Electrical Resistivity Behavior and Small Polaron Conduction Transport Mechanism in Semiconducting RMnO₃ Manganites

Rare earth manganites, denoted by the chemical formula RMnO₃, where R signifies a rare earth element, have garnered significant interest in recent years. These perovskite oxides exhibit intriguing phenomena such as multiferroicity, ferroelectricity, and colossal magnetoresistance, primarily attributed to the role of polarons in conduction. The incorporation of rare earth ions imparts flexibility, making these compounds promising for applications in spintronics, sensors, and information storage devices. This study delves into the electrical resistivity behavior and Small Polaron Conduction (SPC) mechanisms of rare earth manganites, particularly RMnO₃. In this manuscript, electrical resistivity of the pristine RMnO₃ (R = Sm, Eu, Gd) manganites are analyzed within the framework of adiabatic nearest-neighbor hopping of SPC. The high temperature state of RMnO₃ within the SPC mechanism is influenced by polaron concentration, hopping distance, and resistivity coefficient. The localized charge carriers in undoped manganites enable one to estimate the activation energy for the electrical conduction. The activation energy decreases with the decrease in ionic radii from Sm to Gd. Deduced polaron activation energy is low for GdMnO₃ as compared to SmMnO₃ and is attributed to reducing disorder state in GdMnO₃ as compared to SmMnO₃. This work contributes to the fundamental understanding of condensed matter physics and the potential applications of rare earth manganites in emerging technologies. The interplay between electrical resistivity and Small Polaron Conduction offers insights for customizing these materials for specific technological needs.