Tetragonal magnetic phase in ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ from x-ray and neutron diffraction

Combined neutron and x-ray diffraction experiments demonstrate the formation of a low-temperature minority magnetic tetragonal phase in ${\mathrm{Ba}}_{0.76}{\mathrm{K}}_{0.24}{\mathrm{Fe}}_2{\mathrm{As}}_2$ in addition to the majority magnetic, orthorhombic phase. The coincident enhancement in the magnetic ($\frac{1}{2} \frac{1}{2}$ 1) peaks shows that this minority phase is of the same type that was observed in ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($0.24\le x\le 0.28$), in which the magnetic moments reorient along the $c$ axis. This is evidence that the tetragonal magnetic phase is a universal feature of the hole-doped iron-based superconductors. The observations suggest that in this regime the energy levels of the $C_2$ and $C_4$ symmetric magnetic phases are very close.

Figure 1

Overlaid x-ray diffraction scans of ${\mathrm{Ba}}_{0.76}{\mathrm{K}}_{0.24}{\mathrm{Fe}}_2{\mathrm{As}}_2$ at approximately uniform increments from 10.5 to 53.5 K. The top panel shows the (112) reflection and the bottom shows the (114) reflection. The split peak in the orthorhombic phase corresponds to the ($11l$) and ($\overline{1}1l$) components ($I$ cell), which are the ($20l$) and ($02l$) peaks in the conventional F-centered cell.

Figure 2

False color map drawn using the x-ray diffraction data on ${\mathrm{Ba}}_{0.76}{\mathrm{K}}_{0.24}{\mathrm{Fe}}_2{\mathrm{As}}_2$. The top panel shows the temperature range from 10 to 120 K of the (112) reflection, which splits into the (202) and (022) orthorhombic peaks. The bottom panel shows the (114) (corresponding to the (204) and (024) components of the orthorhombic cell) from 10 to 53 K. The arrows point to the peak corresponding to the minority tetragonal phase.

Figure 3

(Left) Temperature-dependent color maps depicting the magnetic peak intensity of the ($\frac{1}{2} \frac{1}{2}$ 1) (top) and ($\frac{1}{2} \frac{1}{2}$ 3) (bottom) reflections. The right panels are peak intensities integrated from a five-point-wide cut through the peak of interest.

Figure 4

Refined lattice parameters for the majority phase in ${\mathrm{Ba}}_{0.76}{\mathrm{K}}_{0.24}{\mathrm{Fe}}_2{\mathrm{As}}_2$ determined from x-ray powder diffraction. (a) $c_1$ is shown in black, and $a_{1,\mathrm{tet}}$ in blue (see text). Orthorhombic (open circles) and tetragonal (closed circles) fits were used below and above 87 K, respectively. (b) The major phase orthorhombic order parameter. Inset is a detailed view around $T_{\mathrm{c}}$ and $T_{\mathrm{r}}$. (c) In-plane lattice parameters: $a$ (black circles) and $b$ (red circles), orthorhombic phase; $a_1$ (blue circle) and $a_2$ (blue triangles), tetragonal phases. Tetragonal lattice parameters are scaled by $\sqrt{2}$. (d) The volume of the majority phase ($V_1$), with blue and black circles being used to demarcate the transition from tetragonal to orthorhombic models, respectively. The inset is the refined phase fraction of the minority phase.

Figure 5

X-ray powder diffraction data from ${\mathrm{Ba}}_{0.775}{\mathrm{K}}_{0.225}{\mathrm{Fe}}_2{\mathrm{As}}_2$. (a) X-ray (11BM) diffractogram of the (220) reflection. (b) Integrated intensity across the ($\frac{1}{2}\frac{1}{2}1$) reflection from the neutron (Wish) powder diffraction data. (c) Neutron powder diffraction data (HRPD) on ${\mathrm{Ba}}_{0.75}{\mathrm{K}}_{0.25}{\mathrm{Fe}}_2{\mathrm{As}}_2$ reproduced from Ref. [11].