Incommensurate Spin-Density Wave Order in Electron-Doped ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ Superconductors

Neutron diffraction studies of $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ reveal that commensurate antiferromagnetic order gives way to incommensurate magnetic order for Co compositions between $0.056<x<0.06$. The incommensurability has the form of a small transverse splitting (0, $\pm ϵ$, 0) from the commensurate antiferromagnetic propagation vector ${\mathbf{Q}}_{\mathrm{AFM}}=(1,0,1)$ (in orthorhombic notation) where $\mathit{ϵ}\approx 0.02-0.03$ and is composition dependent. The results are consistent with the formation of a spin-density wave driven by Fermi surface nesting of electron and hole pockets and confirm the itinerant nature of magnetism in the iron arsenide superconductors.

Figure 1

(a) Reciprocal space plane with $L=\mathrm{\text{odd}}$ indicating commensurate (C, empty circles) and incommensurate (IC, filled circles) magnetic Bragg peak positions at ${\mathbf{Q}}_{\mathrm{AFM}}=(1,0,L=\mathrm{\text{odd}})$ and $\mathit{\tau }=(1,\pm ϵ,L=\mathrm{\text{odd}})$, respectively, in orthorhombic notation. The size of the incommensurability parameter is exaggerated for clarity. Shaded points labeled ${\mathrm{C}}^{*}$ and ${\mathrm{IC}}^{*}$ show the location of magnetic Bragg peaks that are present due to orthorhombic twinning. Dashed arrows illustrate the direction of longitudinal [$H$, 0, 0] and transverse [0, $K$, 0] neutron diffraction scans. Raw (b) transverse and (c) longitudinal scans for $\mathrm{Ba}({\mathrm{Fe}}_{0.941}{\mathrm{Co}}_{0.059}{)}_2{\mathrm{As}}_2$ at $T=23\mathrm{K}\approx T_c$. The lines are Gaussian fits to the data. Ab initio calculations of the generalized susceptibility in the (d) transverse and (e) longitudinal directions through ${\mathbf{Q}}_{\mathrm{AFM}}$.

Figure 2

Transverse neutron diffraction scans at temperatures $T<T_c$ (blue circles), $T\approx T_c$ (green squares), $T_c<T<T_N$ (red triangles), and $T>T_S$ (empty circles) for $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ with $x=$ (a) 0.054, (b) 0.056, (c) 0.057, and (d) 0.059. Scans with $T>T_S$ are an estimate of the background. All scans are performed through the (1, 0, 3) position except the empty green squares in (b), which are measured through (1, 0, 1) and with the intensity divided by a factor of 0.36. The lines are Gaussian fits to the data.

Figure 3

(a) Experimental phase diagram for $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ showing C and IC antiferromagnetic order below $T_N$. Tetragonal (Tet) and orthorhombic (Ort) phases are separated by the phase line at $T_S$. Superconductivity (Sc) appears below $T_c$ and can coexist with both commensurate (C/Sc) and incommensurate (IC/Sc) magnetic order. Open squares represent the magnetic phase transition temperatures determined in this study. (b) Background subtracted transverse neutron diffraction scans at $T\approx T_c$. Scans are offset vertically and scaled (where noted) for clarity. Integrated intensity (squares) and incommensurability parameter $ϵ$ (circles) (c) as a function of Co concentration at $T\approx T_c$ and (d) as a function of temperature for $x=0.056$. Open squares in (d) represent the total magnetic intensity where C and IC peaks cannot be separated.