  Hour-glass-shaped magnetic excitation spectra have been detected in a variety
of doped transition-metal oxides with stripe-like charge order. Compared to the
predictions of spin-wave theory, these spectra display a different intensity
distribution and anomalous broadening. Here we show, based on a comprehensive
modelling of these phenomena for La5/3Sr1/3CoO4, how quenched disorder in the
charge sector causes frustration, and consequently cluster-glass behavior at
low temperatures, in the spin sector. This spin-glass physics, which is
insensitive to the detailed nature of the charge disorder, but sensitive to the
relative strength of the magnetic inter-stripe coupling, ultimately determines
the distribution of magnetic spectral weight and thus causes the hour-glass
spectrum.
