  Ba2Ti2Fe2As4O is a self-doped superconductor exhibiting a Tc ~ 21.5 K and
containing, distinctively with respect to other Fe-based superconductors, not
only [Fe2As2] layers but also conducting [Ti2O] sheets. This compound exhibits
a transition at T* ~ 125 K which has tentatively been assigned in the
literature to a possible density-wave order. However, the nature of this
density wave (whether it is a charge- or spin-induced) is still under debate.
Magnetism in Ba2Ti2Fe2As4O has never been experimentally confirmed, which
raises the question whether this superconductor might be non-magnetic or
exhibiting a very weak magnetism. Here, we report evidence from inelastic
neutron scattering (INS) measurements and ab initio calculations of phonon
spectra pointing towards absence of magnetism in Ba2Ti2Fe2As4O. The INS
measurements did not reveal any noticeable change of the phonon spectra across
Tc, neither could magnetic effects be observed within the accessible (Q, E)
space, setting Ba2Ti2Fe2As4O as an unconventional superconductor. The effect of
magnetism on describing phonon spectra was further investigated by performing
ab initio calculations. In this context, non-magnetic calculations reproduced
well the measured phonon spectra. Therefore, our results indicate a
non-magnetic and unconventional character of the superconductor Ba2Ti2Fe2As4O.
