Abstract
The magnetotransport properties of ${\mathrm{LaMnO}}_{3}$ have been studied using the crystal-field theory and the correlated effective-field theory. The crystal-field theory is used to treat the many-body problem of an atom or ion in the crystal and the correlated effective-field theory is used to treat the many-body effect of the magnetic part of the Hamiltonian. The crystal-field theory exploits the symmetry of the electrostatic field generated by the ligands around the magnetic ion in the transition-metal compounds. The parent compound of colossal magnets, e.g., ${\mathrm{LaMnO}}_{3}$ is a Mott-Hubbard and charge-transfer antiferromagnetic insulator. The magnetotransport properties of this compound have been studied using a theory which goes beyond the mean-field theory. This theory includes fluctuations and explains the experimental results better than the mean-field theory.
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