Striped Multiferroic Phases in Narrow Bandwidth Hole-Doped Manganites

A novel phase with diagonal charge stripes and a complex spin arrangement that allows for ferroelectricity to develop has been recently reported in a model for hole-quarter-doped manganites (S. Dong et al., Phys. Rev. Lett. {\bf 103}, 107204 (2009)). The study of this ``spin-orthogonal stripe'' (SOS) phase is here generalized to other hole doping fractions $x=1/N$ ($N=3$, $5$, $6$, ...), to search for analogous multiferroic states. In this effort, the two-orbital double-exchange model for manganites is studied, employing variational, Monte Carlo, and zero temperature optimization techniques. The phase diagrams obtained by varying the electron-lattice and superexchange couplings also contains exotic C$_{x}$E$_{1-x}$ phases. A systematic procedure to construct new C$_{x}$E$_{1-x}$/SOS$_x$ phases is discussed. Both the Dzyaloshinskii-Moriya interaction and exchange-striction effect may work in these C$_{x}$E$_{1-x}$/SOS$_x$ phases, giving rise to ferroelectricity. In addition, these SOS$_x$/C$_{x}$E$_{1-x}$ phases can be extended into many other similar states, with (almost) degenerate energies but different multiferroic properties.