  An understanding of spin excitations in cuprates is essential since the
mechanism of high-T$_C$ superconductivity might be linked to spin fluctuations.
Band calculations for long "1-dimensional" unit cells of La$_2$CuO$_4$ show
that the coupling between antiferromagnetic spin waves and phonons is larger
for distortions of oxygens than for Cu or La. When this result is applied to a
2-dimensional, free-electron like band, it leads to a q-dependent spin
excitation spectrum in good agreement with recent experiments. It is argued
that important parameters for spin-phonon coupling, which comes out from the
comparison between experiment and theory, are relevant for the mechanism of
superconductivity, and are large enough to explain a high T$_C$.

Superconductivity;Materials Science