Multiferroic grain boundaries in oxygen-deficient ferroelectric lead titanate

Ultimately thin multiferroics arouse remarkable interest, motivated by the diverse utility of coexisting ferroelectric and (anti)ferromagnetic order parameters for novel functional device paradigms. ever, the ferroic order is inevitably destroyed below a critical size of several nanometers. Here, we demonstrate a new path toward realization of atomically thin multiferroic monolayers while resolving a controversial origin for unexpected dilute ferromagnetism emerged in nanocrystals of nonmagnetic ferroelectrics PbTiO3. The state-of-the-art hybrid functional of Hartree?Fock and density functional theories successfully identifies the origin and underlying physics