We propose a computational method that drastically simplifies the inclusion of the spin–orbit interaction in density functional theory when implemented over localized basis sets. Our method is based on a well-known procedure for obtaining pseudopotentials from atomic relativistic ab initio calculations and on an on-site approximation for the spin–orbit matrix elements. We have implemented the technique in the SIESTA (Soler J M et al 2002 J. Phys.: Condens. Matter 14 2745–79) code, and show that it provides accurate results for the overall band-structure and splittings of group IV and III–IV semiconductors as well as for 5d metals.

We analyze the stability and magnetic properties of infinite zigzag atomic chains of a large number of late third, fourth and fifth-row transition metal atoms, as well as of the Group IV elements Si, Ge, Sn and Pb. We find that zigzag chains of third-and fourth-row elements are not stable, while those made of Si, Ge, Sn, Pb, W, Os, Ir, Pt and Au are. These results correlate well with known data in Mechanically Controllable Break Junction experiemnts (MCBJE). We therefore conjecture that the stability of an infinite chain is at least a necessary condition for the formation of a finite sized one in MCBJE. We therefore predict that Sn and Os, and possibly W and Pb chains may be found in those experiments. We also find that the bonds in Hg chains are extremely soft. We finally show that the magnetic moments and anisotropies of Ir and Pt chains show a non-trivial behavior. 71.15.Ap,75.30.Gw The discovery of free-standing atomic chains (AC) of gold atoms in 1998 [1, 2] has spurred an intense experimental and theoretical activity along this decade. Pressing subjects related to their structural properties, like the possible geometry of the necks formed at the atomic constriction, the actual length of the chains and more importantly the search for other elements that could also form AC have been intensively discussed [3,4]. Despite initial reports on the formation of AC of several 3d-and 4d-row elements [5,6,7], unequivocal proof of their existence has only been achieved for Au, Pt and Ir [8,9]. Furthermore, third and fourth-row elements like Ni, Co, Rh, Pd and Ag may only form AC upon addition of O 2 , CO and other gas molecules to the chamber [8,9,10]. Gold chains have also been shown to display several fascinating transport phenomena, that include conductance quantization [1,11] and oscillations due to parity effects [12]. Parity oscillations have been proven to happen in Pt and Ir chains also [8].

Theoretical studies on M 13 (M = Fe, Co, Ni) and M 13 Pt n (for n = 3, 4, 5, 20) clusters including the spin-orbit coupling are done using density functional theory. The magnetic anisotropy energy (MAE) along with the spin and orbital moments are calculated for M 13 icosahedral clusters. The angle-dependent energy differences are modelled using an extended classical Heisenberg model with local anisotropies. From our studies, the MAE for Jahn-Teller distorted Fe 13 , Mackay distorted Fe 13 and nearly undistorted Co 13 clusters are found to be 322, 60 and 5 µeV/atom, respectively, and are large relative to the corresponding bulk values, (which are 1.4 and 1.3 µeV/atom for bcc Fe and fcc Co, respectively.) However, for Ni 13 (which practically does not show relaxation tendencies), the calculated value of MAE is found to be 0.64 µeV/atom, which is approximately four times smaller compared to the bulk fcc Ni (2.7 µeV/atom). In addition, MAE of the capped cluster (Fe 13 Pt 4 ) is enhanced compared to the uncapped Jahn-Teller distorted Fe 13 cluster.

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We analyze the impact of the magnetic anisotropy on the geometric structure and magnetic ordering of small atomic clusters of palladium, iridium, platinum and gold, using Density Functional Theory. Our results highlight the absolute need to include self-consistently the spin orbit interaction in any simulation of the magnetic properties of small atomic clusters, and a complete lack of universality in the magnetic anisotropy of small-sized atomic clusters. PACS numbers: 36.40.Cg, 71,70.Ej, 75.30.Gw Nanostructures of all kinds display a wealth of fascinating geometric, mechanical, electronic, magnetic or optical properties. The exploding field of Nanoscience pretends to understand, handle and tailor these properties for human benefit. Atomic clusters and chains, molecular magnets, and a number of organic molecules like for instance metallocenes indeed show novel magnetic behaviors, that include the enhancement of magnetic moments due to the reduced coordination and symmetry of the geometry [1], and a rich variety of new non-collinear magnetic structures that are absent in bulk materials [2]. Among all these devices, metallic atomic clusters (MACs) [3] stand out since, on the one hand they represent the natural bridge between atomic and materials physics and, in the other, they can be grown, deposited on surfaces or embedded in diverse matrices, and characterized with relatively well-established techniques. Further, the magnetic properties of MACs show promise for a wide spectrum of applications, ranging from medicine to spintronics.Magnetism in small MACs has been extensively studied both experimentally and theoretically along the past decade [4,5]. It is therefore somewhat surprising that, even though spin-orbit effects are also expected to be enhanced in MACs, there are very few published theoretical papers that include the spin-orbit interaction (SOI) in their simulations [6,7,8,9]. Among these, only a handful have actually looked at the explicit effects of the SOI on the magnetism of MAC. Pastor and coworkers have studied the magnetic anisotropy (MA) [10] of clusters of 3d Transition Metal atoms, using a phenomenological tightbinding scheme. To the best of our knowledge, there are no ab initio studies of the impact of the SOI on the magnetism of 4d and 5d MAC. This includes not only explicit calculations of the magnetic anisotropy energy (MAE), but also and more importantly, whether the SOI modifies the ground state and the tower of lowest lying (magnetic) states of a given cluster.We present in this article a series of calculations of selected atomic clusters of 4d-and specially 5d-elements, that show that the SOI is a key ingredient in any ab initio simulation of heavy transition metal MAC, that should not be overlooked. These include Pd n , Ir n , Pt n and Au n , with n=2, 3, 4 and 5, and also Pd 6 and Au 6 , Au 7 . The rationale behind our choice is that 5d MAC are expected to have the largest MAEs; among all 5d elements, gold is monovalent and should display a simpler behavior; comparing the magnetic p...