Density functional theory calculations for magnetic properties of Co₃W systems

Cheaper permanent magnetic nanostructures with magnetic properties equivalent to those of noble-metal or rare-earth nanomagnets have been experimentally developed for their potential applications in ultrahigh storage densities in magnetic memory. To date, their intrinsic magnetic properties are not well understood under the micro-level of local atomic arrangements and electronic structures. In this work, we performed theoretical investigations on the Co₃W bulk, the clean surface, nanoclusters, and the Co|Co₃W bilayers and superlattices for their geometrical structures, magnetic moments, and magnetic anisotropy energies (MAEs). We found that the Co₃W nanostructures we constructed are stable and have the local minima in the energetic landscape, whose stabilities increase with increasing proportion of W and cluster size. The Co and W atoms in clusters are antiferromagnetically coupled, and their local magnetic moments decrease with increasing proportion of W. The breakdown of the Hund's third rule in W atoms observed in experiment can be interpreted as the competition between the intra-atomic spin-orbit coupling in W atoms and interatomic Co-W hybridizations. The highest MAE of about a few tens of meV is obtained in small cluster sizes, whereas it is an order of magnitude reduction in large cluster sizes. The magnetic systems of Co₃W clean surface, Co|Co₃W bilayer and superlattice can present large MAEs, and their easy-axes of magnetization are perpendicular to the (001) surface. Our calculated MAEs are of the same order of magnitude as that of the experimental measurements, and the electronic origin is revealed through the second-order perturbation method.