The temperature-dependent magnetic moment of a magnetically ordered material is fundamental to all aspects of its technological applications. In ferrimagnetic materials with multiple sublattices containing different magnetic ions, the magnetization can vary nonmonotonically with temperature. Computational modeling of these materials provides insight into their sublattice occupancy and prediction of their behavior as a function of composition. Here we develop a python computer code called dionne that models the magnetism of rare earth (RE) iron garnets (${\mathrm{RE}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$, REIGs) using molecular field coefficient theory. The program calculates the exchange interactions and the magnetic moment of each sublattice to determine the net magnetization and angular momentum as a function of temperature. dionne accounts for site occupancy on each sublattice, including the effects of nonmagnetic and magnetic substitutions, vacancies, ${\mathrm{Fe}}^{2+}$, and deviations from the ideal $\mathrm{RE}:\mathrm{Fe}$ stoichiometry by considering their effects on the magnetization and exchange coupling. Unlike previous iterative methods, dionne recursively solves for the moment at each temperature, yielding an excellent match to magnetization versus temperature data for a range of bulk garnets. This work predicts magnetic properties of REIGs with a variety of compositions and point defect levels and enables design of ferrimagnets with useful properties.

• Received 25 September 2023
• Revised 12 December 2023
• Accepted 18 December 2023

DOI:https://doi.org/10.1103/PhysRevApplied.21.014060