Spin wave damping arising from phase coexistence below $T_c$ in colossal magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_3$

While the spin dynamics of La$_{0.7}$Ca$_{0.3}$MnO$_3$ in the ferromagnetic phase are known to be unconventional, previous measurements have yielded contradictory results regarding the damping of spin wave excitations. Neutron spectroscopy measurements on a sample with a transition temperature of $T_c$=257 K, higher than most single crystals, unambiguously reveal an anomalous increase in spin wave damping for excitations approaching the Brillouin zone boundary along the [$100$] direction that cannot be explained as an artifact due to a noninteracting phonon branch. Spin waves throughout the ($HK0$) plane display a common trend where the spin wave damping is dependent upon the excitation energy, increasing for energies above roughly 15 meV and reaching a full width at half maximum of at least 20 meV. The results are consistent with a model of intrinsic spatial inhomogeneity with phase separated regions approximately 18 Å in size persisting over a large range of temperatures below $T_c$.