Muon spin rotation study of the magnetic penetration depth in the intercalated graphite superconductor ${\text{CaC}}_6$

We report temperature- and magnetic field-dependent bulk muon spin rotation measurements in a $c$-axis-oriented superconductor ${\text{CaC}}_6$ in the mixed state. Using both a simple second-moment analysis and the more precise analytical Ginzburg-Landau model, we obtained a field-independent in-plane magnetic penetration depth ${\lambda }_{ab}\left(0\right)=72\left(3\right)\text{nm}$. The temperature dependencies of the normalized muon spin relaxation rate and of the normalized superfluid density result to be identical and both are well represented by the clean limit BCS model with $2\Delta /{\text{k}}_B{T}_c=3.6\left(1\right)$, suggesting that ${\text{CaC}}_6$ is a fully gapped BCS superconductor in the clean limit regime.

Figure 1

(a) Illustration of the ${\text{CaC}}_6$ sample and the Kapton stacks used to degrade the muon beam (see text). (b) Magnetic moment of ${\text{CaC}}_6$ as a function of temperature measured at the same field used in $\text{TF-}\mu \text{SR}$ measurements (120 mT). The closed (open) symbols represent zero-field cooling (field cooling) measurements. Inset to panel (b): magnetic moment on enlarged scale to better show the ZFC data.

Figure 2

(Color online) Magnetic field distribution $P\left(B\right)$ at an applied field of 120 mT above (7 K) and below (3 K) $T_c$ obtained from the measured $\mu \text{SR}$ time spectra by means of fast Fourier transform. The solid lines are fit by using Eq. (6). Inset: the same as in the main panel on larger scales.

Figure 3

Gaussian relaxation as a function of magnetic field at $T=2\text{K}$. The solid line is a fit by Eq. (3).

Figure 4

Magnetic penetration depth as a function of magnetic field obtained from the fit to the $\mu \text{SR}$ time spectra at 2 K.

Figure 5

(Color online) Normalized superfluid density $\rho \left(T\right)/\rho \left(0\right)$ and muon spin relaxation rate $\sigma \left(T\right)/\sigma \left(0\right)$ as a function of the reduced temperature $T/T_c$ measured at 120 mT. Full and dashed lines are BCS clean limit and dirty limit curves, respectively. Inset: temperature dependence of $\rho$ and BCS fits.