Abstract
The coupled magnetic and charge-order transition observed in the manganites of the type ${R}_{1\ensuremath{-}x}{M}_{x}$MnO${}_{3}$ near half filling $(x\ensuremath{\simeq}1/2)$ is shown to be the result of the interplay between the double-exchange, superexchange, and the Coulomb interaction terms in an electronic Hamiltonian. At half filling and temperature $T=0$ we find, as we increase the strength of the extended-Hubbard repulsion, a first-order transition from a charge-nonordered ferromagnetic metal (FN) to a charge-ordered antiferromagnetic and insulating (AFO) ground state. The AFO-FN transition is also obtained by increasing $T$; however, a small degree of charge order remains in the ferromagnetic phase. The charge-ordered state also ``melts,'' as observed, on the application of a magnetic field, which causes a rapid drop in the transition temperature. Qualitative differences in behavior between members of the manganite series can be understood in terms of small variations in the interaction parameters.
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