Orbital and Pauli limiting effects in heavily doped ${\text{Ba}}_{0.05}{\text{K}}_{0.95}{\text{Fe}}_2{\text{As}}_2$

We investigated the thermodynamic properties of the Fe-based lightly disordered superconductor ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$ in external magnetic field $H$ applied along the FeAs layers ($H\left|\right|ab$ planes). The superconducting (SC) transition temperature for this doping level is $T_c=6.6$ K. Our analysis of the specific heat $C(T,H)$ measured for $T<T_c$ implies a sign change of the superconducting order parameter across different Fermi pockets. We provide experimental evidence for the three components superconducting order parameter. We find that all three components have values which are comparable with the previously reported ones for the stoichiometric compound ${\mathrm{KFe}}_2{\mathrm{As}}_2$. Our data for $C(T,H)$ and resistivity $\rho (T,H)$ can be interpreted in favor of the dominant orbital contribution to the pair-breaking mechanism at low fields, while Pauli limiting effect dominates at high fields, giving rise to a gapless superconducting state with only the leading nonzero gap.

Figure 1

Temperature dependence of $C/T$ for ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$ measured in the temperature range $0.5\le T\le 10$ K. The dotted line represents the isoentropic construction used to determine $T_c$. The inset shows a fit of normal state specific heat $C$ data using an expression $C={\gamma }_{n}T+\beta T^3$ ($8\le T\le 35$ K), which is performed to determine the phonon contribution to the measured specific heat.

Figure 2

Plot of the electronic specific heat normalized to its normal state value $C_e/{\gamma }_{n}T$ vs normalized temperature $T/T_c$ (open circle). The solid green line is a fit of the data using the BCS model generalized to three bands (see text). The three dashed lines show the contribution of the three individual superconducting gaps.

Figure 3

Temperature $T$ dependence of the specific heat $C/T$ of ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$ measured for $0.5\le T\le 10$ K and magnetic fields $0\le H\le 14$ T with the $H\left|\right|a$ axis. Inset: $C/T$ as a function of $T^2$ measured at low temperatures. An extrapolation (dashed lines) of these data at $T=0$ gives the zero-temperature Sommerfeld coefficient $\gamma$. Only selected fields are shown in both figures.

Figure 4

Magnetic field $H$ dependence of the zero-temperature Sommerfeld coefficient $\gamma$ of ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$ for the $H\left|\right|a$ axis and the $H\left|\right|c$ axis (inset). The red dashed line is a fit of the low $H$ data with Eq. (3), while the black dotted line is a linear fit of the high $H$ data. The $H_{P1}\left(0\right)$ and $H_{c2}\left(0\right)$ represent the upper critical field with field applied parallel to the $a$ and $c$ axis, respectively.

Figure 5

Temperature dependence of electrical resistivity $\rho \left(T\right)$ of ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$ in a magnetic field up to 14 T with (a) $H\left|\right|c$ and (b) $H\left|\right|a$. The direction of magnetic field $H$ is always perpendicular to the electrical current $I_b$. For $H\left|\right|c, H$ is 0, 0.2, 0.5 T and increases from 0.5 to 6 T in steps of 0.5 T. For $H\left|\right|a, H$ increases in steps of 0.5 T between 0 and 2, and 1 T between 2 and 9 T. Insets of (a) and (b): $T$ dependence of resistivity at high temperature showing an $RRR>100$ and angular dependence of $\rho$ around $H\left|\right|a$ that is used to estimate the misalignment, respectively.

Figure 6

Upper critical field $H_{c2}$ vs $T$ phase diagram of ${\mathrm{Ba}}_{0.05}{\mathrm{K}}_{0.95}{\mathrm{Fe}}_2{\mathrm{As}}_2$. The dashed lines are fits of the data with the WHHM model ignoring the spin-orbit coupling contribution, i.e., $\lambda =0$ [see discussion for Eq. (4) for details].