  The magnetic excitations in the paramagnetic-tetragonal phase of underdoped
Ba(Fe0.953Co0.047)2As2, as measured by inelastic neutron scattering, can be
well described by a phenomenological model with purely diffusive spin dynamics.
At low energies, the spectrum around the magnetic ordering vector Q_AFM
consists of a single peak with elliptical shape in momentum space. At high
energies, this inelastic peak is split into two peaks across the direction
perpendicular to Q_AFM. We use our fittings to argue that such a splitting is
not due to incommensurability or propagating spin-wave excitations, but is
rather a consequence of the anisotropies in the Landau damping and in the
magnetic correlation length, both of which are allowed by the tetragonal
symmetry of the system. We also measure the magnetic spectrum deep inside the
magnetically-ordered phase, and find that it is remarkably similar to the
spectrum of the paramagnetic phase, revealing the strongly overdamped character
of the magnetic excitations.
