Crystallite-size Dependent Harmonic Magneto-electricity in SmFeO3

First- and second-harmonic dielectric susceptibilities are maidenly studied on Samarium Orthoferrite of mesoscopic/500 nm and nanoscopic/55 nm grainsizes. Magneto-electrically coupled to the antiferromagnetic and spin-reorientation transitions, fundamental and harmonic dielectricity consistently reflect the global/local polarization effects of crystallite-size dependent electrical orderings. Bulk and incipient ferroelectricity respectively in nanoscopic and mesoscopic crystallites concur the higher-temperature antiferromagnetic ordering (T_N ~670 K). Upon the spin-reorientation transition at lower-temperature (T_SR ~470 K), re-entrant relaxor state in the nano-crystallites and bulk-like/temperature-windowed ferroelectricity in the meso-crystallites emerge. In the nano-crystallites, magneto-electric signature of interfacial spins' de-pinning (T_SP ~540 K) is exclusively revealed by the scaled-harmonics.