Inhomogeneous phases in a double-exchange magnet with long range Coulomb interactions

We consider a model with competing double-exchange (ferromagnetic) and superexchange (antiferromagnetic) interactions in the regime where phase separation takes place. The presence of a long range Coulomb interaction frustrates a macroscopic phase separation and favors microscopically inhomogeneous configurations. We use the variational Hartree-Fock approach, in conjunction with Monte Carlo simulations, to study the geometry of such configurations in a two-dimensional system. We find that an array of diamond-shaped ferromagnetic droplets is the preferred configuration at low electronic densities, while alternating ferromagnetic and antiferromagnetic diagonal stripes emerge at higher densities. These findings are expected to be relevant for thin films of colossal magnetoresistive manganates.