Muon-spin rotation measurements of the magnetic penetration depth in the iron-based superconductor Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$

Measurements of the magnetic penetration depth $\lambda$ in the Fe-based superconductor Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$ ($x=0.3$, 0.35, 0.4) were carried out using the muon-spin rotation ($\mu$SR) technique. The temperature dependence of $\lambda$ is well described by a two-gap $s+s$-wave scenario with a small gap ${\Delta }_1\approx 1\text{–}3$ meV and a large gap ${\Delta }_2\approx 7\text{–}9$ meV. By combining the present data with those previously obtained for RbFe${}_2$As${}_2$ a decrease of the BCS ratio 2$\Delta$${}_2/$$k_{\mathrm{B}}$$T_{\mathrm{c}}$ with increasing Rb content $x$ is observed. On the other hand, the BCS ratio 2$\Delta$${}_1/$$k_{\mathrm{B}}$$T_{\mathrm{c}}$ is almost independent of $x$. In addition, the contribution of ${\Delta }_1$ to the superfluid density is found to increase with $x$. These results are discussed in light of the suppression of interband processes upon hole doping.

Figure 1

Transverse field (TF) $\mu$SR time spectra obtained in $\mu$${}_0$$H=$ 0.04 T above and below $T_{\mathrm{c}}$ (after field cooling the sample from above $T_{\mathrm{c}}$): (a) Ba${}_{0.7}$Rb${}_{0.3}$Fe${}_2$As${}_2$ and (b) Ba${}_{0.6}$Rb${}_{0.4}$Fe${}_2$As${}_2$. The solid and the dashed lines represent fits to the data by means of Eq. (1).

Figure 2

(a) ZF-$\mu$SR time spectra for Ba${}_{0.7}$Rb${}_{0.3}$Fe${}_2$As${}_2$ recorded above and below $T_{\mathrm{c}}$. The line represents the fit to the data of a standard Kubo-Toyabe depolarization function (Ref. 15). (b) Temperature dependence of the difference between the internal field ${\mu }_0$$H_{\mathrm{int},\mathit{SC}}$ measured in the SC state and the one measured in the normal state ${\mu }_0$$H_{\mathrm{int},\mathit{NS}}$ at $T=$ 42 K.

Figure 3

(a) Temperature dependence of the superconducting muon spin depolarization rate ${\sigma }_{\mathrm{sc}}$ measured in an applied magnetic field of ${\mu }_{0}H=0.04$ T for Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$ ($x=0.3$, 0.35, 0.4). (b) Field dependence of ${\sigma }_{\mathrm{sc}}$ at 1.7 K.

Figure 4

The temperature dependence of ${\lambda }^{-2}$ for Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$, measured in an applied field of ${\mu }_{0}H=0.04$ T: (a) $x=0.3$, (b) $x=0.35$, and (c) $x=0.4$. The dashed lines correspond to a single gap BCS $s$-wave model, whereas the solid ones represent a fit using a two-gap ($s+s$)-wave model.

Figure 5

(a) Superconducting gap to $T_c$ ratios 2${\Delta }_{1,2}/k_{\mathrm{B}}{T}_{\mathrm{c}}$ and (b) the contribution ${\omega }_1$ of the small gap to the superfluid density as a function of the Rb composition for Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$ ($x=$ 0.3, 0.35, 0.4, 1.0). The measurements were performed in an applied magnetic field of ${\mu }_{0}H=0.04$ T. The data for RbFe${}_2$As${}_2$ are taken from Ref. 10. The dashed lines represent guides to the eyes.

Figure 6

Uemura plot for hole- and electron-doped high $T_{\mathrm{c}}$ Fe-based superconductors (after Ref. 28). The Uemura relation observed for underdoped cuprates is also shown (solid line for hole doping and dashed line for electron doping) (after Ref. 32). The point for conventional BCS superconductor Nb is also shown. Data points for the pnictides are taken from Refs. 27, 28, 29,33, 34, 35, 36, 37, 38, 39. The stars show the data for Ba${}_{1-x}$Rb${}_x$Fe${}_2$As${}_2$ ($x=$ 0.3, 0.35, 0.4) obtained in this work. The point for RbFe${}_2$As${}_2$ is taken from Ref. 10.