Investigation of the magnetic and dielectric properties of rare earth (Ho, Er) Co-substitution in stoichiometry modified cobalt ferrites nanocrystals

Stoichiometric-modified cobalt ferrites co-substituted with rare earth (Ho, Er) CoFe_1.98-2xHo_xEr_xO₄ (x = 0.05, 0.10 and 0.15), designated as HESMCF, were synthesized by the sol-gel method. Structural characterization using X-ray diffraction (XRD), Fourier Transform Infrared (FTIR) and Raman spectroscopy confirmed the formation of the spinel structure. XRD analysis indicated a compression of the unit cell (V), a reduction in the crystallite sizes (D) and an increase in microstrain (ε) with co-substitution. The room-temperature magnetic properties of HESMCF were investigated using a Vibrating Sample Magnetometer (VSM). The initial magnetization (MH) curves, fitted to the Law of Approach to Saturation (LAS), demonstrated a reduction in the saturation magnetization (M_s) and magnetocrystalline anisotropy (K₁). The MH curves showed a reduction in loop size, revealing magnetic softening accompanied by a decrease in coercivity (H_c) with co-substitution. The resistivity (Z′) showed enhanced insulating properties with co-substitution. The impedance (Z″) spectra revealed multiple relaxation processes that become more pronounced with increasing temperature, indicating thermally activated relaxation dynamics, which were further elucidated using electric modulus spectroscopy and Nyquist plots. The dielectric constant (ε′) and permittivity (ε′′) decreased with co-substitution due to the redistribution of cations and the reduction in Fe ions within the system, hindering polarization mechanisms. The ac conductivity (σ_ac) was described by Jonscher's Power Law (JPL). The temperature variations of the frequency exponent (s) displayed the transition of conduction mechanisms with the increase in temperature. A comparative analysis was also conducted with Ho and Er co-substitution in standard stoichiometry cobalt ferrites nanocrystal (HESSCF).