  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.
