<p>A series of Cu-doped MgFe₂O₄ nanoparticles were synthesized via a citrate precursor auto-combustion technique. x-ray diffraction (XRD) data of the as-synthesized and annealed nanopowders reveal the formation of the spinel structure single-phase with an fd-3&#xa0;m space group, except for the annealed CuFe₂O₄ with space group I41/amd, which reveals a tetragonal structure, according to the Rietveld analysis. Transmission electron microscope (TEM) and scanning electron microscope (SEM) micrographs display the agglomerations of irregular shapes of Cu_xMg_1-xFe₂O₄ nanoparticles with uniform particle sizes. Moreover, energy-dispersive x-ray analysis (EDX) confirms that the required elements are present. The magnetic analyses at ambient normal temperature showed that ferrimagnetic behavior of ferrites is normal, and a large coercivity value of 1.18 kOe is measured for tetragonal CuFe₂O₄. For the produced Cu_xMg_1-xFe₂O₄ nanoparticles, dielectric characteristics such as the real and imaginary parts of dielectric permittivity (ε′, ε′′) and the loss tangent (tan δ) decreased with increasing frequency. Furthermore, to identify the diffusion of carriers from one state to another, the activation energy was calculated. The study of the electric modulus suggested that relaxation processes in Cu_xMg_1-xFe₂O₄ compositions are of a ‘non-Debye type.</p> Graphical abstract <p></p>