A theoretical study of the interrelation of the crystal structure, charge, orbital, and magnetic subsystems in R1–xAxMnO3 charge-ordered manganites has been carried out (where R3+ is the rare earth ion,
A2+ is the alkaline earth metal ion, x = 0.5, 2/3). The model of orbital-dependent exchange interactions and
single-ion anisotropy is used. The presence of quasi-low-dimensional magnetic structures is exhibited. The
spin waves spectra and antiferromagnetic resonance spectra are calculated.
The magnetic resonance spectra of frustrated manganite compounds La1/3Ca2/3MnO3 and BiMnO3 are calculated within the framework of orbitally dependent magnetic interactions model. The aim of the paper is an investigation of orbital structure influence and superexchange interactions’ competition effects on ferromagnetic or antiferromagnetic resonance spectra of these compounds. The description of the features of the resonance lower branches’ dependencies on the magnitude and direction of the magnetic field is proposed. It is shown that the main influence on the symmetry of dependencies is exerted by single-ion anisotropy of the Mn3+ ion, associated not only with the orbital structure, but also with the tilting distortions of oxygen octahedrons around the ions
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