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 develops in the t-AF phase. The pair breaking peak of this spin density wave 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.
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