X-ray diffraction analysis by Williamson-Hall, strain-size, Halder-Wagner, and Nelson–Riley methods, and its co-relationship with elastic and magnetic properties of Ce3+ substituted Fe-rich cobalt ferrite

Abstract Ce-substituted Fe-rich cobalt ferrite nanoparticles with the general formula Co 0.9 Fe 2.1-x Ce x O 4 ( x = 0.0–0.10) were synthesized by a sol–gel auto-combustion route to investigate the interplay between lattice strain, elastic response, and magnetic anisotropy induced by rare-earth doping. X-ray diffraction combined with four independent strain–size models (Williamson–Hall, Size–Strain Plot, Halder–Wagner, and Nelson–Riley) confirmed the formation of a single-phase spinel structure and revealed that Ce incorporation simultaneously increases crystallite size (~ 20–30 nm) and microstrain due to defect-mediated lattice distortion. FTIR-derived force constants and elastic moduli indicate progressive bond softening and porosity-driven reduction in effective stiffness with increasing Ce content. Magnetic measurements show a systematic enhancement of coercivity from 2.8 to 3.8 kOe and an increase in magnetocrystalline anisotropy, originating from Ce-induced lattice strain, defect-mediated domain-wall pinning, and modified spin–orbit coupling. In contrast, the saturation magnetization decreases due to dilution of B-site Fe 3+ by non-magnetic Ce 3+ and the consequent weakening of A–B superexchange interactions, consistent with Néel’s ferrimagnetic model. By correlating multiple strain-analysis models with elastic and magnetic parameters, this work establishes a unified structure–mechanics–magnetism framework for Ce-doped cobalt ferrites, which has not been previously reported. The combination of enhanced coercivity, tunable anisotropy, and defect-engineered elastic response highlights the potential of these materials for high-frequency magnetic devices, spintronic components, and multifunctional oxide-based applications.