Antiferromagnetic order and superlattice structure in nonsuperconducting and superconducting Rb${}_y$Fe${}_{1.6+x}$Se${}_2$

Neutron diffraction has been used to study the lattice and magnetic structures of the insulating and superconducting Rb${}_y$Fe${}_{1.6+x}$Se${}_2$. For the insulating Rb${}_y$Fe${}_{1.6+x}$Se${}_2$, neutron polarization analysis and single-crystal neutron diffraction unambiguously confirm the earlier proposed $\sqrt{5}\times \sqrt{5}$ block antiferromagnetic structure. For superconducting samples ($T_c=30$ K), we find that in addition to the tetragonal $\sqrt{5}\times \sqrt{5}$ superlattice structure transition at 513 K, the material develops a separate $\sqrt{2}\times \sqrt{2}$ superlattice structure at a lower temperature of 480 K. These results suggest that superconducting Rb${}_y$Fe${}_{1.6+x}$Se${}_2$ is phase separated with coexisting $\sqrt{2}\times \sqrt{2}$ and $\sqrt{5}\times \sqrt{5}$ superlattice structures.

Figure 1

(a) Schematic of Fe nuclear and spin structures in left chirality and (b) in right chirality. The plus and minus signs represent spin directions up and down along the $c$-axis, respectively. The solid and dashed squares are the top views of the tetragonal cell (red) and the $\sqrt{5}\times \sqrt{5}$ superlattice cell (blue), respectively. (c) The expected Bragg peak positions in the $[H_T,K_T]$ tetragonal unit cell notation for left chirality. The red circles with $L=1$ are magnetic peaks and the black circles are nuclear peaks with $L=2$. The brown squares are nuclear peaks for both even and odd $L$. The green star at (0.5,0.5) reciprocal lattice units (rlu) is not an expected Bragg peak position for the present structure. The inset is a schematic of the tetragonal and superlattice unit cell in reciprocal space. (d) The expected Bragg peaks from both left and right chiralities. [(e) and (f)] The same expected Bragg peaks in $[H_S,K_S]$ superlattice unit cell notation.

Figure 2

Portion of the neutron powder diffraction pattern for Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$ at 480 K and its comparison with the expected neutron powder patterns for various proposed magnetic structures of $A_y$Fe${}_{1.6+x}$Se${}_2$.[38] The plus and minus signs denote spin directions parallel and antiparallel to the $c$ axis, respectively. The data and model fitted difference plots are shown below. The weighted $R$ factors for each model are listed as follows: (a) Ferromagnetic or FM, $R_{\mathrm{wp}}=7.81$$\%$; (b) checkerboard AFM, $R_{\mathrm{wp}}=7.56$$\%$; (c) collinear AFM, $R_{\mathrm{wp}}=9.93$$\%$; (d) bicollinear AFM, $R_{\mathrm{wp}}=9.7$$\%$; (e) cell-in-collinear AFM, $R_{\mathrm{wp}}=7.45$$\%$; (f) cell-in-collinear AFM, $R_{\mathrm{wp}}=7.44$$\%$. None of the models can fit the observed neutron powder diffraction pattern.

Figure 3

Two possible AFM structures that can equally well fit the neutron powder diffraction pattern of Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$ at 480 K. (a) Quaternary collinear AFM structure and (b) block AFM structure. The $R_{\mathrm{wp}}$ factors for these two magnetic structures are 7.0 and 6.95$\%$, respectively. Both of these models were proposed earlier.[24, 25]

Figure 4

(a) Zero-field-cooled (ZFC) magnetic susceptibility of 17.12 mg Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$ at 30 Oe with the $H//ab$ plane measured using a commercial SQUID. No superconductivity was observed. (b) Magnetic structure in the $I{112}^{\prime }/m^{\prime }$ space group representation. (c) The experimental data collected from HB-3A. The data plotted are from one chiral domain. In single-crystal diffraction experiments, we compared several peaks from left and right chiral domains and found them to be the same. We used one domain for the data collection, since this can save half of the beam time for a point detector diffractometer. The radius of the circles are proportional to the intensity of the Bragg peaks. The two peaks enclosed in the green ellipse have quite different intensities for the $I4/m^{\prime }$ and $I{112}^{\prime }/m^{\prime }$ AFM models. (d) The rocking curves for Bragg peaks $Q_S=(3,-2,-1)$ (red circle) and $Q_S=(2,-3,-1)$ (blue square). The black and green solid lines are the simulation of the expected magnetic intensities for $(2,-3,-1)$ in $I4/m^{\prime }$ and $I{112}^{\prime }/m^{\prime }$ models, respectively, where the intensity of the $(3,-2,-1)$ peak are normalized to the value of the experiment. Error bars represent one standard deviation. (e) The simulations of the expected Bragg peak intensity with the $I4/m^{\prime }$ model. (f) Identical simulation with the $I{112}^{\prime }/m^{\prime }$ model.

