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We present time-of-fight neutron-scattering measurements on single crystalsof $La_{2-x}Ba_{x}CuO_{4}$ (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 dopingsspans much of the phase diagram relevant to high temperature cupratesuperconductivity, ranging from insulating, three dimensional (3D) commensuratelong 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 clearresonant enhancement of the inelastic scattering coincident with the low energycrossings of the highly dispersive spin excitations and quasi-2D optic phonons.The present work extends these measurements across the phase diagram and showsthis enhancement to be a common feature to this family of layered quantummagnets. Furthermore we show that the low temperature, low energy magneticspectral weight is substantially larger for samples with non-superconductingground states relative to any of the samples with superconducting groundstates. Spin gaps, suppression of low energy magnetic spectral weight as afunction of decreasing temperature, are observed in both superconducting LBCOand LSCO samples, consistent with previous observations for superconductingLSCO.

physical review. b./physical review. b

Neutron Scattering Studies of Spin-Phonon Hybridization and  Superconducting Spin-Gaps in High Temperature Superconductor  $La_{2-x}(Sr,Ba)_{x}CuO_{4}$