Charge ordering via electron-electron interactions in the colossal-magnetoresistive manganites

The coupled magnetic and charge-order transition observed in the manganites of the type $R_{1-x}{M}_x$MnO${}_3$ near half filling $(x\simeq 1/2)$ 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 $T=0\mathrm{}$ 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.