Charge ordering and long-range interactions in layered transition metal oxides: A quasiclassical continuum study

The competition between long-range and short-range interactions among holes moving in an antiferromagnet (AF) is studied within a model derived from t he spin-density-wave picture of layered transition metal oxides.A novel num erical approach is developed that allows one to solve the problem at finite hole densities in very large systems (of the order of hundreds of lattice spacings), albeit in a quasiclassical limit, and to correctly incorporate t he long-range part of the Coulomb interaction. The focus is on the problem of charge ordering and the charge phase diagram: at low temperatures four d ifferent Phases are found, depending on the strength of the magnetic (dipol ar) interaction generated by the spin-wave exchange and the density of hole s. The four phases are the Wigner crystal, diagonal stripes, a grid phase ( horizontal-vertical stripe loops), and a glassy-clumped phase. In the prese nce of both in-plane and out-of-plane charged impurities the stripe orderin g is suppressed, although finite stripe segments persist. At finite tempera tures multiscale (intermittency) dynamics is found, reminiscent of that in glasses. The dynamics of stripe melting and its implications for experiment s is discussed.