With infrared spectroscopy we investigated the spin-reorientation transition from an orthorhombic antiferromagnetic (o-AF) to a tetragonal AF (t-AF) phase and the reentrance of the o-AF phase in the superconducting state of underdoped Ba 1−x K x Fe 2 As 2 . In agreement with the predicted transition from a single-Q to a double-Q AF structure, we found that a distinct spin density wave (SDW) develops in the t-AF phase. The pair breaking peak of this SDW acquires much more low-energy spectral weight than the one in the o-AF state which indicates that it competes more strongly with superconductivity. We also observed additional phonon modes in the t-AF phase which likely arise from a Brillouin-zone folding that is induced by the double-Q magnetic structure with two Fe sublattices exhibiting different magnitudes of the magnetic moment. Similar to the cuprate high-T c superconductors (HTS), the phase diagram of the iron arsenides is characterized by the interaction of superconductivity (SC) with electronic correlations that give rise to competing orders and may also be involved in the SC pairing [1][2][3][4][5][6][7]. The iron arsenides are considered to be archetypal HTS since they exhibit well resolved structural and magnetic phase transitions with long-range ordered states that, unlike the cuprates, are not obscured by strong fluctuation effects. However, the interpretation is still complicated by their multi-band and multi-orbital structure and a sizeable coupling between the charge, spin, orbital and lattice degrees of freedom [1,2]. A prominent example is the combined structural and magnetic transition in undoped and lightly doped samples for which it is still debated whether it is driven by the spin or orbital sectors [6,8,9]. A related, controversial issue is whether the antiferromagnetic (AF) order is better described by an itinerant picture, in terms of a spin density wave (SDW), or in terms of local moments