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Structure and soft magnetic properties of single-domain Mg$_{1-x}$Ni$_x$Fe$_2$O$_4$ ($0 \le x \le 1.0$) nanocrystals

The effects of Ni$^{2+}$ substitution on the structure (lattice parameters, cations distribution, average cations radii, cation-cation/anion bond lengths and angles) and the soft magnetic properties of Mg$_{1-x}$Ni$_x$Fe$_2$O$_4$ ($0 \le x \le 1.0$) nanocrystals have been studied by x-ray diffraction with Rietveld refinement, transmittance electron microscopy, Mossbauer spectroscopy and magnetization measurements. The mostly inverse spinel structure was found in MgFe$_2$O$_4$ nanoparticles and the inversion factor is further increased by Ni-substitution up to a complete inversion in NiFe$_2$O$_4$. The synthesized ferrites with a small particle size (20 - 30 nm) exhibit soft magnetic properties of a single-domain behavior with critical domain size about 30 - 40 nm. An observed monotonic increase in magnetization and drastic decrease in coercivity at 5 K by Ni-substitution result in a lowest anisotropy constant Ku (2.8 kJ/m3) for x = 0.5. We discuss the evolution of magnetic properties by Ni-substitution in a correlation with a subsequent cations-redistribution between sites of the two sublattices and corresponding structural changes in the inter-ionic distances.