Electronic phase separation and other novel phenomena and properties exhibited by mixed-valent rare-earth manganites and related materials

Transition metal oxides, such as the mixed-valent rare-earth manganites $Ln_{(1-x)}AxMnO_3$ (Ln, rare-earth ion, and A, alkaline-earth ion), show a variety of electronic orders with spatially correlated charge, spin and orbital arrangements, which in turn give rise to many fascinating phenomena and properties. These materials are also electronically inhomogeneous, i.e. they contain disjoint spatial regions with different electronic orders. Not only do we observe signatures of such electronic phase separation in a variety of properties, but we can also observe the different ‘phases’ visually through different types of imaging. We discuss various experiments pertaining to electronic orders and electronic inhomogeneities in the manganites and present a discussion of theoretical approaches to their understanding. It is noteworthy that the mixed-valent rare-earth cobaltates of the type $Ln_{(1-x)}AxCoO_3$ also exhibit electronic inhomogeneities just as the manganites