Anisotropic $H_{c2}$, thermodynamic and transport measurements, and pressure dependence of $T_c$ in ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals

We present a detailed study of single crystalline ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and analyze its thermodynamic and transport properties, anisotropic $H_{c2}\left(T\right)$, and initial pressure dependence of $T_c$. In zero field, the temperature-dependent resistivity is metallic. Deviation from a linear temperature dependence is evident below 100 K and a $T^3$ dependence is roughly followed from just above $T_c$ ($\sim 10\mathrm{K}$) to $\sim 40\mathrm{K}$. Anisotropic $H_{c2}\left(T\right)$ data were measured up to 140 kOe with field applied along and perpendicular to the rodlike crystals. For the applied field perpendicular to the rod, $H_{c2}\left(T\right)$ is linear with a slope $\sim -70$ kOe/K. For field applied along the rod, the slope is about $-120$ kOe/K below 70 kOe. Above 70 kOe, the magnitude of the slope decreases to $\sim -70$ kOe/K. The electronic specific heat coefficient $\gamma$, just above $T_c$, is 73 mJ/mol ${\mathrm{K}}^2$; the Debye temperature ${\Theta }_D$ is 220 K. The specific heat jump at the superconducting transition $\Delta C\sim 2.2\gamma T_c$. Finally, for hydrostatic pressures up to $\sim 7$ kbar, $T_c$ decreases under pressure linearly at a rate of $-0.034\mathrm{K}/\mathrm{kbar}$.

Figure 1

(a) A schematic drawing of the ampoule assembly for the material synthesis. (b) Typical habit of the single crystals of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ on a millimeter grid paper. (c) The contact arrangements and external field directions for the resistance measurements. (d) X-ray diffraction data on ground/deformed crystals. The black crosses represent the experimental data and the red solid line represents the calculation based on the crystallographic information. For details of the crystal structure, readers are directed to Ref. [1].

Figure 2

Temperature-dependent resistivity of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$. The left inset shows the normalized resistances vs $T^3$ below 40 K for four different samples. The right inset shows the magnetoresistance measured at 7.5 and 10 K. Solid and open symbols represent transverse and longitudinal magnetoresistance, respectively.

Figure 3

$R\left(T\right)$ data measured for (a) $H\parallel \text{rod}$ and (b) $H\perp \text{rod}$ from 0 Oe up to 140 kOe in 20 uniform field steps ($\Delta H=7368.4$ Oe). (c) Anisotropic $H_{c2}$ of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$. The black and red symbols represent data for $H\parallel \text{rod}$ and $H\perp \text{rod}$. The blue points are from Ref. [1]. The solid and open symbols show data from two different batches of samples. The triangles are data from field sweeps at fixed temperatures. The squares and circles are data from temperature sweeps at fixed field. The inset shows a typical superconducting transition measured at 125 264 Oe, with red solid lines and the arrow indicating the criteria for determining the transition temperature (see more in text).

Figure 4

$C/T$ plotted as a function of $T$ down to 0.4 K. The inset shows the $C_e/\gamma T$ as a function of $T$. The electronic part of the specific heat $C_e$ was obtained by subtracting $\beta T^3$ from the total specific heat.

Figure 5

The magnetic susceptibility measured at 50 kOe on a randomly oriented collection of single crystals. The inset shows the magnetization isotherm measured at 2 K up to 1500 Oe.

Figure 6

Pressure dependence of $T_c$. The dotted line is a guide for the eye. The left inset shows the raw data with Pb serving as a manometer. The right inset shows the zero-field-cooled magnetization data under ambient pressure measured at 50 Oe.