  A correlated inhomogeneous mean-field approach is proposed in order to study
a tight-binding model of the manganite heterostructures (LaMnO3)2n/(SrMnO3)n
with average hole doping x = 1/3. Phase diagrams, spectral and optical
properties of large heterostructures (up to 48 sites along the growth
direction) with a single interface are discussed analyzing the effects of
electron-lattice anti-adiabatic fluctuations and strain. The formation of a
metallic ferromagnetic interface is quite robust with varying the strength of
electron-lattice coupling and strain, though the size of the interface region
is strongly dependent on these interactions. The density of states never
vanishes at the chemical potential due to the formation of the interface, but
it shows a rapid suppression with increasing the electron-lattice coupling. The
in-plane and out-of-plane optical conductivities show sharp differences since
the in-plane response has metallic features, while the out-of-plane one is
characterized by a transfer of spectral weight to high frequency. The in-plane
response mainly comes from the region between the two insulating blocks, so
that it provides a clear signature of the formation of the metallic
ferromagnetic interface.
