Manganites with general formulas RMnO 3 and R 0.5 A 0.5 MnO 3 , where R 3ϩ is a rare-earth ion, and A 2ϩ is an alkaline-earth ion, are known as insulating pure or charge ordered compounds at low temperatures with some R and A. In the present work, it is shown how the charge ordering and crystal structure form the orbital structure, which strongly effects the superexchange interaction. An explicit space group and the magnitudes of the distortions of each crystal were used in the calculations. We assume an ideal insulating state of the crystals. The model presented in this work allows one to explain the CE and A magnetic structures in terms of charge and orbital structures using quantitative estimations of the exchange parameters. The model also allows one to find easy axis and noncollinear components of a multisublattice magnetic structure of manganites.
It is demonstrated that magnetic resonance in a magnetically ordered state is a sensitive indirect method for the investigation of the orbital ground state. This idea is illustrated for two perovskite titanates: LaTiO 3 and YTiO 3 . In contrast to the spin-wave energy spectra, antiferromagnetic resonance spectra in an external magnetic field reveal clear dependence on the orbital state and it can distinguish the state with strong orbital fluctuations from the static orbital order. Our theoretical analysis is based on the model, which explicitly takes into consideration the strong correlation among lattice, orbital, and magnetic degrees of freedom.
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