Monte Carlo Simulations for the Magnetic Phase Diagram of the Double Exchange Hamiltonian

TL;DR

This paper uses Monte Carlo simulations to map the magnetic phase diagram of the double exchange Hamiltonian, finding minimal influence of Berry's phase on critical temperature and proposing an approximation to improve accuracy.

Contribution

Introduces an approximated expression for the double exchange energy to better determine critical temperatures in Monte Carlo simulations.

Findings

Berry's phase has negligible effect on critical temperature

Developed an approximation for the double exchange energy

No anomalies observed near the magnetic transition

Abstract

We have used Monte Carlo simulation techniques to obtain the magnetic phase diagram of the double exchange Hamiltonian. We have found that the Berry's phase of the hopping amplitude has a negligible effect in the value of the magnetic critical temperature. To avoid finite size problems in our simulations we have also developed an approximated expression for the double exchange energy. This allows us to obtain the critical temperature for the ferromagnetic to paramagnetic transition more accurately. In our calculations we do not observe any strange behavior in the kinetic energy, chemical potential or electron density of states near the magnetic critical temperature. Therefore, we conclude that other effects, not included in the double exchange Hamiltonian, are needed to understand the metal-insulator transition which occurs in the manganites.