Effect of spin modulation on electronic phase separation in the double exchange model with Coulomb repulsion

We investigate the effect of spatial modulation of spin on electronic phase separation (PS) in the double exchange model with Coulomb repulsion and electron-phonon coupling. We show that the spatial modulation of the spin-density-wave (SDW) state, as well as the paramagnetic state, of e_g holes has a significant impact on the canted angle in the homogeneous phase and on the stable hole concentration in the segregated phase. The long-range Coulomb interaction plays an important role in stabilizing the segregated two-phase state, and we determine the corresponding critical values analytically. We also study the effects of the external magnetic field and of quantum fluctuation of the SDW order parameter on the PS; our results show that the former favors but the latter inhibits the PS. We discuss the implications of our results for the perovskite manganites La_1-xA_xMnO₃.