The scope of this article is to report very detailed results of the measurements of magnetic relaxation phenomena in the new Cu$_{0.5}$Fe$_{2.5}$O$_{4}$ nanoparticles and known CuFe$_{2}$O$_{4}$ nanoparticles. The size of synthesized particles is (6.5$pm $1.5)nm. Both samples show the superparamagnetic behaviour, with the well-defined phenomena of blocking of magnetic moment. This includes the splitting of zero-field-cooled and field-cooled magnetic moment curves, dynamical hysteresis, slow quasi-logarithmic relaxation of magnetic moment below blocking temperature. The scaling of the magnetic moment relaxation data at different temperatures confirms the applicability of the simple thermal relaxation model. The two copper-ferrites with similar structures show significantly different magnetic anisotropy density and other magnetic properties. Investigated systems exhibit the consistency of all obtained results.
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