| Summary: | MnFe<sub>2</sub>O<sub>4</sub> ferrite nanoparticle was synthesized via the sol–gel method, and structural, morphology and magnetic characteristics were investigated. X-ray diffraction analysis showed that the synthesized sample was in a single phase with a spinel-ferrite-like structure (space group Fd-3m). The scanning electron microscopy displayed homogenous spherical grains with an agglomeration of the particles. The chemical composition determined by energy-dispersive spectroscopy shows the absence of any impurities. To understand the role of magnetic interaction in MnFe<sub>2</sub>O<sub>4</sub> spinel ferrites, the structural and magnetic properties of MnFe<sub>2</sub>O<sub>4</sub> have been explored theoretically. Based on the first-principles methods via density functional theory and Monte Carlo simulations, the magnetic hysteresis cycle has been plotted. Using the generalized gradient and GGA-PBE approximation in the full-potential linearized augmented plane wave (FP-LAPW) method, the exchange coupling interactions between magnetic elements and local magnetic moment were evaluated. Furthermore, the theoretical magnetic properties of MnFe<sub>2</sub>O<sub>4</sub> were found to match the experimental ones. They both revealed that MnFe<sub>2</sub>O<sub>4</sub> is a soft ferromagnetic material. The theoretical curve of magnetization versus temperature indicates that the transition occurred at T<sub>c</sub> = 580.0 K. This was also in good agreement with the experimental Curie temperature.
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