Two spatially separated phases in semiconducting ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$

We report neutron scattering and transport measurements on semiconducting ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$, a compound isostructural and isoelectronic to the well-studied $A_{0.8}{\mathrm{Fe}}_y{\mathrm{Se}}_2(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs},\mathrm{Tl}/\mathrm{K})$ superconducting systems. Both resistivity and dc susceptibility measurements reveal a magnetic phase transition at $T=275\mathrm{K}$. Neutron diffraction studies show that the 275 K transition originates from a phase with rhombic iron vacancy order which exhibits an in-plane stripe antiferromagnetic ordering below 275 K. In addition, the stripe antiferromagnetic phase interdigitates mesoscopically with an ubiquitous phase with $\sqrt{5}\times \sqrt{5}$ iron vacancy order. This phase has a magnetic transition at $T_N=425\mathrm{K}$ and an iron vacancy order-disorder transition at $T_S=600\mathrm{K}$. These two different structural phases are closely similar to those observed in the isomorphous Se materials. Based on the close similarities of the in-plane antiferromagnetic structures, moments sizes, and ordering temperatures in semiconducting ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$ and ${\mathrm{K}}_{0.81}{\mathrm{Fe}}_{1.58}{\mathrm{Se}}_2$, we argue that the in-plane antiferromagnetic order arises from strong coupling between local moments. Superconductivity, previously observed in the $A_{0.8}{\mathrm{Fe}}_y{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ system, is absent in ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$, which has a semiconducting ground state. The implied relationship between stripe and block antiferromagnetism and superconductivity in these materials as well as a strategy for further investigation is discussed in this paper.

Figure 1

(a) Three-dimensional structure of the block AF phase in ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$. (b) The Fe plane of block AF phase with $\sqrt{5}\times \sqrt{5}$ iron order, where a magnetic unit cell with lattice parameter $a_s=\sqrt{5}\times 3.765$ Å has been marked as green. The tetragonal lattice cell used throughout this paper is shaded light orange. The red and blue arrows represent the out-of-plane spin directions up and down. The orange, lime, turquoise, and light gray balls are Rb, Fe, and S atoms and Fe vacancies, respectively. (c) A three-dimensional magnetic unit cell of the in-plane AF order and (d) Fe-plane with the rhombic iron vacancy order. A magnetic unit cell is shaded green. The diagonal Fe bonds are 3.889 Å at 180 K.

Figure 2

(a) In-plane resistivity measurement of semiconducting ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.5}{\mathrm{S}}_2$. (b) 1 T zero-field-cooled (ZFC) and field-cooled (FC) dc magnetic susceptibility measurements with $H\parallel ab$ plane. A spin-glass-like behavior appears below 55 K. A kink corresponding to the stripe AF order transition is observed in both resistivity and susceptibility measurements at $T=275$ K. (c) The well-separated peaks in the $\theta -2\theta$ scans at nuclear reflection wave vector $Q=(1,1,0)$ demonstrate two different sets of in-plane lattice constants at 180 and 590 K. (d) $\theta -2\theta$ scans at $Q=(0,0,2)$ show a single lattice constant $c$ within the instrument resolution. The error bars are one standard deviation and solid lines are fits to a Gaussian function throughout this paper.

Figure 3

Magnetic and nuclear reflection peaks associated with the block AF phase and $\sqrt{5}\times \sqrt{5}$ iron vacancy order. Scans through magnetic peaks at (a) $Q=(0.2,0.4,1)$, (b) $Q=(0.2,0.4,3)$, and (c) $Q=(1.2,1.4,1)$ along the $[H,H+0.2]$ direction at $T=212\mathrm{K}$. The red solid points in panel (a) through $Q=(0.4,0.2,1)$ are from the other chirality. (d) Rocking-curve scans through magnetic peak $Q=(0.2,0.4,1)$ at selected temperatures of $T=300$, 385, 415, and 430 K. (e) Scan through the nuclear peak at $Q=(0.2,0.6,2)$ along the $[H,H+0.4]$ direction associated with the $\sqrt{5}\times \sqrt{5}$ iron vacancy order at $T=300\mathrm{K}$. (f) $\theta -2\theta$ scans through nuclear peak at $Q=(0.4,0.8,2)$ at $T=300$, 585, 597, and 605 K. The inset in panel (b) is the expected magnetic Bragg peaks (solid circles, $L=\mathrm{odd}$) and nuclear Bragg peaks (open squares, $L=\mathrm{even}$) in tetragonal reciprocal space. The red and blue lines indicate two different chiralities. The insets in panels (d) and (f) are color maps of the temperature dependence of reflection peaks corresponding to panels (d) and (f).

Figure 4

Diffraction studies of the in-plane AF phase with rhombic iron vacancy order. Scans of magnetic peaks at wave vector of (a) $Q=(0.5,0.5,1)$, (b) $Q=(0.5,0.5,3)$, (d) $Q=(0.5,0.5,5)$ along the $[H,H]$ direction, and (c) $Q=(0.5,0.5,1)$ along $L$ direction at selected temperatures. The inset of panel (a) is a color map of detailed temperature dependence. Panels (e) and (f) show the nuclear peaks at the wave vectors of $H=0.25,0.5,0.75;L=\mathrm{even}$ and magnetic peaks at $H=0.5,L=\mathrm{odd}$ from the in-plane AF phase in the $[H,3H,L]$ plane at 6 and 280 K, respectively. The nuclear peaks were not changed, but the magnetic peaks disappeared at 280 K. The peaks at $H=0.4,L=\mathrm{even}$ originate from the $\sqrt{5}\times \sqrt{5}$ iron vacancy order in the block AF phase. (g) Scans along $[H,3H,0]$ r.l.u. at peaks of the rhombic iron vacancy order at $Q=(0.25,0.75,0)$ at 180 K, 600 K, 615 K and 630 K. The evolution of $2\theta$ ($S2$) of the peak centers versus temperature indicates an in-plane lattice constant change across the in-plane magnetic structure transition in the inset of (g).

Figure 5

Temperature dependence of order parameters for the in-plane stripe AF, the rhombic iron vacancy, the block AF and the $\sqrt{5}\times \sqrt{5}$ iron vacancy orders. The height of peaks at $Q=(0.5,0.5,1)$ fit from $[H,H]$ scans shown as the black squares represent the stripe AF transition at $T_{N1}=275\mathrm{K}$. The temperature dependence of peak height at $Q=(0.2,0.4,1)$ (green circle) fit from rocking-curve scans shows the block AF transition at $T_{N2}=425\mathrm{K}$. The red diamonds obtained from $\theta -2\theta$ scans through $Q=(0.4,0.8,2)$ indicate a first-order-like transition of the $\sqrt{5}\times \sqrt{5}$ iron vacancies at $T_S=600\mathrm{K}$. The rhombic iron vacancy order parameter integrated from the $\theta -2\theta$ scans at $Q=(0.25,0.75,0)$ was collected from another piece of single crystal with the same composition aligned in the $[H,3H,L]$ zone.