We report muon spin rotation ($mu$SR) measurements of single crystal Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$. From measurements of the magnetic field penetration depth $lambda$ we find that for optimally- and over-doped samp
les, $1/lambda(Tto 0)^2$ varies monotonically with the superconducting transition temperature T$_{rm C}$. 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.
We have performed transverse field muon spin rotation measurements of single crystals of Ba(Fe$_{0.93}$Co$_{0.07})_2$As$_2$ with the applied magnetic field along the $hat{c}$ direction. Fourier transforms of the measured spectra reveal an anisotropic
lineshape characteristic of an Abrikosov vortex lattice. We have fit the $mu$SRSR spectra to a microscopic model in terms of the penetration depth $lambda$ and the Ginzburg-Landau parameter $kappa$. We find that as a function of temperature, the penetration depth varies more rapidly than in standard weak coupled BCS theory. For this reason we first fit the temperature dependence to a power law where the power varies from 1.6 to 2.2 as the field changes from 200G to 1000G. Due to the surprisingly strong field dependence of the power and the superfluid density we proceeded to fit the temperature dependence to a two gap model, where the size of the two gaps is field independent. From this model, we obtained gaps of $2Delta_1=3.7k_BT_c$ and $2Delta_2=1.6k_BT_c$, corresponding to roughly 6 meV and 3 meV respectively.
