Competing Ferromagnetic and Charge-Ordered States in Models for Manganites: The Origin of the Colossal Magnetoresistance Effect

The one-orbital model for manganites with cooperative phonons and superexchange coupling $J_{\mathrm{AF}}$ is investigated via large-scale Monte Carlo simulations. The results for two orbitals are also briefly discussed. Focusing on the electron density $n=0.75$, a regime of competition between ferromagnetic metallic and charge-ordered (CO) insulating states is identified. In the vicinity of the associated bicritical point, colossal magnetoresistance (CMR) effects are observed. The CMR is associated with the development of short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge arrangement of the low-temperature CO state.

Figure 1

Clean-limit MC phase diagram using $8\times 8$ and $12\times 12$ lattices, at $n=0.75$ and $\lambda =1.2$. The $\mathrm{AF}/\mathrm{CO}$ state is schematically shown, with the radius of the circles proportional to the electronic density, and arrows representing the $t_{2g}$ spins. Charge is uniform in the competing FM state. At each temperature, $1\times {10}^5$ thermalization and $5\times {10}^4$ measurement MC steps were carried out for the $8\times 8$ clusters (and $\sim 7500$ and 5000, respectively, for the $12\times 12$ cluster points indicated by red stars). Random starting spin configurations were used in all simulations, but the results have also been checked for convergence using ordered starting configurations. $T_C$ is defined as the temperature where the spin-spin correlations at the maximum cluster distance nearly vanish. Similarly, $T_{\mathrm{AF}/\mathrm{CO}}$ is the temperature where both AF and FM correlations vanish at the maximum allowed distances. At $T_{\mathrm{AF}/\mathrm{CO}}$, the charge structure factor $n(\mathbf{q})$ at $\mathbf{q}={\mathbf{q}}_{\mathrm{CO}}$ also vanishes. Inset: energy vs $J_{\mathrm{AF}}$ at very low $T\sim 0$, with the FM (CO-AF) phase in black (red). Green dots indicate a $G$ ordered AF regime. Here, the spins were frozen to their expected states and the phonons were MC relaxed.

Figure 2

Resistivity $\rho$ vs $T$ curves for various parameters: (a) Fixing $\lambda =1.2$ and varying $J_{\mathrm{AF}}$. Arrows indicate $T_C$’s. Results at $\lambda =0.8$ and $\lambda =1.0$, with $J_{\mathrm{AF}}=0.0$, are also shown. Inset: results fixing $J_{\mathrm{AF}}=0.03$ and varying $\lambda$. (b) Effect of magnetic fields (indicated, in $t$ units) on $\rho$ using $J_{\mathrm{AF}}=0.0325$, on an $8\times 8$ lattice. (c) Same as (b) but for $J_{\mathrm{AF}}=0.035$, on a $12\times 12$ lattice. In (a) and (b), MC steps and the starting configurations are the same as in Fig. 1. In (c), 7500 thermalization and 5000 measurement steps were used. Typical error bars are indicated in (a).

Figure 3

(a) $\rho$ vs $T$ in the presence of quenched disorder $\Delta$. Up to ten different disorder realizations were used in calculations with quenched disorder. Only small changes between configurations were observed. MC steps and starting configurations are as in Fig. 1. (b) $\rho$ vs $T$ using a $4\times 4\times 4$ lattice, parametrized with $\lambda$, at $J_{\mathrm{AF}}=0.03$. (c) Two orbitals $\rho$ vs $T$ results using an $8\times 8$ lattice for $J_{\mathrm{AF}}=0.05$. In (b) and (c), 4000 thermalization and 4000 measurement MC steps were used, $n=0.75$, and the clean-limit $\Delta =0$ was studied.

Figure 4

(a) MC averaged $C(\sqrt{5})$ vs $T$, showing a qualitative similarity with the rescaled resistivity (also shown). This agreement occurs below the $T^{*}$ indicated. At higher $T$, $\rho$ is flat and $C(\sqrt{5})$ nearly vanishes. Also shown is the inverse of $N(\omega =\mu )$, to indicate the PG formation at $T^{\mathrm{pl}}$. (b) Typical MC snapshot with the radius of the circles proportional to the local charge density. Also shown are the hole-hole distances $\sqrt{5}$ and 2 of relevance (see text).