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Effect of transition metal doping on magnetic hardness of CeFe$_{12}$-based compounds

In this work, compositions of CeFe11X and CeFe10X2 with all 3d, 4d, and 5d transition metal substitutions are considered. Since many previous studies have focused on the CeFe11Ti compound, this particular compound became the starting point of our considerations and we gave it special attention. We first determined the optimal symmetry of the simplest CeFe11Ti structure model. We then observed that the calculated magnetocrystalline anisotropy energy (MAE) correlates with the magnetic moment, which in turn strongly depends on the choice of the exchange-correlation potential. MAE, magnetic moments, and magnetic hardness were determined for all compositions considered. Moreover, the calculated dependence of the MAE on the spin magnetic moment allowed us to predict the upper limits of the MAE. We also showed that it does not depend on the choice of the exchange-correlation potential form. The economically justifiable compositions with the highest magnetic hardness values are CeFe11W, CeFe10W2, CeFe11Mn, CeFe10Mn2, CeFe11Mo, CeFe10Mo2, and CeFe10Nb2. However, calculations suggest that, like CeFe12, these compounds are not chemically stable and could require additional treatments to stabilize the composition. Further alloying of the selected compositions with elements embedded in interstitial positions confirms the positive effect of such dopants on hard magnetic properties. Subsequent calculations performed for comparison for selected isostructural La-based compounds lead to similar MAE results as for Ce-based compounds, suggesting a secondary effect of 4f electrons. Calculations were performed using the full-potential local-orbital electronic structure code FPLO18, whose unique fully relativistic implementation of the fixed spin moment method allowed us to calculate the MAE dependence of the magnetic moment.