Orbital Domain State and Finite Size Scaling in Ferromagnetic Insulating Manganites

${}^{55}\mathrm{M}\mathrm{n}$ and ${}^{139}\mathrm{L}\mathrm{a}$ NMR measurements on a high quality single crystal of ferromagnetic (FM) ${\mathrm{L}\mathrm{a}}_{0.80}{\mathrm{C}\mathrm{a}}_{0.20}{\mathrm{M}\mathrm{n}\mathrm{O}}_3$ demonstrate the formation of localized ${\mathrm{M}\mathrm{n}}^{3+,4+}$ states below $70\mathrm{K}$, accompanied by a strong cooling-rate dependent increase of certain FM neutron Bragg peaks. ${}^{55,139}(1/T_1)$ spin-lattice and ${}^{139}(1/T_2)$ spin-spin relaxation rates are strongly enhanced on approaching this temperature from below, signaling a genuine phase transition at $T_{\mathrm{t}\mathrm{r}}\simeq 70\mathrm{K}$. The disappearance of the FM metallic signal by applying a weak external magnetic field, the different NMR radio-frequency enhancement of the FM metallic and insulating states, and the observed finite size scaling of $T_{\mathrm{t}\mathrm{r}}$ with Ca (hole) doping, as observed in powder ${\mathrm{L}\mathrm{a}}_{1-x}{\mathrm{C}\mathrm{a}}_x{\mathrm{M}\mathrm{n}\mathrm{O}}_3$ samples, are suggestive of freezing into an inhomogeneous FM insulating and orbitally ordered state embodying “metallic” hole-rich walls.