Magnetic materials are widely used in technologies ranging from wind turbines to “green” automobiles. Compounds with large magnetocrystalline anisotropies are typically difficult to demagnetize, which is technologically advantageous. Magnetocrystalline anisotropy is inherently strong in heavy, rare-earth elements, but the scarcity of these elements has led scientists to investigate using transition-metal-based compounds as replacements. We demonstrate for the first time how electronic correlations determine the magnetocrystalline anisotropy of transition metals, using the yttrium-cobalt compound ${\mathrm{YCo}}_5$ as a prototypical substance.

We find that the orbital magnetic moment of ${\mathrm{YCo}}_5$ differs from estimates based on covalent-band theory—we propose that this discrepancy is due to dynamical electron correlations. Spin-orbit interactions are weak in transition-metal compounds, and in general, their magnetocrystalline anisotropy depends on a delicate balance of competing interactions: Coulomb repulsion, ligand fields, spin-orbit coupling, and material-dependent hybridization. We apply a dynamical mean-field theoretical approach in combination with density-functional theory—which takes into account the competing interactions—to the representative rare-earth-free magnet ${\mathrm{YCo}}_5$. We demonstrate for the first time the important role of electronic correlations in determining the magnetocrystalline anisotropy.

Our reliable estimates of the orbital moment, mass enhancement, and the magnetocrystalline anisotropy of ${\mathrm{YCo}}_5$ provide critical knowledge and new insight into the design of rare-earth-free magnets and complex magnetic functionality in general.