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. However, 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; oxygen vacancies interacting with grain boundaries (GBs) bring about (anti)ferromagnetism with localized spin moments at the neighboring Ti atoms. This is due to spin-polarized defect states with broken orbital symmetries at GBs. In addition, the energetics of oxygen vacancies indicates their self-assembling nature at GBs resulting in considerably high concentration, which convert the oxygen-deficient GBs into multiferroic monolayers due to their atomically thin interfacial structure. This synthetic concept that realizes multiferroic and multifunctional oxides in a monolayered geometry through the self-assembly of atomic defects and grain boundary engineering opens a new avenue for promising paradigms of novel functional devices.