Conductance as a Function of the Temperature in the Double Exchange Model

TL;DR

This study uses the Kubo formula and Monte Carlo simulations to analyze how electrical conductance varies with temperature in the double exchange model, revealing limitations in explaining the metal-insulator transition.

Contribution

It provides a detailed computational analysis of conductance in the double exchange model across temperatures, highlighting its inability to reproduce the experimental metal-insulator transition.

Findings

System remains metallic for electron concentrations > 0.1 at all temperatures.

Resistivity near critical temperature is significantly lower than experimental values.

Double exchange model does not account for the observed metal-insulator transition.

Abstract

We have used the Kubo formula to calculate the temperature dependence of the electrical conductance of the double exchange Hamiltonian. We average the conductance over an statistical ensemble of clusters, which are obtained by performing Monte Carlo simulations on the classical spin orientation of the double exchange Hamiltonian. We find that for electron concentrations bigger than 0.1, the system is metallic at all temperatures. In particular it is not observed any change in the temperature dependence of the resistivity near the magnetical critical temperature. The calculated resistivity near $T_c$ is around ten times smaller than the experimental value. We conclude that the double exchange model is not able to explain the metal to insulator transition which experimentally occurs at temperatures near the magnetic critical temperature.