  We present time-of-fight neutron-scattering measurements on single crystals
of $La_{2-x}Ba_{x}CuO_{4}$ (LBCO) with 0 $\leq$ x $\leq$ 0.095 and
$La_{2-x}Sr_{x}CuO_{4}$ (LSCO) with x = 0.08 and 0.11. This range of dopings
spans much of the phase diagram relevant to high temperature cuprate
superconductivity, ranging from insulating, three dimensional (3D) commensurate
long range antiferromagnetic order, for x $\leq$ 0.02, to two dimensional (2D)
incommensurate antiferromagnetism co-existing with superconductivity for x
$\geq$ 0.05. Previous work on lightly doped LBCO with x = 0.035 showed a clear
resonant enhancement of the inelastic scattering coincident with the low energy
crossings of the highly dispersive spin excitations and quasi-2D optic phonons.
The present work extends these measurements across the phase diagram and shows
this enhancement to be a common feature to this family of layered quantum
magnets. Furthermore we show that the low temperature, low energy magnetic
spectral weight is substantially larger for samples with non-superconducting
ground states relative to any of the samples with superconducting ground
states. Spin gaps, suppression of low energy magnetic spectral weight as a
function of decreasing temperature, are observed in both superconducting LBCO
and LSCO samples, consistent with previous observations for superconducting
LSCO.
