One- and two-band models for colossal magnetoresistive manganites studied using the truncated polynomial expansion method

Considerable progress has been recently made in the theoretical understanding of the colossal magnetoresistance (CMR) effect in manganites. The existence of inhomogeneous states has been shown to be directly related with this phenomenon, both in theoretical studies and experimental investigations. The analysis of simple models with two competing states and a resistor network approximation to calculate conductances has confirmed that CMR effects can be theoretically reproduced using nonuniform clustered states. However, a direct computational study of the CMR effect in realistic models has been difficult since large clusters are needed for this purpose. In this paper, the recently proposed truncated polynomial expansion method (TPEM) for spin-fermion systems is tested using the double-exchange one-orbital, with finite Hund coupling JH, and two-orbital, with infinite JH, models. Two dimensional lattices as large as 48×48 are studied, far larger than those that can be handled with standard exact diagonalization (DIAG) techniques for the fermionic sector. The clean limit (i.e., without quenched disorder) is analyzed here in detail. Phase diagrams are obtained, showing first-order transitions separating ferromagnetic metallic from insulating states. A huge magnetoresistance is found at low temperatures by including small magnetic fields, in excellent agreement with experiments. However, at temperatures above the Curie transition the effect is much smaller confirming that the standard finite-temperature CMR phenomenon cannot be understood using homogeneous states. By comparing results between the two methods, TPEM and DIAG, on small lattices, and by analyzing the systematic behavior with increasing cluster sizes, it is concluded that the TPEM is accurate enough to handle realistic manganite models on large systems. Our results contribute to the next challenge in theoretical studies of manganites, namely a frontal computational attack of the colossal magnetoresistance phenomenon using double-exchange-like models, on large clusters, and including quenched disorder.