  Effects of coupling between phonon distortions and stripe-like spin waves in
the CuO plane of HgBa$_2$CuO$_4$ are studied by band calculations. Local
exchange enhancements depend sensitively on the local structure around Cu
sites. Interactions where spin waves have twice as long wave length as phonon
waves can lead to a 'dip' in the density of states (DOS) below the Fermi
energy, $E_F$. This type of interaction is compatible with several seemingly
contradictory observations among high-$T_C$ cuprates, like the isotope effect,
anti-ferromagnetic fluctuations, stripes and pseudogaps. It can also account
for a large $T_C$.
