Monte Carlo study of the double and super-exchange model with lattice distortion

Abstract

In this work a magneto-elastic phase transition was obtained in a linear chain due to the interplay between magnetism and lattice distortion in a double and super-exchange model. It is considered a linear chain consisting of localized classical spins interacting with itinerant electrons. Due to the double exchange interaction, localized spins tend to align ferromagnetically. This ferromagnetic tendency is expected to be frustrated by anti-ferromagnetic super-exchange interactions between neighbor localized spins. Additionally, lattice parameter is allowed to have small changes, which contributes harmonically to the energy of the system. Phase diagram is obtained as a function of the electron density and the super-exchange interaction using a Monte Carlo minimization. At low super-exchange interaction energy phase transition between electron-full ferromagnetic distorted and electron-empty anti-ferromagnetic undistorted phases occurs. In this case all electrons and lattice distortions were found within the ferromagnetic domain. For high super-exchange interaction energy, phase transition between two site distorted periodic arrangement of independent magnetic polarons ordered anti-ferromagnetically and the electron-empty anti-ferromagnetic undistorted phase was found. For this high interaction energy, Wigner crystallization, lattice distortion and charge distribution inside two-site polarons were obtained.