Structure, superconductivity, and magnetism in ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$

We report on single-crystal growth, stoichiometry, structure and basic characterization of ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ crystals where Se is substituted by S. The temperature and magnetic field dependence of magnetic and thermodynamic properties of all samples was studied by differential-scanning calorimetry, magnetic susceptibility, electrical conductivity, and specific heat. The experimental results are discussed within a $T-z$ phase diagram, which includes vacancy-ordered and vacancy-disordered antiferromagnetic (AFM), superconducting (SC), and nonsuperconducting phases. The structural study reveals change in the local environment of the Fe tetrahedrons depending on substitution: a reduction of the Fe-Fe and Fe-Ch(chalcogen) bond lengths and a tendency for six out- of eight bond angles to approach values realizing a regular tetrahedron and hence, suggesting a reduction of structural distortions with substitution. With increasing substitution, a nonmonotonic decrease of the superconducting transition temperature $T_c$ was observed; the SC state disappears at a substitution level above $z=1.2$. The SC state coexists with the AFM state that persists in all samples independent of substitution. The transition temperature into the AFM state, $T_N$, decreases gradually with increasing substitution indicating a weakening of the AFM interactions. The AFM phase exhibits an iron-vacancy-ordered structure below the structural transition temperature $T_s$. $T_s$ shows a nonmonotonous variation: a decrease with increasing $z$ up to 1.3, followed by an increase on further increasing $z$. The electronic specific heat reveals a significant reduction of the anomaly at the SC transition temperature indicating a reduction of the density of states at the Fermi energy and a weakening of the electronic correlations that can explain the suppression of the superconductivity with substitution.

Figure 1

Variation of the lattice parameters $a$ and $c$ as function of sulfur concentration $z$ in ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$.

Figure 2

(a) Crystal structure of ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ for $z=0$. Fe1 ions are in position (0.5, 0, 0.25), Fe2 in position (x, y, z); Rb1 (0, 0, 0.5), Rb2 (x, y, 0.5), Se1(S1) in position (0.5, 0.5, $z$), and Se2(S2) in (x, y, z)(b) Schematic view of different Fe tetrahedrons: Fe2 with three Se2(S2) neighbors and one neighboring Se1(S1); Fe1 with four equivalent Se2(S2) neighbors. Clusters of four Fe2 ions are marked by rectangles.

Figure 3

Structural variations with sulfur concentration $z$. Frame (a): four equivalent Fe1-Ch2 bond distances, Fe2-Ch1 bond distance and three Fe2-Ch2bond distances. Frame (b): ratio of Fe2-Ch1 bond distance to Fe1-Ch2, intercluster Fe2-Ch2 distances to Fe1-Ch2, intracluster Fe2-Ch2 distances to intercluster Fe2-Ch2. Vertical dashed line separates superconducting samples from nonsuperconducting ones.

Figure 4

Structural variations with sulfur concentration $z$. (a) Intercluster Fe2-Fe2 distances, intracluster Fe2-Fe2 distances, and Fe1-Fe2 distances. (b) Ratio of Fe1-Fe2 to intercluster Fe2-Fe2 distance, intracluster Fe2-Fe2 to intercluster Fe2-Fe2 distance.

Figure 5

Variation with substitution of bond angles (in degrees). (a) Fe1 tetrahedron (two angles ${\alpha }_1$ and four angles ${\alpha }_2$. [(b) and (c)] Fe2 tetrahedron (angles from ${\alpha }_3$ to ${\alpha }_8$). Vertical dashed line separates superconducting samples from the nonsuperconducting ones.

Figure 6

Variations with substitution: of occupancy of Fe1 and Fe sites (a), and of anion-height from Ch (Se,S) to Fe2-Fe1 plane and from Ch to Fe2-Fe2 plane (b).

Figure 7

Temperature dependence of DSC signals for ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ crystals with different sulfur concentration $z$: (a) $z=0$, (b) 0.1, (c) 1, and (d) 2. Red curves show data on heating, blue ones on cooling. Vertical dashed lines mark phase transition temperatures on heating.

Figure 8

Concentration dependence of the structural phase transition temperatures $T_s$, and $T_p$, and of the magnetic transformation $T_N$ for ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$. Data are taken from DSC curves measured on heating. Solid lines are drawn to guide the eye.

Figure 9

Temperature dependent susceptibility ${\chi }_{\left|\right|}$ for superconducting (a) and nonsuperconducting (b) ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples measured in an external magnetic field of 1 T applied along $c$ axis. Arrow indicates the SC transition temperature for the sample with $z=1.1$. Additionally, the susceptibility ${\chi }_{\perp }$ measured in a magnetic field applied perpendicular to the $c$ axis is shown for the sample with $z=2$.

Figure 10

Temperature dependent susceptibilities (ZFC and FC) for different superconducting ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples measured in an external magnetic field of 10 Oe applied along $c$ axis. Arrow indicates the temperature of the onset of superconducting transition for the sample with $z=0$.

Figure 11

Hysteresis loops measured at 2 K with the magnetic field applied along $c$ axis for different superconducting ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples.

Figure 12

Temperature dependence of the electrical resistivity for superconducting ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ with concentrations as indicated in the figure. Arrows indicate critical temperatures.

Figure 13

Temperature dependent resistivity for nonsuperconducting ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ for sulfur concentrations $z$ as indicated in the figure.

Figure 14

Temperature dependent electrical resistivity in different applied magnetic fields in the vicinity of superconducting transition for ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ with sulfur concentrations: (a) $z=0.1$, (b) 0.25, (c) 1.0, and (d) 1.2.

Figure 15

Temperature dependence of upper critical field $H_{c2}$ for samples with different sulfur concentrations as indicated in the figure.

Figure 16

Concentration dependence of the critical temperature $T_c$ (left scale) and of upper critical field $H_{c2}\left(0\right)$ (right scale). Closed circles and squares show $T_c$ estimated from resistivity and susceptibility measurements, respectively. Lines are drawn to guide the eye.

Figure 17

Temperature dependent specific heat $C$ for selected ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples with different sulfur concentrations as indicated in the figure. The inset shows $C/T\mathrm{vs}{T}^2$ . The solid lines represent fits as described in the text.

Figure 18

Temperature dependent electronic specific heat $C_{\mathrm{el}}$ for ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2$ samples ($z=0$) from different batches. Arrow marks $T_c$ taken from the susceptibility data.

Figure 19

Difference of the heat-capacity values measured in zero field and in an external magnetic field of 9 T $vs$ temperature $T$ for several samples of nonsubstituted ${\mathrm{Rb}}_{0.8}{\mathrm{Fe}}_{1.6}{\mathrm{Se}}_2(z=0)$.

Figure 20

Temperature dependent electronic specific heat $C_{\mathrm{el}}$ for ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples with different sulfur concentration $z$ as indicated in the figure. The dashed vertical line indicates $T_c$.

Figure 21

Difference in the heat-capacity values measured in zero field and in field of 9 T vs temperature $T$ for ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ samples with different sulfur concentration $z$. The dashed vertical line indicates $T_c$.

Figure 22

$T-z$ phase diagram of the ${\mathrm{Rb}}_{1-x}{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ system. SC: superconducting state, AFM VO M: antiferromagnetic vacancy ordered metallic, PM VO: paramagnetic vacancy ordered, and PM VD: paramagnetic vacancy disordered. Vertical dashed line separates SC and nonsuperconducting samples. The solid lines are drawn to guide the eye.