Accurate Estimation of Magnetic Moments in 4f and 3d Magnetic Ions

ABSTRACT We propose a method for calculating magnetic moments of 4f and 3d ions, applicable to both free ions and those within a crystal field. Based on angular momentum theory, this method provides efficient expressions for calculating magnetic moments. Applicable to individual electronic substates, it facilitates the selection and tuning of magnetic states in materials. Our method shows excellent agreement with published data for free 4f ions and offers efficient approximations for dilute 3d systems and single‐molecule magnets. We successfully validated our formulism by reproducing experimental results for Nd 3 ⁺ in NdAl₂. Additionally, predicted moments for Fe 2 ⁺ in FeF₂ agree well with our estimates and existing data, demonstrating the method's effectiveness for ions in crystals.