Magnetic response of Ho³⁺ doped Ni_0.4Cu_0.6Ho_yFe_2-yO₄ spinel ferrites and their correlation with crystallite size

This study investigates the magnetic response of Ho³⁺ doped Ni_0.4Cu_0.6Ho_yFe_2-yO₄ (y = 0.0, 0.02, 0.04, 0.06, and 0.08) spinel ferrites (SFs) and their correlation with crystallite size. The synthesis was achieved using a sol-gel auto-combustion (SGAC) route and performed different characterizations, including X-ray diffraction (XRD), Scanning electron microscope (SEM), Energy dispersive x-ray (EDX), Inductively coupled plasma atomic emission spectroscopy (ICP-AES), and vibrating sample magnetometer (VSM) analysis. The cubic spinel phase was verified via XRD in pure NCF and Ho³⁺ doped NCF samples. The lattice constant (a) was improved from 8.344 Å to 8.378 Å. The substitution of Ho³⁺ ions led to a decrease in porosity from 42.22 % to 39.54 %. The introduction of Ho³⁺ ions also reduced the crystallite size (D) from 37.05 nm to 27.72 nm. The specific surface area (S) was increased from 27.44 g/cm² to 36.14 g/cm² with the doping of Ho³⁺. The average particle size (D_S) was decreased from 54 nm to 35 nm. The EDX and ICP-AES analyses confirmed the good agreement with the theoretical composition. The VSM measurements provided insights into their magnetic properties. Furthermore, the doping of Ho³⁺ ions enhanced coercivity (H_C), while reducing saturation magnetization (M_S) from 64.35 emu/g to 16.22 emu/g. The decrease in crystalline anisotropy (K) observed at higher concentrations of Ho³⁺ may result from the increase in coercivity, potentially attributable to the smaller crystallite size of the single-domain SFs particles. The single-phase matrix and their magnetic behaviour showed that the Ho³⁺ doped Ni–Cu SFs samples are suitable for high-frequency applications.