  In cuprate superconductors superconductivity develops as a unique cross over
between the two extremal phases characterizing these compounds. The extremal
phases are known to be an antiferromagnetic (AF) Mott insulator one, on one
side, and a non-superconducting itinerant metal on the other. Numerous
inelastic neutron scattering studies on underdoped samples shows most directly
that the static AF order of the parent phase does not disappear by doping but
transforms in such a way that at least fluctuating and local AF order persists,
coexisting with superconductivity. Structurally, the model of stripe-type
correlations accounts for the coexistence while its genuine dynamics might hide
the most interesting physics of cuprates, including the pairing mechanism.
Indeed, there is an impressive accumulation of knowledge in favour of AF
correlations underlying the pairing. Some crucial properties of these
correlations have been recently pointed out: they should involve small velocity
collective modes of the wave vector identical to that of static AF order while
their energy scale (<50 meV) should be rather low compared with any other
involved. In this work we show on phenomenological ground that the very concept
of a disordered AF phase interpenetrated with non-magnetic boundaries
comprises, irrespective of structural details of stripe order, the dynamical
ingredients (fractons) which may be important for pairing. The model elaborated
below introduces a new energy scale (10-50 meV) associated with slow (or almost
localized) and well-defined AF excitations, interpreting simultaneously most of
the neutron scattering results in a consistent and a natural way.
