Effect of Coulomb Correlation on the Magnetic Properties of Mn Clusters

In spite of decades of research, a fundamental understanding of the unusual magnetic behavior of small Mn clusters remains a challenge. Experiments show that Mn₂ is antiferromagnetic while small clusters containing up to five Mn atoms are ferromagnetic with magnetic moments of 5 μ_B/atom and become ferrimagnetic as they grow further. Theoretical studies based on density functional theory (DFT), however, find Mn₂ to be ferromagnetic, with ferrimagnetic order setting in at different sizes that depend upon the computational methods used. While quantum chemical techniques correctly account for the antiferromagnetic ground state of Mn₂, they are computationally too demanding to treat larger clusters, making it difficult to understand the evolution of magnetism. These studies clearly point to the importance of correlation and the need to find ways to treat it effectively for larger clusters and nanostructures. Here, we show that the DFT+ U method can be used to account for strong correlation. We determine the on-site Coulomb correlation, Hubbard U self-consistently by using the linear response theory and study its effect on the magnetic coupling of Mn clusters containing up to five atoms. With a calculated U value of 4.8 eV, we show that the ground state of Mn₂ is antiferromagnetic with a Mn-Mn distance of 3.34 Å, which agrees well with the electron spin resonance experiment. Equally important, we show that on-site Coulomb correlation also plays an important role in the evolution of magnetic coupling in larger clusters, as the results differ significantly from standard DFT calculations. We conclude that for a proper understanding of magnetism of Mn nanostructures (clusters, chains, and layers) one must take into account the effect of strong correlation.