Structural, elastic, magnetic, magnetocaloric, and critical properties of Bi-substituted Cu0.5Cd0.5Fe2-xBixO4 ferrites prepared by sol–gel synthesis

Abstract

A series of Cu_0.5Cd_0.5Fe_2-xBi_xO₄ spinel ferrites with x = 0, 0.05, and 0.1 was synthesized by the sol–gel technique in order to assess the influence of Bi³⁺ substitution on their XPS, structural, elastic, magnetic, magnetocaloric, and critical characteristics. The oxidation states and lattice-site distributions of the metal cations were characterized via X-ray photoelectron spectroscopy (XPS). X-ray diffraction (XRD) and Rietveld refinement confirmed a cubic spinel structure ($Fd\bar{3}m$), with a secondary Bi₂O₃ phase detected in the Bi-substituted compositions (x = 0.05 and 0.10). Lattice parameters, crystallite size, and X-ray density increased with x, attributed to the larger ionic radius of Bi³⁺. Infrared spectroscopy and derived elastic constants revealed a significant enhancement in lattice stiffness, force constants, and Debye temperature, indicating strengthened interatomic bonding. Magnetization measurements showed a decrease in Curie temperature (T_C) and magnetization with increasing Bi concentration, due to the dilution of Fe³⁺–O²⁺–Fe³⁺ superexchange interactions by non-magnetic Bi³⁺ ions. The ferrimagnetic–paramagnetic transition remains of second order, as confirmed by the Arrott plot analysis. Under an applied magnetic field of 5 T, the maximum magnetic entropy change ($\left|\Delta S_M^{\max }\right|$) and the relative cooling power (RCP) reach 1.67 J kg⁻¹ K⁻¹ and 115 J kg⁻¹, respectively, for the undoped sample (x = 0), and both quantities systematically decrease with increasing Bi substitution. Critical exponent analysis, employing modified Arrott plots and the Kouvel-Fisher method, demonstrated that the phase transition belongs to the three-dimensional Heisenberg universality class (β = 0.365, γ = 1.336, δ = 4.8). Moreover, increasing Bi content leads to a systematic decrease in β and increase in γ and δ, reflecting enhanced critical spin fluctuations due to the progressive magnetic dilution of the Fe³⁺ sublattice by non-magnetic Bi³⁺ ions.