Anisotropic physical properties and large critical current density in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ single crystal

We present a systematic study of electrical resistivity, Hall coefficient, magneto-optical imaging, magnetization, and scanning transmission electron microscopy (STEM) analyses of $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ single crystals. Sharp diamagnetic transition and magneto-optical imaging reveal homogeneity of single crystal and prominent Bean-like penetrations of vortices. Large anisotropy of electrical resistivity, with ${\rho }_c/{\rho }_{ab}>100$, and semiconductorlike ${\rho }_c$ suggest that the electronic state is quasi-two-dimensional. Hall effect measurements indicate that $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ is a multiband system with holes as main carriers. Magnetization measurements reveal significantly larger $J_{\mathrm{c}}$ compared with that in other iron-based superconductors with different values of $J_{\mathrm{c}}$ depending on the direction of magnetic field. The origin of these $J_{\mathrm{c}}$ characteristics is discussed based on microstructural observations using STEM. In addition, further enhancement of $J_{\mathrm{c}}$ in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ for future high-field application is demonstrated in terms of heavy-ion irradiation.

Figure 1

Temperature dependence of the zero-field-cooled magnetization at $H=5\mathrm{Oe}$ along the $c$ axis in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$.

Figure 2

Differential MO images of $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ in the remanent state at (a) 5 K and (b) 20 K after cycling the field up to 1.6 kOe for 0.2 s. (c) An optical micrograph of $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$. (d) Local magnetic induction profiles at different temperatures taken along the dashed line in (a). Both the yellow bar in (a) and black bar in (c) correspond to 200 μm.

Figure 3

(a) Schematic drawings of the two samples with electrical contacts for measurements of in-plane electrical resistivity (${\rho }_{ab}$). (b) Temperature dependence of ${\rho }_{ab}$ in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ samples No. 3 and No. 4 measured in a temperature range of 30–300 K. The inset in (b) shows ${\rho }_{ab}-T$ near $T_{\mathrm{c}}$.

Figure 4

Temperature dependence of in-plane electrical resistivity (${\rho }_{ab}$) in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ (No. 3) below 40 K under various magnetic fields parallel to the (a) $c$ axis and (b) $ab$ plane. (c) Anisotropic $H_{\mathrm{c}2}$ and $H_{\mathrm{irr}}$ evaluated from temperature-dependent resistivity in (a) and (b). $H_{\mathrm{c}2}$ is defined by two different criteria of $0.9{\rho }_{\mathrm{n}}$ and $0.5{\rho }_{\mathrm{n}}$. Here, ${\rho }_{\mathrm{n}}$ is the normal state resistivity estimated from the extrapolation of the resistivity using the power-law form with $n=1.3$ as shown in the dashed line in (a). $H_{\mathrm{irr}}$ is defined by the criteria of ${\rho }_{ab}\sim 0.5\mu \mathrm{\Omega }\mathrm{cm}$.

Figure 5

(a) Schematic drawings of the electrical contacts for the measurement of out-of-plane electrical resistivity (${\rho }_c$). (b) Temperature dependence of ${\rho }_c$ in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ in a temperature range of 30–300 K under zero magnetic field. The inset in (b) shows ${\rho }_c\text{−}T$ near $T_{\mathrm{c}}$. (c) Temperature dependence of the anisotropy of the resistivity, ${\rho }_c/{\rho }_{ab}$. ${\rho }_{ab}$ of sample No. 3 shown in Fig. 3 is used for the calculation.

Figure 6

(a) Hall resistivity ${\rho }_{yx}$ as a function of field at various temperatures in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$. (b) Temperature dependence of the Hall coefficient $R_{\mathrm{H}}$ in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$.

Figure 7

(a) Magnetic field dependence of magnetization in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ at various temperatures for $H\parallel c$ axis. (b) Magnetic field dependence of in-plane $J_{\mathrm{c}}$ evaluated using the data shown in (a).

Figure 8

Magnetic field dependence of magnetic $J_{\mathrm{c}}$ at various temperature in 2.6 GeV U-irradiated ($B_{\mathrm{\Phi }}=40\mathrm{kOe}$) $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$. Open circles with a dashed line show the data of the pristine sample at 2 K shown in Fig. 7 for comparison.

Figure 9

(a) Magnetic field dependence of magnetic $J_{\mathrm{c}}$ in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ at various temperatures for $H\parallel ab$ plane. (b) Temperature dependence of magnetic $J_{\mathrm{c}}$ under the self-field in $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ for $H\parallel c$ axis and $H\parallel ab$ plane.

Figure 10

STEM images of (a), (b) the pristine and (c), (d) 2.6 GeV U-irradiated $\mathrm{K}{\mathrm{Ca}}_2{\mathrm{Fe}}_4{\mathrm{As}}_4{\mathrm{F}}_2$ for an electron beam injected along the $a$ axis. Scale bars in (a)–(d) correspond to 100, 10, 100, and 20 nm, respectively. Yellow dashed squares in (a), (c), (d) emphasize the location of horizontal black lines in STEM images, which we interpret to be thin planar defects. White arrows in (d) emphasize the columnar defects generated by 2.6 GeV U irradiation.