Charge ordering and long-range interactions in layered transition metal oxides

We study the competition between long-range and short-range interactions among holes within the spin density wave picture of layered transition metal oxides. We focus on the problem of charge ordering and the charge phase diagram. We show that the main interactions are the long-range Coulomb interaction and a dipolar short-range interaction generated by the short-range antiferromagnetic fluctuations. We find four different phases depending on the strength of the dipolar interaction and the density of holes: Wigner crystal, diagonal stripes, horizontal-vertical stripes (loops) and a glassy-clumped phase. We discuss the effect of temperature, disorder and lattice effects on these phases.