Magnetic ordering and structural distortion in Ru-doped BaFe${}_2$As${}_2$ single crystals studied by neutron and x-ray diffraction

We present a systematic investigation of the antiferromagnetic ordering and structural distortion for the series of Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ compounds ($0⩽x⩽0.246$). Neutron and x-ray diffraction measurements demonstrate that, unlike for the electron-doped compounds, the structural and magnetic transitions remain coincident in temperature. Both the magnetic and structural transitions are gradually suppressed with increased Ru concentration and coexist with superconductivity. For samples that are superconducting, we find strong competition between superconductivity, the antiferromagnetic ordering, and the structural distortion.

Figure 1

Temperature evolution of (a) the neutron diffraction rocking scans through the ($\frac{1}{2}$ $\frac{1}{2}$ 3) magnetic Bragg peak and (b) high-resolution x-ray diffraction [$\xi \xi 0$] scans through the (1 1 10) Bragg peak in Ba(Fe${}_{0.927}$Ru${}_{0.073}$)${}_2$As${}_2$. For this sample, $T_S=T_N=109\pm 1$ K. The data are shown with arbitrary offsets.

Figure 2

Plots of the magnetization ($\frac{M}{H}$) and its temperature derivative $\frac{d(\frac{M}{H})}{\mathit{dT}}$, the normalized resistance ($\frac{R}{R_{300\mathrm{K}}}$) and its temperature derivative, the measured orthorhombic distortion ($\delta =\frac{a-b}{a+b}$), and the integrated magnetic intensity at ($\frac{1}{2}$ $\frac{1}{2}$ 3) for Ba(Fe${}_{0.927}$Ru${}_{0.073}$)${}_2$As${}_2$ are shown in panels (a)–(d) and for Ba(Fe${}_{0.795}$Ru${}_{0.205}$)${}_2$As${}_2$ in panels (e)–(h). For $x=0.073$, the measured magnetization, resistance, and their derivatives show sharp signatures at $T_S=T_N=107$ K, close to the value ($109\pm 1$ K) measured by the x-ray and neutron scattering measurements. For $x=0.205$, the signatures at $T_S=T_N$ are significantly broader. The maxima of the derivatives of the magnetization and resistance are found at 49 K, whereas the x-ray and neutron scattering value is $52\pm 1$ K.

Figure 3

(a) Temperature dependence of the ordered magnetic moment calculated from the integrated intensity of the ($\frac{1}{2}$ $\frac{1}{2}$ 3) magnetic Bragg peak from Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$. (b) The extrapolated ordered moment at zero temperature as a function of Ru concentration $x$.

Figure 4

(a) Comparison of the suppression of AFM order below $T_c$ between the 20.5% Ru (filled circles) and the 4.7% Co-doped (open triangles) (Ref. 39) BaFe${}_2$As${}_2$ samples. Intensities of the ($\frac{1}{2}$ $\frac{1}{2}$ 3) magnetic Bragg peak are normalized for comparison. (b) Orthorhombic distortion for Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ with $x=0.205$ (circles) and 0.246 (stars). The reduction in the distortion below $T_c$ is not clearly observable for $x=0.205$, but it is evident for $x=0.246$. The gray dashed lines are guides for the eyes.

Figure 5

Compositional phase diagrams for (a) Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ from Ref. 19, (b) Ba(Fe${}_{1-x}$Ru${}_x$)${}_2$As${}_2$ from this paper and Ref. 36, and (c) Ba(Fe${}_{1-x}$Mn${}_x$)${}_2$As${}_2$ from Ref. 27. The gray open triangles and open circles denote data taken from resistance and magnetization data, respectively. The gray open squares denote bulk measurements of $T_c$. Filled red triangles denote $T_S$ measured by x-ray diffraction, filled blue circles denote $T_N$ measured by neutron diffraction, and the filled orange squares represent values for $T_c$ from the x-ray and neutron data. Filled magenta circles denote $T^{*}$ determined for the Mn-doped sample by neutron measurements (see Ref. 27).