Monte Carlo study of double exchange interaction in manganese oxide

In this paper we study the magnetoresistance properties attributed by double exchange (DE) interaction in manganese oxide by Monte Carlo simulation. We construct a model based on mixed-valence Mn³⁺ and Mn⁴⁺ on the general system of Re_2/3Ae_1/3MnO₃ in two dimensional system. The conduction mechanism is based on probability of e_g electrons hopping from Mn³⁺ to Mn⁴⁺. The resistivity dependence on temperature and the external magnetic field are presented and the validity with related experimental results are discussed. We use the resistivity power law to fit our data on metallic region and basic activated behavior on insulator region. On metallic region, we found our result agree well with the quantum theory of DE interaction. From general arguments, we found our simulation agree qualitatively with experimental results.