Precision microwave electrodynamic measurements of K- and Co-doped ${\text{BaFe}}_2{\text{As}}_2$

We have studied the microwave electrodynamics of single-crystal iron-based superconductors ${\text{Ba}}_{0.72}{\text{K}}_{0.28}{\text{Fe}}_2{\text{As}}_2$ (hole doped, $T_{\text{c}}\approx 30\text{K}$) and $\text{Ba}{\left({\text{Fe}}_{0.95}{\text{Co}}_{0.05}\right)}_2{\text{As}}_2$ (electron doped, $T_{\text{c}}\approx 20\text{K}$), by cavity perturbation and broadband spectroscopy. Meissner curves were used to confirm the quality and homogeneity of the samples under study. Through cavity perturbation techniques, the temperature dependence of the in-plane London penetration depth $\Delta \lambda \left(T\right)$, and therefore the superfluid phase stiffness ${\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)$ was measured. Down to 0.4 K, the data do not show the exponential saturation at low temperatures expected from a singly, fully gapped superconductor. Rather, both the electron- and the hole-doped systems seem to be best described by a power-law behavior with ${\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)\sim T^n$ and $n\approx 2.5$. In the three samples we studied, a weak feature near the sensitivity limit of our measurements appears near $T/T_{\text{c}}=0.04$, hinting at a corresponding low-energy feature in the superconducting density of states. The data can also be relatively well described by a simple two-gap $s$-wave model of the order parameter but this yields parameters which seem unrealistic and dependent on the fit range. Broadband surface resistance measurements reveal a sample-dependent residual loss whose origin is unclear. The data from the ${\text{Ba}}_{0.72}{\text{K}}_{0.28}{\text{Fe}}_2{\text{As}}_2$ samples can be made to scale as ${\omega }^2$ if the extrinsic loss is treated as an additive component, indicating large scattering rates. Finally, the temperature dependence of the surface resistance at 13 GHz obeys a power law very similar to those observed for $\Delta \lambda \left(T\right)$.

Figure 1

(Color online) The magnetic moment $m$ of the ${\text{Ba}}_{0.72}{\text{K}}_{0.28}{\text{Fe}}_2{\text{As}}_2$ sample A, as measured by a (Quantum Design Magnetic Property Measurement System) SQUID magnetometer. The data have been multiplicatively scaled to fit on the same plot. Even at high applied magnetic fields, the width of the superconducting transition remains sharp.

Figure 2

(Color online) The change in the London penetration depth, $\lambda \left(T\right)-\lambda \left(0\right)$, as a function of temperature for all three samples. Solid lines are a guide to the eyes.

Figure 3

(Color online) The anomalous “bump” in the London penetration depth. For all three samples, the bump occurs at $T/T_{\text{c}}\approx 0.04$.

Figure 4

(Color online) Extracted superfluid density of all three samples, using three different choices of $\lambda \left(0\right)$ (symbols are $2000\text{Å}$, dashed lines are $1500\text{Å}$, and dotted lines are $2500\text{Å}$). Inset: the superfluid transition of all three samples. Dotted lines are linear guide to the eyes and show that deviations from linearity occur only very near $T_{\text{c}}$ in the form of feet that indicate minor inhomogeneities in the $T_{\text{c}}$ of the sample.

Figure 5

(Color online) Two gap $s$-wave [solid line, Eq. (3)] and power-law [dashed line, Eq. (4)] fits over 0–3 K to the superfluid phase stiffness. Notice the very fine scale of ${\lambda }^2\left(0\right)/{\lambda }^2\left(T\right)$. For clarity, the superfluid phase stiffness of samples C and B have been shifted vertically by 0.004 and 0.002, respectively.

Figure 6

(Color online) In-plane surface resistance of sample B from 0.5 to 20 GHz. The loss of the sample B at 20 GHz and base temperature is a factor of 3.5 less than that of sample A. The solid line is $\propto {\omega }^2$.

Figure 7

(Color online) In-plane surface resistance of sample A from 0.5 to 20 GHz.

Figure 8

(Color online) $\Delta R_{\text{S}}\left(\omega ,T\right)=R_{\text{S}}\left(\omega ,T\right)-R_{\text{S}}\left(\omega ,T_0\right)$ for samples A (solid symbols) and B (open symbols). $\Delta R_{\text{S}}\left(\omega ,T\right)$ is seen to be the same for both samples indicating that sample A (the thicker of the two) has an extra temperature-independent loss. The dashed lines have a slope of 2 $\left(\Delta R_{\text{S}}\propto {\omega }^2\right)$.

Figure 9

(Color online) Scanning electron microscope image of the edge of a platelet ${\text{Ba}}_{0.72}{\text{K}}_{0.28}{\text{Fe}}_2{\text{As}}_2$ crystal, showing delaminated edges.

Figure 10

Estimates of the quasiparticle conductivity spectral widths $\Gamma /2\pi$ of samples A and B as a function of temperature.

Figure 11

(Color online) $\Delta R_{\text{S}}\left(\omega ,T\right)$ at 13 GHz as a function of $T/T_{\text{c}}$ for several superconductors. Solid symbols were taken using the broadband spectrometer. Open symbols were taken using a 13 GHz resonator. The conventional $s$-wave superconductors (${\text{Pb}}_{0.95}{\text{Sn}}_{0.05}$, Nb, and Sn) exhibit a very weak temperature dependence for $T/T_{\text{c}}<0.4$. The ${\text{Ba}}_{0.72}{\text{K}}_{0.28}{\text{Fe}}_2{\text{As}}_2$ samples obey a power law $\Delta R_{\text{S}}\left(\omega ,T\right)\propto T^{\gamma }$ down to the lowest measurement temperature.