The Relation of Crystallite Size and Ni2+ Content to Ferromagnetic Resonance Properties of Nano Nickel Ferrites

The ferromagnetic resonance and other magnetic properties dependence on $Ni^{2+}/Fe^{3+}$ ratio and crystallite size were investigated for nano nickel ferrite ($NiFe_2O_4$). The crystallite size was controlled by controlling the nickel content in the starting material solution. The XRD and TEM were utilized to measure the crystallite size through Scherrer formula and particle size respectively. The most frequent particle sizes were lower than crystallite size, which ranged from 16.5 to 44.65 nm. The general behavior of M-H loop shapes and parameters showed superparamagnetic one. The saturation magnetization had a maximum value at $Ni^{2+}/Fe^{3+}$ molar ratio equal to 0.186. The FMR signals showed, generally, broad linewidths, where the maximum width and minimum resonance field were for the sample of the lowest crystalline size. Furthermore, FMR resonance field shows linear dependence on crystalline size. The fitting relation was estimated to express this linear dependency on the base of behavior coincidence between particle size and the inverse of saturation magnetization. The given interpretations to understand the intercept and the slope meanings of the fitted relation were based on Larmor equation, and inhomogeneous in the anisotropy constant.