This study explored the microstructural and magnetic features of NiFe_2−xDy_xO₄ (x ≤ 0.10) NPs (nanoparticles) that were synthesized by sol–gel auto-combustion method. The single phase of spinel ferrite has been verified for all samples without any impurity. The cubic morphology of the products was also showed by SEM. Room temperature (300 K) and 10 K magnetization curves were recorded applying a dc magnetic field up to ±50 kOe and it was observed that magnetic features of NiFe₂O₄ NPs significantly changed by the substitution of Dy³⁺ ion. Magnetization measurements showed low order of 300 and 10 K magnetic parameters (such as K_eff, coercivity and anisotropy field values), revealing soft ferrimagnetic behaviors of all pristine and doped NiDy_xFe_2−xO₄ (0.00 ≤ x ≤ 0.10) NPs at both 300 and 10 K. Pristine NiFe₂O₄ has maximum magnetic moment and saturation magnetization values among all samples. Dy³⁺ substitution showed a slight decrement in magnetization values compared with pristine sample. A slight increase in coercivity was noticed with Dy³⁺ substitution. Squareness ratios (SQRs) have a range between 0.144 and 0.324. These values are smaller than the theoretical limit of 0.50, implying the multi-domain nature for NPs. Blocking temperature (T_B) was calculated as 28 K for NiFe₂O₄ NPs.

Pure phase of NiDy_xFe_2−xO₄ (0.00 ≤ x ≤ 0.10) nanoparticles were prepared via sol–gel auto-combustion process. The structure, morphology, and magnetic properties were investigated.

本研究探讨的NiFe的微观结构和磁性特征_{2- X}的Dy _X ø ₄（X  ≤0.10）通过溶胶-凝胶自燃烧法合成的纳米颗粒（纳米颗粒）。尖晶石铁氧体的单相已针对所有样品进行了验证，没有任何杂质。SEM也显示出产物的立方形态。在高达±50 kOe的直流磁场下记录了室温（300 K）和10 K的磁化曲线，并且观察到NiFe ₂ O ₄ NPs的磁学特征因Dy ³⁺离子的取代而显着变化。磁化测量显示300和10 K的低磁性参数（例如K_EFF，矫顽力和各向异性磁场的值），揭示所有原始的软铁磁行为和掺杂NiDy _X的Fe _{2- X} ø ₄（0.00≤  X  ≤0.10）在两端300和10 K.质朴的NiFe的NP ₂ ö ₄具有最大的磁矩所有样品之间的饱和磁化强度值。与原始样品相比，Dy ³⁺取代显示出磁化值略有下降。Dy ³⁺使矫顽力略有增加替代。矩形比（SQRs）的范围介于0.144和0.324之间。这些值小于理论极限值0.50，这意味着NP具有多域性质。阻断温度（Ť_乙）计算为28 K中的NiFe ₂ ö _4周的NP。

NiDy的纯相_X的Fe _{2- X} ø ₄（0.00≤  X  ≤0.10）通过溶胶-凝胶自燃烧过程中制备纳米颗粒。研究了其结构，形态和磁性能。