Multiferroic Properties of Pure, Transition‐Metal and Rare‐Earth–Doped BaFe12O19 Nanoparticles

Different properties of pure and Ni, Zr, and Sm‐doped BaFe12O19—bulk and nanoparticles—are investigated using a microscopic model and the Green's function technique. The magnetization Ms increases whereas the coercive field Hc decreases with increasing particle size. The doping leads to a decrease of Ms and the bandgap energy Eg with increasing Zr concentration x due to tensile strain and to an increase of Ms and Eg after Ni doping due to compressive strain as well as due to size effects. The behavior of the spontaneous polarization Ps and the real part ϵ′ of the dielectric constant is opposite. The ϵ′ of a pure BaFe12O19 nanoparticle decreases with increasing magnetic field h. The effects of Sm substitution at Ba or Fe sites on ϵ′ and Ms are also studied. Multiferroic nanoparticles display an increase of the magnetization M and a decrease of the coercitive field with increasing particle size. Zr doping reduces M, whereas it is enhanced by Ni doping. The polarization and the dielectric function offer the opposite behavior. The dielectric function depends strongly on the position of the dopant Sm at Fe or Ba sites.