Octahedral-Site Engineering by Er3+ Substitution Enables Tunable Magneto-Dielectric Response in Ni–Zn–Cr Spinel Ferrites

Ni 0.7 Zn 0.3 Cr 0.5 Fe 1.5-x Er x O 4 (x = 0.00–0.05) nanoferrites were synthesized by sol–gel auto-combustion to establish how low-level Er 3+ substitution controls cation distribution, local bonding, dielectric transport, and ferrimagnetic ordering. Rietveld-refined XRD patterns confirmed single-phase cubic spinel formation, with Er 3+ inducing slight lattice expansion, increased microstrain, and crystallite-size reduction from 20.3 to 12.7 nm. Bertaut-type cation-distribution analysis suggested a most probable average configuration, with a nearly stable tetrahedral arrangement, (Zn 0.3 Fe 0.7 ) A , and preferential replacement of Fe 3+ by Er 3+ at octahedral B-sites. This B-site modification increased r B from 0.6533 to 0.6594 Å and a th from 8.3519 to 8.3682 Å, while tetrahedral bond parameters remained nearly unchanged. FTIR-derived force constants decreased with Er addition, indicating weakening of the metal–oxygen framework, particularly at octahedral sites. Elastic softening was confirmed by the decrease in C 11 from 161.83 to 154.52 GPa and Young’s modulus from 47.62 to 45.47 GPa. Dielectric spectra followed Maxwell–Wagner-Koops behavior, while ac conductivity obeyed Jonscher’s power law, evidencing localized hopping transport. Magnetically, Ms decreased from 40.9 to 30.6 emu g -1 , whereas Hc remained nearly constant near 750 Oe. The decrease in n B(exp) and increase in θ YK confirmed enhanced B-sublattice spin canting. These results identify Er 3+ substitution as an effective route for tuning octahedral-site chemistry, lattice rigidity, dielectric polarization, and magnetic exchange in Ni–Zn–Cr ferrites for high-frequency magneto-dielectric applications.