Spin Gaps and Spin Dynamics in La_{2-x}Sr_xCuO_4 and YBa_2Cu_3O7_\delta

A magnetic susceptibility which decreases with decreasing temperature is observed in all $CuO_2$ based superconductors with less than optimal doping. We propose that in $La_{2-x} Sr_x CuO_4$ this is due to antiferromagnetic ordering which is prevented by the low spatial dimensionality while in $YBa_2 Cu_3 O_{6.6}$ it is due to the interplay between antiferromagnetic fluctuations within a plane and singlet pairing of electrons between nearest neighbor planes.