  We report muon spin rotation (muSR) and infrared (IR) spectroscopy
experiments on underdoped BaFe1.89Co0.11As2 which show that bulk magnetism and
superconductivity (SC) coexist and compete on the nanometer length scale. Our
combined data reveal a bulk magnetic order, likely due to an incommensurate
spin density wave (SDW), which develops below Tmag \approx 32 K and becomes
reduced in magnitude (but not in volume) below Tc = 21.7 K. A slowly
fluctuating precursor of the SDW seems to develop alrady below the structural
transition at Ts \approx 50 K. The bulk nature of SC is established by the muSR
data which show a bulk SC vortex lattice and the IR data which reveal that the
majority of low-energy states is gapped and participates in the condensate at T
<< Tc.
