Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
1997-06-17
Physics
Condensed Matter
Strongly Correlated Electrons
13 pages, 6 eps figures, submitted to Phys Rev B
Scientific paper
10.1103/PhysRevB.57.7755
Using a Rayleigh-Schr\"odinger perturbation expansion of multi-band Hubbard models, we present analytic expressions for the super-exchange coupling constants between magnetic transition metal ions of arbitrary separation in Mott-Hubbard insulators. The only restrictions are i) all ligand ions are closed shell anions and ii) all contributing interaction paths are of equal length. For short paths, our results essentially confirm the Goodenough-Kanamori-Anderson rules, yet in general there does not exist any simple rule to predict the sign of the magnetic coupling constants. The most favorable situation for ferromagnetic coupling is found for ions with less than half filled d shells, the (relative) tendency to ferromagnetic coupling increases with increasing path length. As an application, the magnetic interactions of the Cr compounds Rb$_2$CrCl$_4$, CrCl$_3$, CrBr$_3$ and CrI$_3$ are investigated, all of which except CrCl$_3$ are ferromagnets.
Feldkemper Stefan
Weber Werner
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