  We study the interplay of magnetic and superconducting order in single
crystalline hole doped Ba1-xNaxFe2As2 using muon spin relaxation. We find
microscopic coexistence of magnetic order and superconductivity. In a strongly
underdoped specimen the two forms of order coexist without any measurable
reduction of the ordered magnetic moment by superconductivity, while in a
nearly optimally doped sample the ordered magnetic moment is strongly
suppressed below the superconducting transition temperature. This coupling can
be well described within the framework of an effective two-band model
incorporating inter- and intra-band interactions. In optimally doped
Ba1-xNaxFe2As2 we observe no traces of static or dynamic magnetism and the
temperature dependence of the superfluid density is consistent with two s-wave
gaps without nodes.
