Multiferroic Domain Walls in Ferroelectric PbTiO3 with Oxygen Deficiency.

Atomically thin multiferroics with the coexistence and cross-coupling of ferroelectric and (anti)ferromagnetic order parameters are promising for novel magnetoelectric nanodevices. However, such ferroic order disappears at a critical thickness in nanoscale. Here, we show a potential path toward ultrathin multiferroics by engineering an unusual domain wall (DW)-oxygen vacancy interaction in nonmagnetic ferroelectric PbTiO3. We demonstrate from first-principles that oxygen vacancies formed at the DW unexpectedly bring about magnetism with a localized spin moment around the vacancy. This magnetism originates from the orbital symmetry breaking of the defect electronic state due to local crystal symmetry breaking at the DW. Moreover, the energetics of defects shows the self-organization feature of oxygen vacancies at the DW, resulting in a planar-arrayed concentration of magnetic oxygen vacancies, which consequently changes the deficient DWs into multiferroic atomic layers. This DW-vacancy engineering opens up...