Anisotropic thermodynamic and transport properties of single-crystalline ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ ($x=0$ and 0.45)

Single crystals of ${\text{BaFe}}_2{\text{As}}_2$ and ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ have been grown out of excess Sn with 1% or less incorporation of solvent. The crystals are exceptionally micaceous, are easily exfoliated, and can have dimensions as large as $3\times 3\times 0.2{\text{mm}}^3$. The ${\text{BaFe}}_2{\text{As}}_2$ single crystals manifest a structural phase transition from a high-temperature tetragonal phase to a low-temperature orthorhombic phase near 85 K and do not show any sign of superconductivity down to 1.8 K. This transition can be detected in the electrical resistivity, Hall resistivity, specific heat, and the anisotropic magnetic susceptibility. In the ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ single crystals this transition is suppressed and instead superconductivity occurs with a transition temperature near 30 K. Whereas the superconducting transition is easily detected in resistivity and magnetization measurements, the change in specific heat near $T_c$ is small, but resolvable, giving $\Delta C_p/\gamma T_c\approx 1$. The application of a 140 kOe magnetic field suppresses $T_c$ by only $\sim 4\text{K}$ when applied along the $c$ axis and by $\sim 2\text{K}$ when applied perpendicular to the $c$ axis. The ratio of the anisotropic upper critical fields, $\gamma =H_{c2}^{\perp c}/H_{c2}^{\parallel c}$, varies between 2.5 and 3.5 for temperatures down to $\sim 2\text{K}$ below $T_c$.

Figure 1

Photograph of a single crystal of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ on a millimeter grid. The crystallographic $c$ axis is perpendicular to the plane of the plate. Droplets of Sn flux can be seen on the surface.

Figure 2

Electron microscope image of plate of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. Elemental analysis was performed via WDS at each of the points marked by a star. The average $K$ substitution value was found to be 0.44 with a 0.07 standard deviation.

Figure 3

Powder x-ray diffraction patterns from ${\text{BaFe}}_2{\text{As}}_2$ (upper panel) and ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ (lower panel). Powdered Si was added as a standard and Sn reflections are present due to small amounts of residual flux on the surfaces of the crystal that were ground to provide the powder.

Figure 4

(a) Temperature dependence of the in-plane electrical resistivity of ${\text{BaFe}}_2{\text{As}}_2$ for 0 and 70 kOe applied magnetic field. (b) Temperature dependence of the Hall resistivity divided by applied magnetic field. The inset shows the linearity of the Hall resistivity at $T=2\text{K}$.

Figure 5

Temperature-dependent anisotropic magnetization divided by applied field for ${\text{BaFe}}_2{\text{As}}_2$.

Figure 6

(Color online) Temperature-dependent specific heat of ${\text{BaFe}}_2{\text{As}}_2$. Upper inset: $C_p/T$ as a function of $T^2$ for low-temperature data; lower inset: expanded view near the $T\sim 85\text{K}$ phase transition.

Figure 7

X-ray diffraction scans along the (110) direction through the position of the tetragonal (1 1 10) reflection for selected temperatures. The lines represent the fitted curves to obtain the reflection positions for the data shown in Fig. 8. The offset between each data set is 100 counts/s.

Figure 8

Lattice parameters and unit-cell volume for the tetragonal and orthorhombic phases as extracted from the data shown in Fig. 7 for the (1 1 10) reflection and from the (0 0 10) reflection (not shown). The open squares in the lower panel represent the lattice parameter corresponding to the central reflection which coexists with the pair of reflections related to the orthorhombic phase (seen clearly in the 70 K data set in Fig. 7). For clarity, the $a$-lattice parameter in the high-temperature tetragonal phase has been multiplied by a factor of $\sqrt{2}$ so as to allow for comparison to the low-temperature orthorhombic phase data. The middle panel presents the temperature dependence of the $c$-lattice parameter and the upper panel presents the calculated unit-cell volume. The error bars represent the relative precision; the absolute error is method-related and significantly larger.

Figure 9

Temperature dependence of the in-plane electrical resistivity of two crystals of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. Inset: expanded scale for temperatures near the superconducting transition.

Figure 10

(Color online) Temperature-dependent anisotropic magnetization divided by applied field for ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. The dashed and solid lines are the data on ${\text{BaFe}}_2{\text{As}}_2$ from Fig. 5 for comparison.

Figure 11

(Color online) Anisotropic low-field $M/H$ data for a ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ single-crystal plate. Field-cooled warming and zero-field-cooled warming data are shown for both orientations of the sample. For $H\perp c$ the demagnetization factor will be the closest to zero.

Figure 12

(Color online) Temperature dependent specific heat of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$. Upper inset: $C_p/T$ as a function of $T^2$ for low-temperature data. Lower inset: expanded view near $T_c\sim 30\text{K}$ with linear extrapolations of $T>30\text{K}$ and $T<24\text{K}$ extended past $T_c$ to more clearly show the jump in $C_p$ at $T_c$.

Figure 13

(Color online) Temperature dependence of the electrical resistivity of ${\text{Ba}}_{0.55}{\text{K}}_{0.45}{\text{Fe}}_2{\text{As}}_2$ near $T_c$ in constant applied magnetic fields of up to 140 kOe for $H\perp c$ (upper panel) and $H\parallel c$ (lower panel). Data (from higher transition temperature to lower) are for applied magnetic fields of 0, 10, 30, 60, 90, 120, and 140 kOe, respectively. The lines drawn on the 140 kOe data in the lower panel illustrate the onset criterion that has been used to determine $T_c$ for each field.

Figure 14

Anisotropic $H_{c2}\left(T\right)$ plot for $H\le 140\text{kOe}$. Inset: $\gamma =H_{c2}^{\perp c}/H_{c2}^{\parallel c}$ as a function of temperature just below $T_c$.

Figure 15

(Color online) Curie-Weiss fits to high- and low-temperature (above and below $T\sim 85\text{K}$) $M/H$ data for ${\text{BaFe}}_2{\text{As}}_2$ with $H\perp c$.