments are smaller than ∼0.3μ${}_B$, resulting in an original nanoscale texture. This situation contrasts with that of Co substitution, challenging the apparent universality of the phase diagram in Fe-based superconductors.

Figure 1

Top: Phase diagrams established from transport measurements (red and blue dots) for Ru (left) and Co (right) substitutions (Refs. 10 and 11). The dashed boxes indicate the expected percolation transition (see text). Bottom : Evolution of the magnetic and superconducting volume fractions at low temperature (the latter being corrected from a demagnetization factor of 1/3 to account for the Ru more or less spherical grain shapes) (for Co, fractions extracted from Refs. 15, 16, 17).

Figure 2

NMR powder spectra for different Ru contents at low temperature ($T<T_N$ for 0$\%$ and 5$\%$ and $T=8$ K otherwise). Inset: Temperature dependence of the paramagnetic fraction measured by integration of the spectral weight of the central line—experiment (circles), simulations (envelopes), and the percolation threshold for the magnetic ordering.

Figure 3

Magnetic fraction vs Ru nominal content: Experiment (circle, Ru 0$\%$ and 100$\%$ from Refs. 14 and 16) and simulations (solid lines) using a local Ru content model. Inset: (a) Random distribution of Ru (black dots) in a layer of Fe sites (only a portion of size 25 $\times$ 25 ofthis layer is shown); a moving $N$ $\times$ $N$ averaging of this layer leads to (b) for $N$ $=$ 4 and (c) for $N$ $=$ 20.

Figure 4

Top: NMR experimental spectrum for Ru 15$\%$ (dark gray) vs simulations (colored) done with the magnetic textures computed for $N$ $=$ 2, 4, 7, and 20. Bottom: Typical distribution of the AF magnetic moment amplitude for $N$ $=$ 4 in a 100 $\times$ 100 Fe layer. Blue lines encompass areas where SC and AF coexist.