Correlation between vacancies and magnetoresistance changes in FM manganites using the Monte Carlo method

The Metropolis algorithm and the classical Heisenberg approximation were implemented by the Monte Carlo method to design a computational approach to the magnetization and resistivity of La_2/3Ca_1/3MnO₃, which depends on the Mn ion vacancies as the external magnetic field increases. This compound is ferromagnetic, and it exhibits the colossal magnetoresistance (CMR) effect. The monolayer was built with L×L×d dimensions, and it had L=30 umc (units of magnetic cells) for its dimension in the x–y plane and was d=12 umc in thickness. The Hamiltonian that was used contains interactions between first neighbors, the magnetocrystalline anisotropy effect and the external applied magnetic field response. The system that was considered contains mixed-valence bonds: Mn^3+eg'–O–Mn^3+eg, Mn^3+eg–O–Mn^4+d3 and Mn^3+eg'–O–Mn^4+d3. The vacancies were placed randomly in the sample, replacing any type of Mn ion. The main result shows that without vacancies, the transitions T_C (Curie temperature) and T_MI (metal–insulator temperature) are similar, whereas with the increase in the vacancy percentage, T_MI presented lower values than T_C. This situation is caused by the competition between the external magnetic field, the vacancy percentage and the magnetocrystalline anisotropy, which favors the magnetoresistive effect at temperatures below T_MI. Resistivity loops were also observed, which shows a direct correlation with the hysteresis loops of magnetization at temperatures below T_C. - Highlights: • Changes in the resistivity of FM materials as a function of the temperature and external magnetic field can be obtained by the Monte Carlo method, Metropolis algorithm, classical Heisenberg and Kronig–Penney approximation for magnetic clusters. • Increases in the magnetoresistive effect were observed at temperatures below T_MI by the vacancies effect. • The resistive hysteresis loop presents two peaks that are directly associated with the coercive field in the magnetic hysteresis loop