  Polarized neutron reflectivity measurements of a ferromagnetic
[(LaMnO$_3$)$_{11.8}$/(SrMnO$_3$)$_{4.4}$]$_6$ superlattice reveal a modulated
magnetic structure with an enhanced magnetization at the interfaces where
LaMnO$_3$ was deposited on SrMnO$_3$ (LMO/SMO). However, the opposite
interfaces (SMO/LMO) are found to have a reduced ferromagnetic moment. The
magnetic asymmetry arises from the difference in lateral structural roughness
of the two interfaces observed via electron microscopy, with strong
ferromagnetism present at the interfaces that are atomically smooth over tens
of nanometers. This result demonstrates that atomic-scale roughness can
destabilize interfacial phases in complex oxide heterostructures.
