Quasi-Two Dimensional Spin and Phonon Excitations in $La_{1.965}Ba_{0.035}CuO_{4}$

We present time-of-flight inelastic neutron scattering measurements of $La_{1.965}Ba_{0.035}CuO_{4}$ (LBCO), a lightly doped member of the high temperature superconducting La-based cuprate family. By using time-of-flight neutron instrumentation coupled with single crystal sample rotation we obtain a four-dimensional data set (three {\bf Q} and one energy) that is both comprehensive and spans a large region of reciprocal space. Our measurements identify rich structure in the energy dependence of the highly dispersive spin excitations, which are centered at equivalent ($\frac{1}{2},\frac{1}{2}, L$) wave-vectors. These structures correlate strongly with several crossings of the spin excitations with the lightly dispersive phonons found in this system. These effects are significant and account for on the order of 25$\%$ of the total inelastic scattering for energies between $\sim$5 and 40 meV at low $|{\bf Q}|$. Interestingly, this scattering also presents little or no $L$-dependence. As the phonons and dispersive spin excitations centered at equivalent ($\frac{1}{2},\frac{1}{2}, L$) wave-vectors are common to all members of La-based 214 copper oxides, we conclude such strong quasi-two dimensional scattering enhancements are likely to occur in all such 214 families of materials, including those concentrations corresponding to superconducting ground states. Such a phenomenon appears to be a fundamental characteristic of these materials and is potentially related to superconducting pairing.