Approach to the metal-insulator transition in ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3\hspace{0.5em}(0\mathrm{}<~x<~0.2):$ Magnetic inhomogeneity and spin-wave anomaly

We describe the evolution of the static and dynamic spin correlations of ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ for $x=0.1,$ 0.125, and 0.2, where the system evolves from the canted magnetic state towards the insulating ferromagnetic state, approaching the metallic transition $\mathrm{}(x=0.22\mathrm{}).$ In the $x=0.1\mathrm{}$ sample, the observation of two spin-wave branches typical of two distinct types of magnetic coupling and of a modulation in the elastic diffuse-scattering characteristic of ferromagnetic inhomogeneities confirms the static and dynamic inhomogeneous features previously observed at $x<\mathrm{}\mathrm{0.1.}\mathrm{}$ The anisotropic q dependence of the intensity of the low-energy spin wave suggests a bidimensional character for the static inhomogeneities. At $x=0.125,$ which corresponds to the occurrence of a ferromagnetic and insulating state, one spin wave branch, anisotropic, is detected. At this concentration, an anomaly appears at ${\mathbf{q}}_0=(1.25,1.25,0).$ At $x=0.2,$ the spin-wave branch appears as isotropic. In addition to the anomaly observed at $q_0,$ extra magnetic excitations are observed at larger q, forming an optical branch.