  We re-examine the experimental results for the magnetic response function
$\chi''({\bf q}, E, T)$, for ${\bf q}$ around the anti-ferromagnetic vectors
${\bf Q}$, in the quantum-critical region, obtained by inelastic neutron
scattering, on an Fe-based superconductor, and on a heavy Fermion compound. The
motivation is to compare the results with a recent theory, which shows that the
fluctuations in a generic anti-ferromagnetic model for itinerant fermions map
to those in the universality class of the dissipative quantum-XY model. The
quantum-critical fluctuations in this model, in a range of parameters, are
given by the correlations of spatial and of temporal topological defects. The
theory predicts a $\chi''({\bf q}, E, T)$ (i) which is a separable function of
$({\bf q -Q})$ and of ($E$,$T$), (ii) at crticality, the energy dependent part
is $\propto \tanh (E/2T)$ below a cut-off energy, (iii) the correlation time
departs from its infinite value at criticality on the disordered side by an
essential singularity, and (iv) the correlation length depends logarithmically
on the correlation time, so that the dynamical critical exponent $z$ is
$\infty$ . The limited existing experimental results are found to be consistent
with the first two unusual predictions from which the linear dependence of the
resistivity on T and the $T \ln T$ dependence of the entropy also follow. More
experiments are suggested, especially to test the theory of variations on the
correlation time and length on the departure from criticality.
