Anisotropic magnetism, superconductivity, and the phase diagram of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$

We report the crystal growth and structural, magnetic, conductivity, and specific heat investigations of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ single crystals with varying stoichiometry prepared by self-flux and Bridgman methods. The system exhibits a strongly anisotropic antiferromagnetic behavior below 400 K. Bulk superconductivity is found in samples with Fe concentrations $1.53<2-y<1.6$, whereas for $2-y<1.5$ and $2-y>1.6$, insulating and semiconducting behavior is observed, respectively. Within the measured range of variation of the Rb concentration (0.6–0.8) no correlation between the Rb content and the lattice parameters of the samples was found. The superconducting samples show the smallest value of the lattice parameter $c$ compared to the nonsuperconducting samples. The sharpest transition to the superconducting state, the highest transition temperature $T_c$ of 32.4 K, and the highest diamagnetic response corresponding to a critical current density $j_c$ of $1.6\times {10}^4$ A/cm${}^2$ (at 2 K) is found for compositions close to Rb${}_2$Fe${}_4$Se${}_5$. Upper critical fields $H_{c2}$ of $\sim$250 kOe for the in-plane and 630 kOe for the interplane configurations are estimated from resistivity studies in magnetic fields. In the nonsuperconducting samples with the Fe concentration below 1.45, both specific heat and susceptibility revealed an anomaly at 220 K, which is not related to antiferromagnetic or structural transformations. Comparison with the magnetic behavior of nonsuperconducting samples provides evidence for the coexistence of superconductivity and static antiferromagnetic order.

Figure 1

X-ray diffraction patterns for different superconducting Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples. Inset: image of the single crystals BR 26 subtracted from the ingot. Sample labels BR and F stand for those grown by Bridgman and flux methods, respectively.

Figure 2

X-ray diffraction patterns for different nonsuperconducting Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples.

Figure 3

Temperature dependencies of the field-cooled susceptibility for superconducting Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples from different batches measured in a field of 10 kOe applied along the $c$ axis. The arrow indicates the SC transition temperature.

Figure 4

Temperature dependence of the field-cooled susceptibility for nonsuperconducting Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples from different batches measured in a field of 10 kOe applied along the $c$ axis. The arrow marks the temperature of the maximum of the susceptibility $T^{*}$ for sample BR 17.

Figure 5

Temperature dependence of the field-cooled susceptibility for two SC (BR 16) and non-SC (BR 19) Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples measured in a field of 10 kOe applied parallel and perpendicular to the $c$ axis.

Figure 6

Magnetization curves for the SC sample BR 16 for different temperatures measured with the magnetic field applied along the $c$ axis and within the $ab$ plane.

Figure 7

Magnetization curves for the non-SC sample BR 19 measured at different temperatures with the magnetic field applied along the $c$ axis and within the $ab$ plane. Data for 2 K (full squares) and 40 K (open squares) are almost coinciding.

Figure 8

Temperature dependencies of ZFC and FC susceptibilities for different superconducting Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples measured in a field of 10 Oe applied along the $c$ axis. The arrow indicates the temperature of the onset of the superconducting transition $T_c^{\text{on}}=32.4$ K for sample BR 16.

Figure 9

Hysteresis loops measured at 2 K with magnetic field applied along the $c$ axis for different SC samples Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$. For clarity, the data for samples F 266 and BR 18 are magnified by factors of five and ten, respectively.

Figure 10

Hysteresis loop for SC sample BR 16 at 2 K (solid circles) measured with the magnetic field applied perpendicular to the $c$ axis together with the magnetization curve at 40 K (open squares).

Figure 11

(a) Temperature dependencies of the in-plane resistivity ${\rho }_{ab}$ and interplane resistivity ${\rho }_c$ for the SC sample BR 16 (left scale) and for the in-plane resistivity for the SC sample F 266 (right scale) measured on cooling in zero external magnetic field. (b) Temperature dependencies of the in-plane resistivity for the non-SC samples. Dashed curves mark the Arrhenius fits at high temperatures, solid lines are the MVRH fits al lower temperatures as described in the text.

Figure 12

(a) Temperature dependence of the in-plane resistivity ${\rho }_{ab}$ for the sample BR 16 measured in various magnetic fields applied parallel to the $c$ axis. (b) Temperature dependence of the interplane resistivity ${\rho }_c$ for the sample BR 16 measured in various magnetic fields applied perpendicular to the $c$ axis. Inset: temperature dependence of the upper critical field for interplane (closed symbols) and in-plane (open symbols) configurations as described in the text.

Figure 13

Temperature dependencies of the specific heat for different Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples. The arrow marks the anomaly in the specific heat at $T^{*}=220$ K for the sample BR 17.

Figure 14

Temperature dependence of the specific heat in the representation $C/T$ vs $T^2$ for different Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples at temperatures below 12 K. Upper inset: $C/T$ vs $T^2$ in different applied magnetic fields for the sample BR 16. Lower inset: magnetic field dependence of the residual Sommerfeld coefficient ${\gamma }_r$ for different superconducting samples with high SC parameters.

Figure 15

Temperature dependence of the electronic specific heat $C_e/T$ vs $T$ for different Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ samples calculated by subtraction of the magnon and lattice contributions. The arrows mark $T_c$ for the samples F 266 and BR 16.

Figure 16

Phase diagram of Rb${}_{1-x}$Fe${}_{2-y}$Se${}_2$ system presenting dependencies of the lattice constant $c$, transition temperature $T_c$, and the Néel temperature $T_N$ for three different regions with distinct structural, magnetic, and conducting behaviors.