Combined experimental and DFT + U analysis of lattice distortion and spin-resolved behavior in Ca-substituted Ni-Zn...

Ca-substituted Ni-Zn spinel ferrite Ni_0.32Zn_0.58Ca_0.10Fe₂O₄ was synthesized by co-precipitation and investigated using experimental characterization and spin-polarized density functional theory calculations with an on-site Hubbard correction (DFT + U). X-ray diffraction (XRD) confirmed a dominant cubic spinel phase, while preliminary whole-pattern profile analysis yielded a = 8.4119 Å, V = 595.235 ų, R _p = 4.02%, and R _wp = 5.01%. The average crystallite size was approximately 38 nm, with microstrain and dislocation-density values indicating Ca-induced lattice distortion. Raman spectroscopy revealed metal-oxygen vibrational modes associated with tetrahedral and octahedral sites, suggesting local disorder and possible cation redistribution. Scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS) confirmed agglomerated morphology and the presence of Ni, Zn, Ca, Fe, and O. For the selected approximate computational configuration, DFT + U calculations produced energy gaps of approximately 2.2 and 2.9 eV along the examined Γ-X-Γ direction for the spin-up and spin-down channels, respectively, and a total magnetic moment of 7.5µ _B for the 70-atom supercell, corresponding to 0.75µ _B per formula unit.