The effects of Ce–Dy co-doping on the crystal structure, optical, dielectric, magnetic properties, and hyperfine interactions of Ni–Co spinel ferrite microspheres synthesized hydrothermally have been studied. A series of ferrites with the general formula Ni0.5Co0.5CexDyxFe2-2xO4 were synthesized with x values ranging from 0.00 to 0.10. The phase, crystallinity, and morphology of ferrite microspheres were analyzed by X-ray powder diffractometry (XRD), scanning and transmission electron microscopes (SEM and TEM), respectively. The structural analyses of the synthesized ferrite microspheres confirmed their high purity and cubic crystalline phase. The Diffuse reflectance spectroscopic (DRS) measurements were presented to calculate direct optical energy band gaps (Eg) and is found in the range 1.63 eV - 1.84 eV. 57Fe Mossbauer spectroscopy showed that the hyperfine magnetic field of tetrahedral (A) and octahedral (B) sites decreased with the substitution of Dy3+-Ce3+ ions that preferrentially occupy the B site. The impact of the rare-earth content (x) on the magnetic features of the prepared NiCo ferrite microspheres was investigated by analyzing M-H loops, which showed soft ferrimagnetism. The magnetic features illustrate a great impact of the incorporation of Ce3+-Dy3+ ions within the NiCo ferrite structure. The saturation magnetization (Ms), remanence (Mr), and coercivity (Hc) increased gradually with increasing Ce–Dy content. At x = 0.04, Ms, Mr, and Hc attain maximum values of about 31.2 emu/g, 11.5 emu/g, and 512.4 Oe, respectively. The Bohr magneton (nB) and magneto-crystalline anisotropy constant (Keff) were also determined and evaluated with correlation to other magnetic parameters. Further increase in Ce3+-Dy3+ content (i.e., x ≥ 0.06) was found to decrease Ms, Mr, and Hc values. The variations in magnetic parameters (Ms, Mr, and Hc) were largely caused by the surface spins effect, the variations in crystallite/particle size, the distribution of magnetic ions into the different sublattices, the evolutions of magneto-crystalline anisotropy, and the variations in the magnetic moment (nB). The squareness ratios were found to be lower than the predicted theoretical value of 0.5 for various samples, indicating that the prepared Ce–Dy substituted NiCo ferrite microspheres are composed of NPs with single-magnetic domain (SMD). Temperature and frequency-dependent electrical and dielectric measurements have been done to estimate the ac/dc conductivity, dielectric constant, and tangent loss values for all the samples. The ac conductivity measurements confirmed the power-law rules, largely dependent on Ce–Dy content. Impedance analysis stated that the conduction mechanisms in all samples are mainly due to the grains-grain boundaries. The dielectric constant of NiCo ferrite microspheres give rise to normal dielectric distribution, with the frequency depending strongly on the Ce–Dy content. The observed variation in tangential loss with frequency can be attributed to the conduction mechanism in ferrites, like Koop's phenomenological model.
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