Helical magnetic structures in cubic perovskites

One-dimensional helical structures with a finite Hund interaction have been considered in detail. The analytical expressions for the electron spectrum of charge carriers in simplest one-dimensional and three-dimensional helical structures in a simple cubic lattice, which simulates the manganese sublattice in the crystal structure of perovskite, have been derived in the tight-binding approximation. It has been shown that this approach can explain qualitatively the formation of the antiferromagnetic A structure in LaMnO$_3$.