$\left({\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16}\right){\mathrm{OHFe}}_{0.98}\mathrm{Se}$ superconductor: Ion-exchange synthesis of large single-crystal and highly two-dimensional electron properties

A large and high-quality single crystal $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$, the optimal superconductor of a reported $(\mathrm{L}{\mathrm{i}}_{1-x}\mathrm{F}{\mathrm{e}}_x)\mathrm{OHF}{\mathrm{e}}_{1-y}\mathrm{Se}$ system, has been successfully synthesized via a hydrothermal ion-exchange technique. The superconducting transition temperature $\left(T_c\right)$ of 42 K is determined by magnetic susceptibility and electric resistivity measurements, and the zero-temperature upper critical magnetic fields are evaluated as 79 and 313 T for the field along the $c$ axis and the $ab$ plane, respectively. The ratio of out-of-plane to in-plane electric resistivity ${\rho }_c/{\rho }_{ab}$ is found to increase with decreasing temperature and to reach a high value of 2500 at 50 K, with an evident kink occurring at a characteristic temperature $T^{*}=120\mathrm{K}$. The negative in-plane Hall coefficient indicates that electron carriers dominate in the charge transport, and the hole contribution is significantly reduced as the temperature is lowered to approach $T^{*}$. From $T^{*}$ down to $T_c$ we observe the linear temperature dependencies of the in-plane electric resistivity and the magnetic susceptibility for the FeSe layers. Our findings thus reveal that the normal state of $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ becomes highly two dimensional and anomalous prior to the superconducting transition, providing an insight into the mechanism of high-$T_c$ superconductivity.

Figure 1

Illustration of hydrothermal ion-exchange process. (a) A schematic illustration of the hydrothermal ionic exchange reaction with the starting materials of big matrix crystals of ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_2, \mathrm{LiOH}{\mathrm{H}}_2\mathrm{O}$, Fe, and $\mathrm{C}{\mathrm{H}}_4{\mathrm{N}}_2\mathrm{Se}$. The spacing between the adjacent FeSe layers of thus synthesized $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ crystal with the space group $P4/nmm$ is consequently enlarged by $\sim 32\%$ [from $\sim 7.067\AA$ in ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_2$ to $\sim 9.318\AA$ in $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}]$. For clarity, the H-Se and K-Se bondings in the structures are not shown. (b) and (c) The XRD patterns of ($00l$) type for the ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_2$ and the $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ crystal pieces, respectively, demonstrating their crystal orientations along (001) planes. The insets show the corresponding photographs of the crystals.

Figure 2

Magnetic properties of ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_2$ and $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ crystals. (a) The temperature dependence of the static magnetic susceptibility of ${\mathrm{K}}_{0.8}\mathrm{F}{\mathrm{e}}_{1.6}\mathrm{S}{\mathrm{e}}_2$ exhibits an antiferromagnetic transition at 538 K. (b) The magnetic susceptibilities corrected for demagnetization factor under zero-field cooling (ZFC) and field cooling (FC, 1 Oe along the $c$ axis) for $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ show that a sharp diamagnetic transition occurs at 42 K. The ZFC curve shows a 100% superconducting shielding and the FC one a Meissner signal up to $\sim 21\%$.

Figure 3

The in-plane electric resistivity under different magnetic fields and the upper critical magnetic fields. (a) The in-plane electric resistivity of $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ displays the superconducting transitions under different applied magnetic fields along the $c$ axis. (b) The in-plane electric resistivity under different applied magnetic fields along the $ab$ plane. Up to 9 T, the onset superconducting transition temperature remains almost unchanged in both (a) and (b), but the temperature of zero resistance state shifts quickly from 40 K to lower temperatures with increasing field. (c) The anisotropic upper critical magnetic field ${H_c}_2$ as functions of temperature deduced from (a) and (b), from which the zero-temperature upper critical fields can be extrapolated according to the Werthamer-Helfand-Hohenberg (WHH) formula (the inset).

Figure 4

The electric resistivity, Hall coefficient, and static magnetic susceptibility of $\left(\mathrm{L}{\mathrm{i}}_{0.84}\mathrm{F}{\mathrm{e}}_{0.16}\right)\mathrm{OHF}{\mathrm{e}}_{0.98}\mathrm{Se}$ single crystal. (a) The in-plane electric resistivity and the ratio of the out-of-plane resistivity to the in-plane one as functions of temperature. Around $T^{*}=120\mathrm{K}$, the slope of the resistivity curve undergoes a prominent reduction and a corresponding kink occurs in the curve of ${\rho }_c/{\rho }_{ab}$. The inset figure shows the linearly temperature dependent range from 80 K down to $T_c$ for ${\rho }_{ab}$. (b) The in-plane Hall coefficient $R_{\mathrm{H}}$ as a function of temperature exhibits a dip feature around $T^{*}=120\mathrm{K}$. The black curve is a guide to the eye. (c) The temperature dependencies of static magnetic susceptibility $\chi =M/H$ under magnetic fields along the $c$ axis. The results slightly depend on the magnitude of the applied field. The sudden drops in the magnetic susceptibility are due to the appearance of the superconductivity. In the high temperature range, all the data can be fitted to a modified Curie-Weiss law ${\chi }_m={\chi }_0+{\chi }_{\mathrm{CW}}$. But a deviation is clearly visible below $T^{*}=120\mathrm{K}$ as well. Further lowering temperature, the rest magnetic susceptibility in which the Curie-Weiss term is subtracted shows the nearly linear temperature dependence in a narrow temperature range (the inset).