Magnetic properties of Pr bulk and clusters determined using density functional theory calculations

Lanthanide-based nanostructures have the potential to meet the current miniaturization demands of advanced devices such as magnetic memories with ultrahigh-storage densities. However, many questions about their fundamental properties remain unaddressed even for bulk and small nanostructures. From the application and scientific point of view, it is crucial to determine their structural stability, magnetic coupling, and magnetic anisotropy, as well as to identify the best structure that can simultaneously consider these properties. With the help of experimental measurements on Pr bulk and clusters, we quantitatively calculated the spin and orbital magnetic moments by using the density functional theory (DFT) method, where spin-orbit coupling (SOC) and non-collinearity are included self-consistently. We found that Pr bulk is in a singlet state with the atomic magnetic moments anti-ferromagnetically coupled along the in-plane direction, and it shows strong in-plane magnetic anisotropy. Obeying Hunds rule of negative values, the orbital magnetic moment remarkably contributes to total moments in the bulk and cluster phases. However, they cannot determine the experimental oscillation of cluster magnetism. The oscillation behavior, as a function of cluster size, as well as the enhanced magnetic moment with increasing temperature, can be interpreted as the anti-ferromagnetic coupling between atomic magnetic moments. Giant magnetic anisotropy energy of several hundreds of meV has been derived in both Pr bulk and clusters, which is an order of magnitude larger than the transition metal counterparts.