Figure 5

Neutron polarization analysis with neutron guide field in the horizontal scattering plane along the wave vector direction for Rb${}_{0.89}$Fe${}_{1.58}$Se${}_2$. (a) Schematics of the reciprocal space probed in the $[H_T,K_T]$ plane. The scans are along the arrow direction that depends on the lower goniometer arc tilting angles $\alpha$. The observed scattering intensity in SF and NSF channels are plotted in the ${[H,H\tan \alpha ,L]}_T$ plane of reciprocal space. (b) Magnetic peak $Q_T=(1.2,0.6,1)$ appears in the SF (flipper on) channel and disappears in the (c) NSF channel. [(d) and (e)] Magnetic peak $Q_T=(1.4,1.2,1)$ in the SF and NSF channels, respectively.[(f)–(i)] Nuclear peaks $Q_T=(0.6,0.2,2)$ and $Q_T=(1.4,0.2,2)$ show no observable scattering in the SF channel and the entire peak appears in the NSF channel. The color bars indicate the strength of the neutron scattering intensity.

Figure 6

(a) In-plane resistivity of Rb${}_{0.75}$Fe${}_{1.63}$Se${}_2$ indicating $T_c=30$ K. (b) Susceptibility measurements with 20 mT in-plane field on a 14.2-mg Rb${}_{0.75}$Fe${}_{1.63}$Se${}_2$ single crystal confirm the superconducting transition temperature $T_c=30$ K. The left axis is the calculated volume magnetic susceptibility indicating a $\sim$8$\%$ superconducting volume fraction. The right axis shows magnetic susceptibility in units of emu (1 $\mathrm{emu}={10}^{-3}$ A m${}^2$). (c) Neutron powder diffraction pattern at 500 K showing the refinement results for the sample including the $\sqrt{5}\times \sqrt{5}$ superlattice distortion. The superlattice induced peaks are marked with arrows. (d) The neutron refinement results in the paramagnetic state at 550 K.

Figure 7

Triple-axis measurements on a single crystal of Rb${}_{0.75}$Fe${}_{1.63}$Se${}_2$ on HB-1A. (a) Elastic $[0.51,0.51,L]$ scans at different temperature. The scattering is above background scattering at all $L$ values. The background scattering is determined from $[H,H]$ scans. All the peaks are centered at $H\approx 0.5$ (not exactly at 0.5 due possibly to a small crystal misalignment on HB-1A). The strong $L$ modulation disappears at 640 K. (b) Rocking curves of the (0.51,0.51,3) reflection at 2 K and 540 K. (c) Temperature dependence of the peak intensity for the (0.51,0.51,3) reflection shows a first-order-like transition above 480 K as marked by the arrow. (d) Temperature dependence of the $[H,H,3]$ scans shows that the $(0.5,0.5)$ lattice distortion disappears at 495 K, below the tetragonal to $\sqrt{5}\times \sqrt{5}$ superlattice reflection. (e) Widths of the (2,2,0) nuclear reflection indicates a second-order-like structural transition at 513 K. The solid lines are guides to the eye.

Figure 8

Low-temperature triple-axis measurements on Rb${}_{0.75}$Fe${}_{1.63}$Se${}_2$. (a) The $[0.51,0.51,L]$ scans below and above $T_c$. The background is from ${[H,H]}_T$ scans and the solid lines are guides to the eye. [(b–(g)] Elastic ${[H,H,L]}_T$ scans at $L=0,1,2,3,1.5,2.5$ below and above $T_c$. The lattice distortion is not affected by the superconductivity.

Figure 9

Polarized neutron scattering measurements near the $[0.5,0.5,L]$ Bragg peak for Rb${}_{0.75}$Fe${}_{1.63}$Se${}_2$ at room temperature. The experimental configuration is the same as that for Fig. 5. While the NSF scattering on the left panel shows clear nuclear scattering centered around the $[0.5,0.5,L]$ positions, there is no evidence of SF scattering in the same reciprocal region. This means that there is no elastic magnetic scattering at the same wave vector as the iron pnictides such as LaFeAsO.[7]

Figure 10

Neutron powder diffraction measurements on Rb${}_{0.75}$Fe${}_{1.50}$Se${}_2$ at 480 K. They are fit using a combination of $62.3\%I4/m$ and $37.7\%Pmna$ phases. The purple trace indicates the intensity difference between the observed (green solid line) and calculated (red crosses) structures. The left inset is a schematic of the $Pmna$ phase which can induce nuclear peaks at ${[m\pm 0.5,n\pm 0.5,L]}_T$ ($m,n=0,\pm 1,\pm 2,\pm 3,\cdots$).