Multiferroic Properties of Pure, Transition‐Metal and Rare‐Earth–Doped BaFe 12 O 19 Nanoparticles

Different properties of pure and Ni, Zr, and Sm‐doped BaFe 12 O 19 —bulk and nanoparticles—are investigated using a microscopic model and the Green's function technique. The magnetizationM sincreases whereas the coercive fieldH cdecreases with increasing particle size. The doping leads to a decrease of M s and the bandgap energy E g with increasing Zr concentration x due to tensile strain and to an increase of M s and E g after Ni doping due to compressive strain as well as due to size effects. The behavior of the spontaneous polarization P s and the real part ϵ′ of the dielectric constant is opposite. The ϵ′ of a pureBaFe 12 O 19nanoparticle decreases with increasing magnetic field h . The effects of Sm substitution at Ba or Fe sites on ϵ′ and M s are also studied.