  Magnetism and superconductivity are physical phenomena whose foundations are
rooted in quantum mechanics and whose technological applications do not cease
to surprise us. In this article we describe a class of magnetic materials, we
call modulated antiferromagnetic systems (MAS), that has a prominent
representative in the copper-oxide high-temperature superconductors. The class,
however, is not exclusive to these superconductors. Indeed, several materials
that belong to that class are insulators. The magnetic spectral weight of MAS
displays the following universal properties: a local intensity maximum
(resonance peak) at the commensurate antiferromagnetic wave vector; peaks at
the nearly-antiferromagnetic wave vectors for excitation energies well below
the resonance, and at wave vectors rotated by 45 degrees for energies above
resonance. Moreover, we predict an observable rotation by 45 degrees of the
peaks immediately below the resonance. All these universal signatures,
condensed in a twisted hour-glass-like spectrum, are merely consequences of the
unique topological characteristics of the single-particle magnetic dispersion
relation. We thus provide a unifying scenario that explains the phenomenology
that has been observed in inelastic neutron scattering experiments of the
high-temperature superconductors.
