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Hexagonal manganese oxides RMnO$_3$ show intriguing topological ferroelectric-domain walls with variable conductivity, leading to domain wall engineering. Despite the numerous experimental studies on the polar nanoscale structures, controlling ferroelectric domains has not been sufficiently investigated. Here, we reveal the unprecedented coexistence of polar-nonpolar nanoscale domains that can be formed by substituting Ti ions in HoMnO$_3$. Unusual polar nanoscale domains are embedded in nonpolar domains with different crystallographic symmetry. This polar-nonpolar coexisting structure is naturally assembled by adjusting the lattice length during a solid-state reaction process. Furthermore, the comprehensive study reveals that the reversible microstructural change with a nonpolar-polar transition is strongly correlated with the oxygen storage properties in Ho(Mn, Ti)O$_{3+\delta}$. The present results provide important insight into the nanoscale polar-nonpolar domain coexistence in functional rare-earth manganese oxides, RMnO$_3$.

All-solid-state batteries using sodium are promising candidates for next-generation rechargeable batteries due to the limited lithium resources. A practical sodium battery requires an electrolyte with high conductivity. Cubic Na$_3$PS$_4$ exhibiting high conductivity of over 10$^{-4}$ S cm$^{-1}$ is obtained by crystallizing amorphous Na$_3$PS$_4$ synthesized by ball milling. Amorphous Na$_3$PS$_4$ crystallizes in a cubic structure and then is transformed into a tetragonal phase upon heating. In this study, in situ observation by transmission electron microscopy demonstrates that the crystallite size drastically increases during the transition from the cubic phase to the tetragonal phase. Moreover, an electron diffraction analysis reveals that amorphous domains and nano-sized crystallites coexist in the cubic Na$_3$PS$_4$ specimen, while the tetragonal phase contains micro-sized crystallites. The nano-sized crystallites and the composite formed by crystallites and amorphous domains are most likely responsible for the increase in conductivity in the cubic Na$_3$PS$_4$ specimens.