Theoretical study of half-doped models for manganites: Fragility of CE phase with disorder, two types of colossal magnetoresistance, and charge-ordered states for electron-doped materials

Abstract

A comprehensive analysis of half-doped manganites is presented using Monte Carlo simulations applied to the double-exchange model with cooperative Jahn-Teller lattice distortions in two dimensions. A variety of results are reported. In particular (i) The phase diagram is established in the $\lambda -J_{\mathrm{AF}}$ plane, with $\lambda$ the electron-phonon coupling and $J_{\mathrm{AF}}$ the antiferromagnetic exchange between classical $t_{2\mathrm{g}}$ spins. The results include standard phases, such as the CE-insulating and FM-metallic regimes, but they also include states, such as a ferromagnetic charge-ordered (CO) orbital-ordered phase originally predicted by Hotta et al. This state is compatible with recent experimental results by Loudon et al. (ii) For realistic couplings, it was observed that the charge disproportionation $\delta$ of the CO phase is far from the widely accepted extreme limit $\delta =0.5\mathrm{}$ of a $3+/4+$ charge separation. A far smaller $\delta$ appears more realistic, in agreement with recent experiments by Garcia et al. and Daoud-Aladine et al. (iii) Colossal magnetoresistance (CMR) effects are found in calculations of cluster resistances using the Landauer formalism. This occurs near the ubiquitous first-order phase transitions between the insulating and metallic states. The present result reinforces the previous conjecture that CMR phenomenology exists in two forms: the low-temperature CMR addressed here and the more standard CMR above the Curie temperature. (iv) The CE state is found to be very sensitive to disorder since its long-range order rapidly disappears when quenched disorder is introduced, contrary to the FM state which is more robust. This is also in qualitative agreement with recent experiments by Akahoshi et al. and Nakajima et al. (v) The phase diagram in the half-doped electron doping regime is briefly discussed as well. A charge-ordered state is found, which is the analog of the $x=0.5\mathrm{}$ CE phase. It contains a $3+/2+$ charge arrangement at large $\lambda .$ Numerical results suggest that an approximate symmetry exists between the hole- and electron-doped systems in the large Hund coupling limit.