This paper investigates the bismuth ions leverage on magnetic and dielectric features of magnesium–copper nanoferrites Mg_0.5Cu_0.5Bi_xFe_2-xO₄ (MCBF). The Mg_0.5Cu_0.5Bi_0.1Fe_1.9O₄ nanoferrite exhibits superior magnetic properties compared to the pure Mg-Cu sample. These properties include a higher magnetization of 31.31 emu/g, with an enhancing ratio of 1.50 %. Additionally, it demonstrates a higher initial permeability of 17.84, with an enhancing ratio of 55.12 %. Furthermore, their coercivity is lower at 59.90 Oe, with an enhancing ratio of 50 %. All MCBF nanoferrites exhibit a high-frequency response between 6.106 and 6.926 GHz, making them suitable for microwave technology. The dielectric parameters dispersion shows normal behavior at different frequencies and temperatures. As for dielectric parameters dependence on Bi content, it exhibited a peculiar manner. At a temperature of 297 K and a frequency of 50 Hz, the nanoferrite Mg_0.5Cu_0.5Bi_0.1Fe_1.9O₄ exhibits superior dielectric properties compared to the pure Mg-Cu sample. Specifically, it demonstrates the highest dielectric constant of 360.68, with an enhancing ratio of 125.97 %. Additionally, it displays the highest conductivity of 691.4 µ(Ω.m)^-1, with an enhancing ratio of 1543.23 %. Furthermore, the nanoferrite exhibits a lower dielectric loss of 6.49, with an enhancing ratio of 80.22 % compared to the pure Mg-Cu sample. The conduction mechanism of the Mg_0.5Cu_0.5Bi_xFe_2-xO₄ nanoferrites was determined by fitting the σ_ac results via the Jonscher power law. This conduction mechanism is attributed to correlated barrier hopping (CBH) model up to 473 K, followed by small polaron tunneling (SPT), which reaches higher temperatures. Hence, the Mg_0.5Cu_0.5Bi_0.1Fe_1.9O₄ nanoferrite has a remarkable magnetic and dielectric nature, which can be used as functional soft ferrite material in transformers and high-frequency electronic devices.

本文研究了铋离子对镁铜纳米铁氧体 Mg _0.5 Cu _0.5 Bi _x Fe _2-x O ₄ (MCBF) 磁性和介电特性的影响。与纯Mg-Cu样品相比，Mg _0.5 Cu _0.5 Bi _0.1 Fe _1.9 O _{4纳米铁氧体表现出优异的磁性能。}这些特性包括高达 31.31 emu/g 的磁化强度，增强率为 1.50%。此外，它还表现出较高的初始渗透率，达到17.84，增强率为55.12%。此外，它们的矫顽力较低，为59.90 Oe，增强率为50%。所有 MCBF 纳米铁氧体均表现出 6.106 至 6.926 GHz 之间的高频响应，使其适用于微波技术。介电参数色散在不同频率和温度下表现出正常行为。至于介电参数对Bi含量的依赖性，它表现出一种特殊的方式。在297 K的温度和50 Hz的频率下，纳米铁氧体Mg _0.5 Cu _0.5 Bi _0.1 Fe _1.9 O ₄与纯Mg-Cu样品相比表现出优异的介电性能。具体而言，其介电常数最高为360.68，增强率为125.97%。此外，其电导率最高为691.4 µ(Ω.m) ^-1，增强率为1543.23 %。此外，纳米铁氧体的介电损耗较低，为6.49，与纯Mg-Cu样品相比，增强率为80.22%。_{Mg 0.5} Cu _0.5 Bi _x Fe _2-x O ₄纳米铁氧体的传导机制是通过 Jonscher 幂律拟合 σ _{ac结果来确定的。}这种传导机制归因于高达 473 K 的相关势垒跳跃 (CBH) 模型，随后是小极化子隧道 (SPT)，可达到更高的温度。因此，Mg _0.5 Cu _0.5 Bi _0.1 Fe _1.9 O ₄纳米铁氧体具有显着的磁和介电性质，可用作变压器和高频电子器件中的功能软铁氧体材料。