Influence of variation of structural parameters on magnetic properties of Al-substituted Ni spinel ferrite

It is very important to study the structural properties of the material to understand the physical properties. According to suggested cations distribution of Ni–Al ferrite as the formula \(({\text{Fe}}_{1 - t}^{3 + } {\text{Al}}_{t}^{3 + } )\left\{ {{\text{Ni}}^{2 + } {\text{Al}}_{x - t}^{3 + } {\text{Fe}}_{1 - x + t}^{3 + } } \right\}{\text{O}}_{4}^{2 - }\), with (\(0.0 \le x \le 0.5\)) and (\(0.0 \le t \le 0.1\)), the structural parameters were studied. The cations radii of tetrahedral (\(R_{{\text{T}}}\)) did not change, but octahedral (\(R_{O}\)) sites decreased with increasing Al³⁺ ions. Lattice constants (\(a_{{{\text{th}}}}\)) decreased with increasing Al content. The values of \(u^{{\overline{4}3m}}\) changed over the ranged 0.3818538155, whereas the values of \(u^{{\overline{3}m}}\) varied from 0.25685 to 0.25655. With increasing Al content, M–M lengths decreased, in addition, the bond lengths q, r, and s decreased except p. In addition, with increasing Al³⁺ ions, \(\theta_{1}\), \(\theta_{2}\), and \(\theta_{5}\) decreased but \(\theta_{3}\) and \(\theta_{4}\) increased. \(d_{{{\text{TE}}}}\) and \(d_{{{\text{TL}}}}\) were constant, whereas \(d_{{{\text{OEu}}}}\), \(d_{{{\text{OL}}}} ,\) and \(d_{{{\text{OE}}}}\) decreased with increasing Al³⁺ ions. \(L_{{{\text{T{-}T}}}}\), \(L_{{{\text{O{-}O}}}} ,\) and \(L_{{{\text{T{-}O}}}}\) reflected the same behavior as that of \(a_{{{\text{th}}}}\), where they decreased with increasing Al³⁺ ions concentration. As a result, the incorporation of non-magnetic Al³⁺ ions into the given ferrite system reduces the strength of the magnetic interactions, which relates to the changing on structural parameters.