Phase diagram of the Kondo necklace model with planar and local anisotropies

We present a detailed temperature-dependent Raman light scattering study of optical phonons in molecular-beam-epitaxy-grown films of the electron-doped superconductor La_{2 -x} Ce _x CuO₄ close to optimal doping (x ~ 0.08, T _c = 29 K and x ~ 0.1, T _c = 27 K). The main focus of this work is a detailed characterization and microstructural analysis of the films. Based on micro-Raman spectroscopy in combination with X-ray diffraction, energy-dispersive X-ray analysis, and scanning electron microscopy, some of the observed phonon modes can be attributed to micron-sized inclusions of Cu₂O. In the slightly underdoped film (x ~ 0.08), both the Cu₂O modes and others that can be assigned to the La_{2 -x} Ce _x CuO₄ matrix show pronounced softening and narrowing upon cooling below T ~ T _c . Based on control measurements on commercial Cu₂O powders and on a comparison to prior Raman scattering studies of other high-temperature superconductors, we speculate that proximity effects at La_{2 -x} Ce _x CuO₄/Cu₂O interfaces may be responsible for these anomalies. Experiments on the slightly overdoped La_{2 -x} Ce _x CuO₄ film (x ~ 0.1) did not reveal comparable phonon anomalies.