Electronic, lattice, and spin interactions at the interfaces between crystalline complex transition metal oxides can give rise to a wide range of functional electronic and magnetic phenomena not found in bulk. At hetero-interfaces, these interactions may be enhanced by combining oxides where the polarity changes at the interface. The physical structure between non-polar SrTiO$_3$ and polar La$_{1-x}$Sr$_x$MnO$_3$(x=0.2) is investigated using high resolution synchrotron x-ray diffraction to directly determine the role of structure in compensating the polar discontinuity. At both the oxide-oxide interface and vacuum-oxide interfaces, the lattice is found to expand and rumple along the growth direction. The SrTiO$_3$/La$_{1-x}$Sr$_x$MnO$_3$ interface also exhibits intermixing of La and Sr over a few unit cells. The results, hence, demonstrate that polar distortions and ionic intermixing coexist and both pathways play a significant role at interfaces with polar discontinuities.
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