Deciphering temperature-driven magnetic transformations and canting mechanism in the Y₃Fe_5-<i>x</i>Cd<i> _x </i>O₁₂ compound: a coupled molecular field and phenomenological analysis

Their excellent electric and magnetic properties make the yttrium iron garnet (YIG)-based materials suitable for a wide variety of technological applications, such as microwave and magneto-optical devices. So, theoretical and experimental investigations are of great importance to understand and modify their properties. In this study, the Y₃Fe_5-<i>x</i>Cd<i>_x</i>O₁₂compounds were synthesized via the sol-gel method for Cd doping levels of<i>x</i>= 0.00, 0.01, 0.03, 0.05, and 0.07. X-ray diffraction analysis revealed that the single YIG phase is maintained at 100% for<i>x</i>= 0.00 and 0.01, while minor secondary CdO phases are detected at higher doping levels, 0.13% for<i>x</i>= 0.03%, 1.17% for<i>x</i>= 0.05, and 4.42% for<i>x</i>= 0.07. Concurrently, the lattice parameter increased from 12.3808 Å (<i>x</i>= 0.00) to 12.4012 Å (<i>x</i>= 0.07), and the unit cell volume expanded from 1897.8 ųto 1907.4 ų, reflecting the incorporation of some Cd²⁺ions in place of Fe³⁺. Magnetic measurements performed between 100 K and 300 K indicated a systematic decrease in saturation magnetization (<i>M</i>_s) with increasing temperature. The experimental<i>M</i>_svalues, determined by fitting the high-field data (800-10 000 Oe) with the law of approach to saturation, were quantitatively reproduced using a coupled theoretical model that integrates Dionne's modifications to the molecular field coefficients with a phenomenological analysis of cation distribution. The relevance of coupling the models lies in the dependence of the molecular field coefficients on cation distribution, which is critical for accurately calculating the saturation magnetization and understanding the underlying physical mechanisms. Remarkably, considering magnetic moment canting resulted in a maximum relative deviation of only 7.50% from experimental values, compared to discrepancies as high as 38.7% when assuming a collinear arrangement of magnetic moments. The preferential occupancy of Cd²⁺in octahedral sites, with an occupation probability seven orders of magnitude greater than in tetrahedral sites, further underlines its role in modulating the net magnetic moment.