Oxygen-isotope-substitution-induced nanoscale crystallinity and origin of metal-insulator transition in Sm$_{0.5}$Sr$_{0.5}$MnO$_{3}$*

Competing effects of $^{16}$O$\rightarrow^{18}$O isotope substitution and magnetic field on the phase separation and structural property in Sm$_{0.5}$Sr$_{0.5}$MnO$_{3}$ have been studied by using high-resolution high-energy X-ray diffraction under magnetic fields up to 7 T. A close correlation between physical properties and the crystallinity of the compounds is observed. The oxygen-isotope-substitution-induced metal-insulator transition is caused by nanoscale crystallite formation in the compound with $^{18}$O below a phase-separation temperature T$_{ps} \sim 100$ K. Different lattice effects on the magnetoresistance are identified, among which the largest one is due to magnetic field enhanced crystallization of the nanoscale crystallites.