In ferrites, magnetic properties are explicable based on Neel’s two sub-lattice model of ferrimagnetism and the cation distribution over A and B-sites. As per this model the inter sub lattice A-B super-exchange interaction among ions is more effectual than intra sub lattice A-A and B-B interactions. The resultant magnetic moment, nB is the difference in magnetic moments of B and A sublattices, i.e. nB = MB – MA 31. The magnetic moment per ion for Ni2+, Mn2+ , Zn2+, Gd3+ and Fe3+ are 2µB, 5µB ,0, 7µB and 5µB respectively, where µB is the Bohr magneton. The substituted Gd3+ ions preferably occupy octahedral (B) sites owing to their large ionic radius. Rare earths are known to exhibit low temperature magnetic ordering and hence Gd ions, inspite of their large magnetic moment per ion behave like non magnetic entities at room temperature 32. Moreover, nickel and zinc ions are known to occupy octahedral and tetrahedral sites respectively. These factors will reduce the magnetic moment of the B-sub lattice resulting in the decrease of Ms with Gd3+ content 33. This kind of explanation is valid for collinear ferrimagnetism, provided the strongest A-B interaction persists among various cations existing on A and B sublattices. Consequently, for the present ferrite systems based on the proposed cation distribution, the theoretical magnetic moment nB is given by 34, 35
nB = 0.6*2+0.04*5+(1.36-x)*5-(0.16*5+0.64*5) =4.2-5x
The experimental magnetic moment nB’ for ferrite samples has been estimated by the equation 36
where MW is the relative molecular mass, Ms is the specific saturation magnetization in emu g-1 and nB’ is in Bohr magneton and the magnetic factor is 5585.
Calculated experimental and theoretical magnetic moments for different samples have been tabulated in Table 2 and the same is depicted in Fig.5. A huge difference in these two magnetic moments is due to strong deviation from collinear ferrimagnetism. When number of magnetic ions at A site are decreased, A-B interaction weakens and B-B interaction strengthens which result in random spin canting (non collinear spin moments) on B site with respect to the direction of spins of the A site. This leads to decrease in experimental magnetic moment. The spin arrangements in the samples were analyzed by calculating the Yafet-Kittel angles by the relation
Cos? Y_K = (nB’ + M A )/ M B