Mesoscale charge-ordering in transition metal oxides: Formation and signatures

We briefly outline the value of an inhomogeneous (unrestricted) Hartree-Fock plus Random Phase approach for understanding the types and properties of mesoscopic patterns of localized small polarons in transition metal oxides. Using a multiband Peierls-Hubbard model for a hole-doped CuO2 layer as an illustrative example, we demonstrate the appearance of correlated high-energy (electronic) and low-energy (localized phonon and spin-wave) signatures of various vertical, diagonal, metal-centered, and oxygen-centered mesoscopic stripe patterns of localized holes (small polarons). This represents important inhomogeneous magneto-elastic coupling.