Ferromagnetic zigzag chains and properties of the charge-ordered perovskite manganites

The low-temperature properties of the so-called ''charge-ordered'' state in 50% doped perovskite manganites are described from the viewpoint of the magnetic spin ordering. In these systems, the zigzag antiferromagnetic ordering, combined with the double exchange physics, effectively divides the whole sample into the one-dimensional ferromagnetic zigzag chains and results in the anisotropy of electronic properties. The electronic structure of one such chain is described by an effective 3x3 Hamiltonian in the basis of Mn(3de(g)) orbitals. We treat this problem analytically and consider the following properties: (i) the nearest-neighbor magnetic interactions; (ii) the distribution of the Mn(3 de(g)) and Mn(4p) states near the Fermi level, and their contribution to the optical conductivity and the resonant x-ray scattering near the Mn K-absorption edge. We argue that the anisotropy of magnetic interactions in the double exchange limit, combined with the isotropic superexchange interactions, readily explains both the local and the global stability of the zigzag antiferromagnetic state. The twofold degeneracy of e(g) levels plays a very important role in the problem and explains the insulating behavior of the zigzag chain, as well as the appearance of the orbital ordering in the double exchange model. Importantly, however, the charge ordering itself is expected to play only a minor role and is incompatible with the ferromagnetic coupling within the chain. We also discuss possible effects of the Jahn-Teller distortion and compare the tight-binding picture with results of band-structure calculations in the local-spin-density approximation.