Anisotropic superconducting properties of single-crystalline ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$

Iron-chalcogenide single crystals with the nominal composition ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ and a transition temperature of $T_c\simeq 14.6\text{K}$ were synthesized by the Bridgman method. The structural and anisotropic superconducting properties of those crystals were investigated by means of single crystal x-ray and neutron powder diffraction, superconducting quantum interference device and torque magnetometry, and muon-spin rotation (μSR). Room temperature neutron powder diffraction reveals that 95% of the crystal volume is of the same tetragonal structure as PbO. The structure refinement yields a stoichiometry of ${\text{Fe}}_{1.045}{\text{Se}}_{0.406}{\text{Te}}_{0.594}$. Additionally, a minor hexagonal ${\text{Fe}}_7{\text{Se}}_8$ impurity phase was identified. The magnetic penetration depth $\lambda$ at zero temperature obtained by means of μSR was found to be ${\lambda }_{ab}\left(0\right)=491\left(8\right)\text{nm}$ in the $ab$ plane and ${\lambda }_c\left(0\right)=1320\left(14\right)\text{nm}$ along the $c$ axis. The zero-temperature value of the superfluid density ${\rho }_s\left(0\right)\propto {\lambda }^{-2}\left(0\right)$ obeys the empirical Uemura relation observed for various unconventional superconductors, including cuprates and iron pnictides. The temperature dependences of both ${\lambda }_{ab}$ and ${\lambda }_c$ are well described by a two-gap $s+s$-wave model with the zero-temperature gap values of ${\Delta }_S\left(0\right)=0.51\left(3\right)\text{meV}$ and ${\Delta }_L\left(0\right)=2.61\left(9\right)\text{meV}$ for the small and the large gap, respectively. The magnetic penetration depth anisotropy parameter ${\gamma }_{\lambda }\left(T\right)={\lambda }_c\left(T\right)/{\lambda }_{ab}\left(T\right)$ increases with decreasing temperature, in agreement with ${\gamma }_{\lambda }\left(T\right)$ observed in the iron-pnictide superconductors.

Figure 1

Magnetic moment $m$ as a function of temperature $T$ in a magnetic field of 1 mT applied parallel to the $c$ axis of single crystal ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$, recorded in the Meissner state in zfc mode and in fc mode. The onset transition temperature $T_c\simeq 14.6\text{K}$ (vertical arrow) is characteristic for optimal doping $x\simeq 0.5$ of ${\text{FeSe}}_x{\text{Te}}_{1-x}$.

Figure 2

(Color online) Polarized light microscopic photographs of polished surfaces of the ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ crystal. (a) Microphotography of the crystal surface cut perpendicular to the cleaving facet. Domains with different crystallographic orientations and/or different phases are visible. (b) Micrography of the resulting polished cleaving facet.

Figure 3

The reciprocal space sections of the ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ crystal: (a) $h0l$ reciprocal layer, (b) $0kl$ reciprocal layer, and (c) $hk0$ reciprocal layer.

Figure 4

(Color online) Rietveld refinement pattern (upper–red) and difference plot (lower–blue) of the neutron diffraction data for the crystal with the nominal composition of ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$. The rows of ticks show the Bragg peak positions for the main phase and two impurity phases. The refined stoichiometry of the main tetragonal phase is ${\text{Fe}}_{1.045}{\text{Se}}_{0.406}{\text{Te}}_{0.594}$ (see text for details).

Figure 5

(Color online) Temperature dependence of the magnetic moment measured in zfc and fc modes in a magnetic field of 1 T applied parallel to the $c$ axis of the crystal with nominal composition ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$.

Figure 6

(Color online) Irreversibility line $H_{\text{irr}}\left(T\right)$ derived from SQUID measurements for two field configurations, $H$ parallel to the $c$ axis and $H$ parallel to the $ab$ plane of the ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ crystal. The solid black and red lines correspond to fits using the power-law ${\left(1-T/T_c\right)}^n$ with an exponent $n\simeq 1.5$. The inset illustrates how $T_{\text{irr}}$ was determined. The lines are guides to the eyes.

Figure 7

(Color online) $H_{\text{c}1}$ as a function of temperature for both orientations $H$ parallel to the $c$ axis and $H$ parallel to the $ab$ plane for single crystal ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$. The inset illustrates the deviation from the linear $B^{1/2}\left(H\right)$ dependence plotted as ${\left(BV\right)}^{1/2}$ vs ${\mu }_0{H}_{\text{int}}$.

Figure 8

Symmetrized torque ${\tau }_{symm}$ for the studied crystal of ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ in the superconducting state as a function of the angle $\theta$. The torque data are well described by Eq. (3), yielding an anisotropy parameter $\gamma =3.1\left(4\right)$ close to $T_c$.

Figure 9

(Color online) (a) ZF $\mu \text{SR}$ time spectra for ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ recorded at 1.6 K and above $T_c$. The solid lines represent fits using Eq. (4). [(b) and (d)] TF $\mu \text{SR}$ time spectra for $H$ parallel to the $c$ axis and $H$ parallel to the $ab$ plane, taken at 1.6 K and above $T_c$. [(c) and (e)] The corresponding magnetic field distributions $P\left(B\right)$. The solid lines represent fits using Eq. (5). The insets show the counter plots of the local field variation at 1.6 K, (c) ${\lambda }_a={\lambda }_b$ and (e) ${\lambda }_c=2.7{\lambda }_{ab}$.

Figure 10

(Color online) Temperature dependence of the penetration depth components ${\lambda }_{ab}$ and ${\lambda }_c$ of single crystal ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$. The solid lines correspond to fits using Eq. (7). The corresponding fit parameters are listed in Table .

Figure 11

(Color online) Uemura plot for a selection of some Fe-based HTS. The Uemura relation observed for underdoped cuprates is included for comparison as a dashed line for hole doping and as a dotted line for electron doping (after Ref. 56). ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$ data from Refs. 13, 57 (●), Ref. 58 (▲), and Ref. 59 (◆); ${\text{NdFeAsO}}_{1-x}{\text{F}}_x$ data from Ref. 60 (●) and Ref. 59 (▲); ${\text{SmFeAsO}}_{1-x}{\text{F}}_x$ data from Ref. 60 (●) and Ref. 14 (▲); ${\text{CeFeAsO}}_{1-x}{\text{F}}_x$ data from Ref. 59, ${\text{FeSe}}_{1-x}$ data from Refs. 45, 61, LiFeAs data from Ref. 62, ${\text{Ba}}_{1-x}{\text{K}}_x\text{FeAs}$ data from Ref. 63, and ${\text{Fe}}_{1+y}{\text{Se}}_{1-x}{\text{Te}}_x$ data from Ref. 54 (●). The red star $(\star )$ is showing the data for ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ obtained in this work.

Figure 12

(Color online) Comparison of the temperature dependence of the magnetic penetration depth anisotropy parameter ${\gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}$ measured by $\mu \text{SR}$ and by SQUID for single crystal ${\text{FeSe}}_{0.5}{\text{Te}}_{0.5}$ with the $H_{\text{c}2}$-anisotropy parameter ${\gamma }_{H_{\text{c}2}}=H_{\text{c}2}^{\parallel ab}/H_{\text{c}2}^{\parallel c}$ obtained from resistivity measurements for ${\text{Fe}}_{1.11}{\text{Se}}_{0.4}{\text{Te}}_{0.6}$ by Fang et al. (Ref. 33) and for ${\text{Fe}}_{1.02}{\text{Se}}_{0.39}{\text{Te}}_{0.61}$ by Lei et al. (Ref. 38). The lines are guides to the eyes.