Common Crystalline and Magnetic Structure of Superconducting $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs},\mathrm{Tl}$) Single Crystals Measured Using Neutron Diffraction

Single-crystal neutron diffraction studies on superconductors $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$, where $A=\mathrm{Rb}$, Cs, (Tl, Rb), and (Tl, K) ($T_c\sim 30\mathrm{K}$), uncover the same Fe vacancy ordered crystal structure and the same block antiferromagnetic order as in ${\mathrm{K}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$. The Fe order-disorder transition occurs at $T_S=500–578\mathrm{K}$, and the antiferromagnetic transition at $T_N=471–559\mathrm{K}$ with an ordered magnetic moment $\sim 3.3{\mu }_B/\mathrm{Fe}$ at 10 K. Thus, all recently discovered $A$ intercalated iron selenide superconductors share the common crystalline and magnetic structure, which are very different from previous families of Fe-based superconductors, and constitute a distinct new 245 family.

Figure 1

(a) Magnetic susceptibility of $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ [$A=\mathrm{Rb}$, Cs, (Tl, K), and (Tl, Rb)] showing the superconducting transition. (b) Common crystal and magnetic structure in the tetragonal $I4/m$ unit cell. The cyan sphere represents Se, the yellow sphere the intercalating $A$, the orange cube the ${\mathrm{Fe}}_1$ vacancy site, and the purple sphere the occupied ${\mathrm{Fe}}_2$ site with a $+(-)$ sign indicating the up(down) magnetic moment along the $c$ axis. There are 4 f.u. per cell. (c) The top Fe-Se layer. The dark and light cyan plaquettes emphasize the four-spin blocks of the up and down spins, respectively, which forms a checkerboard nearest-neighbor antiferromagnetic pattern. From one Fe layer to another, magnetic moments are antiferromagnetically coupled. The solid line denotes the $I4/m$ unit cell, one of the two twins, which breaks the high-temperature symmetry of the $I4/mmm$ unit cell (dashed line) at the Fe order-disorder transition at $T_S$.

Figure 2

Single-crystal neutron diffraction pattern of (a) ${\mathrm{Cs}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$, (b) ${\mathrm{Rb}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$, (c) $(\mathrm{Tl},\mathrm{Rb}{)}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$, and (d) $(\mathrm{Tl},\mathrm{K}{)}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ measured in the $(h0\ell )$ plane of the $I4/m$ unit cell at $T=295\mathrm{K}$. In addition to Bragg peaks of the high temperature $I4/mmm$ structure, two new types of contributions to the Bragg reflection appears: (1) structural $\{200\}$, $\{202\}$, $\{400\}$, $\{402\}$, etc., caused by the Fe vacancy order, and (2) magnetic $\{103\}$, $\{301\}$, $\{303\}$, $\{701\}$, etc., caused by antiferromagnetic order of the Fe moments.

Figure 3

(a) Magnetic (103) and structural (118) Bragg peaks vs the temperature, serving as order parameters for the antiferromagnetic and Fe vacancy order-disorder transitions, respectively, in ${\mathrm{Cs}}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$. (b) Normalized magnetic Bragg intensity representing the squared magnetic moment as a function of the temperature for $A_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ superconductors. Inset: Magnetic (101) peak of $(\mathrm{Tl},\mathrm{Rb}{)}_2{\mathrm{Fe}}_4{\mathrm{Se}}_5$ showing that its intensity saturates when $T_c$ is approached.