Magnetic form factor of ${\text{SrFe}}_2{\text{As}}_2$: Neutron diffraction measurements

Neutron diffraction measurements have been carried out to investigate the magnetic form factor of the parent ${\text{SrFe}}_2{\text{As}}_2$ system of the iron-based superconductors. The general feature is that the form factor is approximately isotropic in wave vector, indicating that multiple $d$ orbitals of the iron atoms are occupied as expected based on band theory. Inversion of the diffraction data suggests that there is some elongation of the spin density toward the As atoms. We have also extended the diffraction measurements to investigate a possible jump in the $c$-axis lattice parameter at the structural phase transition but find no detectable change within the experimental uncertainties.

Figure 1

(Color online) Measurement of the square of the magnetic form factor as a function of $Q=4\pi \text{sin}\left(\theta \right)/\lambda$. Circles denote reflections which are predominantly along (0,0,L). Squares represent reflections which are predominantly along (H,0,0). The solid curve shows the form factor of metallic iron (Ref. 4). Error bars are statistical in nature and represent one standard deviation.

Figure 2

(Color online) (a) Fourier inversion of the experimental form factor, yielding the projection of the magnetization density onto the $a\text{−}c$ plane of the crystal structure. The different (red and blue) shaded regions with the arrows reversed indicate the oppositely directed magnetization of the antiferromagnetic structure. Note the elongation of the density along the Fe-As bond, indicated for the As ions above (small red circles) for one spin direction and below (large blue circles) the Fe plane for the other spin direction. (b) Magnetization density in the Fe plane obtained from the simulated data, where higher $Q$ as well as $K\ne 0$ reflections have been calculated and included in the inversion. The similarity of the two plots demonstrates that the features obtained from the actual data are robust against termination effects and the absence of $K\ne 0$ data. (c) Maximum entropy reconstruction of the magnetization density, which also yields the same basic magnetization density. For all plots, the densities have been normalized.

Figure 3

Intensity of the (0,0,4) Bragg peak, as measured in a radial $\left(\theta :2\theta \right)$ scan, as a function temperature. The black horizontal line represents the temperature of the tetragonal-orthorhombic transition at $\sim 220\text{K}$. The inset shows the position of the reflection, which exhibits a smooth variation with temperature with no indication of a structural phase transition. In most cases, error bars are smaller than the marker size.