Two-dimensional electron gas at the interface of Ba$_{0.8}$Sr$_{0.2}$TiO$_3$ ferroelectric and LaMnO$_3$ antiferomagnet

The temperature dependence of the electrical resistance has been studied for heterostructures formed by antiferromagnetic LaMnO$_3$ single crystals of different orientations with epitaxial films of ferroelectric Ba$_{0.8}$Sr$_{0.2}$TiO$_3$ deposited onto them. The measured electrical resistance is compared to that exhibited by LaMnO$_3$ single crystals without the films. It is found that, in the samples with the film, for which the axis of polarization in the ferroelectric is directed along the perpendicular to the surface of the single crystal, the electrical resistance decreases significantly with temperature, exhibiting metallic behavior below 160 K. The numerical simulations of the structural and electronic characteristics of the BaTiO$_3$/LaMnO$_3$ ferroelectric-antiferromagnet heterostructure has been performed. The transition to the state with two-dimensional electron gas at the interface is demonstrated.