We investigate the structures and magnetic properties of small Mn(n) clusters in the size range of 2-13 atoms using first-principles density functional theory. We arrive at the lowest energy structures for clusters in this size range by simultaneously optimizing the cluster geometries, total spins, and relative orientations of individual atomic moments. The results for the net magnetic moments for the optimal clusters are in good agreement with experiment. The magnetic behavior of Mn(n) clusters in the size range studied in this work ranges from ferromagnetic ordering (large net cluster moment) for the smallest (n=2, 3, and 4) clusters to a near degeneracy between ferromagnetic and antiferromagnetic solutions in the vicinity of n=5 and 6 to a clear preference for antiferromagnetic (small net cluster moment) ordering at n=7 and beyond. We study the details of this evolution and present a picture in which bonding in these clusters predominantly occurs due to a transfer of electrons from antibonding 4s levels to minority 3d levels.

First-principles density-functional-theory investigations of small Mn n (nϭ2 -7,13) clusters reveal a competition between ferromagnetic and antiferromagnetic ordering of atomic magnetic moments. For smaller sizes (nр6), this competition results in a near degeneracy between the two types of orderings, whereas AF arrangements are clearly favored for larger clusters. The calculations thus predict a size-dependent transition in the magnetic ordering of Mn clusters.The study of magnetism in transition-metal clusters is motivated largely by the desire to understand how magnetic properties change when the dimensions of a material are reduced to nanometer length scales, a question of potentially great technological importance. A variety of interesting magnetic behavior has been discovered, ranging from enhanced magnetic moments in clusters of ferromagnetic metals such as Fe ͓1͔, to the prediction of net magnetic moments in clusters of nonmagnetic bulk materials ͓2͔. Generally, the magnetic properties of clusters show a dependence on cluster size ͓3-5͔ and systematic studies of these systems hold the promise of yielding new insight into magnetic ordering in materials.Manganese clusters are particularly interesting. An early electron-spin-resonance study ͓6͔ on small Mn clusters in an inert matrix suggested ferromagnetic ordering with atomic moments of ϳ5 B , the Hund's rule value for the free atom. More recently, Stern-Gerlach ͑SG͒ molecular-beam experiments ͓5͔ were carried out on larger clusters (Mn 11 -Mn 99 ). Analysis of the data assuming superparamagnetic behavior ͓7͔ in the clusters found small, but nonzero, average atomic magnetic moments. This result can be interpreted in one of two ways. If ferromagnetic ͑FM͒ ordering is assumed, the atoms must all have small individual moments. A second possibility is that the atomic moments remain large, but their orientation flips from site to site, so that the net cluster moments are small. The latter possibility has been found to be the preferred one for small Fe n (nϭ2 -4) clusters of low spin ͓8͔. This antiferromagnetic ͑AF͒ interpretation is compelling, since ␣-Mn, the most stable form of bulk manganese, is AF. It is also supported by new density-functional theory ͑DFT͒ calculations that found AF solutions to be more stable than FM solutions in intermediate size Mn n clusters (nϭ13, 15, 19, and 23͒ ͓9͔.Given these results, it appears that Mn clusters undergo a change in magnetic behavior from FM ordering for the smallest sizes to AF ordering for intermediate sizes and beyond. We address the nature of this transition in this paper. Our DFT calculations on Mn n clusters (nϭ2 -7,13) show that the smaller clusters are characterized by a close competition between FM and AF solutions. FM ordering is clearly favored for nϭ2 and 4, but AF and FM states are nearly degenerate for nϭ3, 5, and 6. A radical change occurs at n ϭ7 where the AF solution is much more stable than the FM. A similar behavior is found for nϭ13, suggesting that AF ordering is a general feature of the larger c...

Extending DFT-based genetic algorithms by atom-to-place re-assignment via perturbation theory: A systematic and unbiased approach to structures of mixed-metallic clusters Automated fit of high-dimensional potential energy surfaces using cluster analysis and interpolation over descriptors of chemical environment A new methodology for finding the low-energy structures of transition metal clusters is developed. A two-step strategy of successive density functional tight binding ͑DFTB͒ and density functional theory ͑DFT͒ investigations is employed. The cluster configuration space is impartially searched for candidate ground-state structures using a new single-parent genetic algorithm ͓I. Rata et al., Phys. Rev. Lett. 85, 546 ͑2000͔͒ combined with DFTB. Separate searches are conducted for different total spin states. The ten lowest energy structures for each spin state in DFTB are optimized further at a first-principles level in DFT, yielding the optimal structures and optimal spin states for the clusters. The methodology is applied to investigate the structures of Fe 4 , Fe 7 , Fe 10 , and Fe 19 clusters. Our results demonstrate the applicability of DFTB as an efficient tool in generating the possible candidates for the ground state and higher energy structures of iron clusters. Trends in the physical properties of iron clusters are also studied by approximating the structures of iron clusters in the size range nϭ2 -26 by Lennard-Jones-type structures. We find that the magnetic moment of the clusters remains in the vicinity of 3 B /atom over this entire size range.

Geometric structures and electronic properties of small beryllium clusters (Be(n), 2< or = n< or =9) are investigated within the gradient-corrected density functional theory. The computations are performed with the Becke exchange and Perdew-Wang correlation functionals. Both low and high multiplicity states are considered. A predominance of higher multiplicity states among the low-energy isomers of the larger clusters is found. An analysis of the variations in the structural and electronic properties with cluster size is presented, and the results are compared with those of earlier studies.

A recently developed two-step computational strategy ͓P. J. Chem. Phys. 116, 3576 ͑2002͔͒ is used to investigate the geometric and magnetic properties of Fe 13 . The method combines an unbiased search of the cluster energy surface using a density-functional-based tight-binding method, followed by fully self-consistent density-functional theory ͑DFT͒ calculations for detailed studies of the low-lying structures. The calculations indicate that the geometry of the Fe 13 cluster is a distorted icosahedron. Careful investigations of the optimal spin state of Fe 13 show the existence of two different magnetic orderings for the cluster-a ferromagnetically ordered state in which all atoms have approximately the same magnetic moment (3 B ) and a nominally antiferromagnetic state in which the moment of the central atom is flipped with respect to those of the surface atoms. The relationship between cluster bond lengths and the magnetic ordering suggests that a transition in spin ordering could be driven by uniformly changing the geometric parameters in this cluster.