  Band calculations show that a stripe-like anti-ferromagnetic spin wave is
enforced by a 'half-breathing' phonon distortion within the CuO plane of
HgBa_2CuO_4. This spin-phonon coupling is increased further by shear distortion
and by increased distance between Cu and apical oxygens. The effects from
spin-phonon coupling are consistent with many observations in high-T_C
materials. Spin-phonon coupling can be important for the mechanism of spin
fluctuations and superconductivity, although the effects are quantitatively
weak when using the local density potential.
