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We report muon spin rotation ($\mu$SR) measurements of single crystalBa(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$. Frommeasurements of the magnetic field penetration depth $\lambda$ we find that foroptimally- and over-doped samples, $1/\lambda(T\to 0)^2$ varies monotonicallywith the superconducting transition temperature T$_{\rm C}$. Within thesuperconducting state we observe a positive shift in the muon precessionsignal, likely indicating that the applied field induces an internal magneticfield. The size of the induced field decreases with increasing doping but ispresent for all Co concentrations studied.

Superfluid Density and Field-Induced Magnetism in Ba(Fe1-xCox)2As2 and Sr(Fe1-xCox)2As2 Measured with Muon Spin Relaxation