**Abstract**

Multiferroic magnetoelectric material has significance for new design nanoscale spintronic devices. In single-phase multiferroic BaTiO3, the magnetism occurs with doping of transition metals, TM ions, which has partially filled d-orbitals. Interestingly, the magnetic ordering is strongly related with oxygen vacancies, and thus, it is thought to be a source of ferromagnetism of TM:BaTiO3. The nanostructural MFe2O4 (M = Mn, Co, Ni, Cu, Zn, etc.) ferrite has an inverse spinel structure, for which M2+ ions in octahedral site and Fe3+ ions are equally distributed between tetrahedral and octahedral sites. These antiparallel sublattices (cations M2+ and Fe3+ occupy either tetrahedral or octahedral sites) are coupled with O2- ion due to superexchange interaction to form ferrimagnetic structure. Moreover, the future spintronic technologies using diluted magnetic semiconductors, DMS materials might have realized ferromagnetic origin. A simultaneous doping from TM and rare earth ions in ZnO nanoparticles could increase the antiferromagnetic ordering to achieve high-Tc ferromagnetism. The role of the oxygen vacancies as the dominant defects in doped ZnO that must involve bound magnetic polarons as the origin of ferromagnetism.

**Keywords:** magnetically ordered material, oxygen vacancies, spin glass
