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

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.