Superfluid density and field-induced magnetism in $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ measured with muon spin relaxation

We report muon spin rotation $\left(\mu \text{SR}\right)$ measurements of single-crystal $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. From measurements of the magnetic field penetration depth $\lambda$ we find that for optimally and overdoped samples, $1/\lambda {\left(T\to 0\right)}^2$ varies monotonically with the superconducting transition temperature $T_C$. Within the superconducting state we observe a positive shift in the muon precession signal, likely indicating that the applied field induces an internal magnetic field. The size of the induced field decreases with increasing doping but is present for all Co concentrations studied.

Figure 1

(Color online) Fourier transforms of TF-$\mu \text{SR}$ spectra for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$, showing anisotropic line shapes characteristic of an Abrikosov vortex lattice.

Figure 2

(Color online) Measured $1/{\lambda }^2$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ measured in $\text{TF}=0.02\text{T}$ (filled symbols) and 0.1 T (open symbols).

Figure 3

(Color online) Superconducting $T_C$’s and $1/{\lambda }^2\left(T\to 0\right)$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of Co concentration $x$, measured in $\text{TF}=0.02\text{T}$ and 0.1 T, and extrapolated to $B=0$. The open points and dashed lines are the measured $T_C$’s and the superconducting dome taken from Ref. 2 for $\text{Ba}{\left(\text{Fe},\text{Co}\right)}_2{\text{As}}_2$ and Refs. 7, 27 for $\text{Sr}{\left(\text{Fe},\text{Co}\right)}_2{\text{As}}_2$.

Figure 4

(Color online) Superconducting $T_C$ vs $1/{\lambda }^2\left(T\to 0\right)$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of Co concentration $x$, measured in $\text{TF}=0.02\text{T}$ and 0.1 T and extrapolated to $B=0$.

Figure 5

(Color online) $1/{\lambda }^2\left(T\to 0\right)$ vs superconducting $T_C$ for $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ and $\text{Sr}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$ as a function of Co concentration $x$, measured in $\text{TF}=0.02$ and 0.1 T and extrapolated to $B=0$, plotted with $\Delta C_P/T_C$ from Ref. 29. The dashed line has a slope $n=2$ and is a guide to the eye.

Figure 6

(Color online) Fractional shift of muon precession frequency ${\nu }_{\mu }/{\nu }_{\mu N}-1$ relative to the normal state frequency ${\nu }_{\mu N}$. Superconducting transition temperatures indicated by triangle symbols.