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 $M_{\mathrm{s}}$ increases whereas the coercive field $H_{\mathrm{c}}$ decreases 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 pure ${\text{BaFe}}_{12}{\mathrm{O}}_{19}$ nanoparticle decreases with increasing magnetic field h. The effects of Sm substitution at Ba or Fe sites on ϵ′ and M_s are also studied.

中文翻译：

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纯过渡金属和稀土掺杂 BaFe12O19 纳米颗粒的多铁性

使用微观模型和格林函数技术研究了纯的和 Ni、Zr 和 Sm 掺杂的 BaFe ₁₂ O _19（块状和纳米颗粒）的不同特性。磁化${米}_{\mathrm{秒}}$ 增加而矫顽场 $H_{\mathrm{C}}$随粒径增大而减小。由于拉伸应变，随着 Zr 浓度x的增加，掺杂导致M _s和带隙能量E _g降低，并且由于压缩应变和尺寸效应导致在 Ni 掺杂后M _s和E _g增加。自发极化的行为P _s和介电常数的实部ϵ'是相反的。纯的ϵ′${\text{BaFe}}_{12}{\mathrm{哦}}_{19}$纳米粒子随着磁场h 的增加而减小。还研究了 Sm 取代在 Ba 或 Fe 位点对ϵ'和M _s的影响。