Anisotropic magnetic form factor in a detwinned single crystal of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$

We have performed neutron diffraction measurements at 12 K on a single crystal of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, which serves as the parent compound of iron-based superconductors. To investigate the in-plane anisotropy of the magnetic form factor in the antiferromagnetic phase, the single crystal was detwinned. The magnetic structure factor and magnetic form factor are well explained by the spin densities comprising $3d_{yz}$ electrons with a fraction of approximately 40% and electrons in the other four $3d$ orbitals each with a fraction of approximately 15%. It is a direct observation of the largely anisotropic spin density relative to the small orthorhombic lattice distortion, $(a-b)/(a+b)\sim 0.3\%$.

Figure 1

Peak profiles of the (a) 040 and (b) 400 nuclear Bragg reflections obtained under the scattering configurations employed to collect the intensity of the $hkh$ and $h0l$ reflections, respectively. The data were collected at 12 K (solid circles) and room temperature (open circles).

Figure 2

Observed squared nuclear structure factor $|F_N{|}_{\text{obs}}^2$ is plotted against squared nuclear structure factor $|F_N{|}_{\text{cal}}^2$ calculated using the atomic positions reported in Ref. [18]. The solid line is the fitting result using the formula $|F_N{|}_{\text{obs}}^2=A|F_N{|}_{\text{cal}}^2(1-B|F_N{|}_{\text{cal}}^2)$.

Figure 3

(a) Magnetic structure in the antiferromagnetic phase of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. (b) $R$ factors estimated from ${\left|F\right|}_{\text{obs}}^2$ and ${\left|F\right|}_{\text{cal}}^2$, and (c) those from $f_{\text{obs}}\left(\mathit{Q}\right)$ and $f_{\text{cal}}\left(\mathit{Q}\right)$ (c), are plotted against $\varphi$ and $w_{yz}$.

Figure 4

(a) ${\left|F\right|}_{\text{obs}}^2$ and (b) $f_{\text{obs}}\left(\mathit{Q}\right)$ are plotted against ${\left|F\right|}_{\text{cal}}^2$ and $f_{\text{cal}}\left(\mathit{Q}\right)$, respectively. Straight lines indicate that ${\left|F\right|}_{\text{obs}}^2={\left|F\right|}_{\text{cal}}^2$ and $f_{\text{obs}}\left(\mathit{Q}\right)=f_{\text{cal}}\left(\mathit{Q}\right)$. (c) The $f_{\text{obs}}\left(\mathit{Q}\right)$ obtained at $h01$ (solid circles), $1k1$ (small open circles), $h03$ (solid triangles), and $10l$ (large open circles) reflections are plotted against $Q$. Thin solid and dashed lines represent the magnetic forms factors calculated at $h01$ and $h03$, and bold dashed and solid lines are the magnetic form factors calculated at $1k1$ and $10l$, respectively. The bold dashed line corresponds with the bold solid line. (d) A schematic representation of the spin density of Fe ions in the orthorhombic unit cell in the $a-b$ plane.