Effect of magnesium deficiency on magnetic properties tuning and cation redistributions of magnesium ferrite nanoparticles

Magnesium nano ferrite Mg_1−xFe₂O₄ with deficient Mg (0 ≤ x ≤ 0.5) has been prepared with the co-precipitation method. The Mg deficiency was examined from the samples elemental compositions obtained by energy-dispersive X-ray spectroscopy. The impact of the Mg deficiency on the structural and magnetic characteristics has been inspected applying X-ray diffraction, Fourier transforms infrared and vibrating sample magnetometer. The structural analysis applying Rietveld method indicated the variation of cation distribution between the octahedral B-site and tetrahedral A-site with the Mg content. The lattice parameter, crystallite size, oxygen coordinates, bond angles and bond lengths are calculated as the function of Mg-deficient content in the samples. From the analysis, the defect spinel structure Mg_1−xFe₂O₄ with Mg²⁺ deficiency could be considered as a solid solution of stoichiometric (1-x)MgFe₂O₄ and (x)${\text{Fe}}_{2.667}^{3+}{◻}_{0.333}{\text{O}}_4$, (□ symbolize cation vacancies) which corresponding to a general formula $\left({\text{Mg}}_{y-x}^{2+}{\text{Fe}}_{1-y}^{3+}\right)\left[{\text{Mg}}_{1-y}^{2+}{\text{Fe}}_{1+y-x/3}^{3+}{◻}_{x/3}\right]{\text{O}}_4$. Fourier transform infrared was used to identify the different ions (Fe³⁺, Fe²⁺, Mg²⁺) in each sample and their location either in A or B sites. The magnetic measurement showed that the samples exhibited a superparamagnetic behavior. Yafet-Kittel and core–shell models were applied in order to understand the samples magnetic behavior. The competition between the amount of Fe²⁺ in B site and crystallite size controlled the coercivity and magnetocrystalline anisotropy behavior of the samples.