Size and structural dependence of the magnetic properties of small 3d-transition-metal clusters

Chiral Magnetic Interactions in Small Fe Clusters Triggered by Symmetry-Breaking Adatoms

The chirality of the interaction between the local magnetic moments in small transition-metal alloy clusters is investigated in the framework of density-functional theory. The Dzyaloshinskii–Moriya (DM) coupling vectors Dij between the Fe atoms in Fe2X and Fe3X with X = Cu, Pd, Pt, and Ir are derived from independent ground-state energy calculations for different noncollinear orientations of the local magnetic moments. The local-environment dependence of Dij and the resulting relative stability of different chiral magnetic orders are analyzed by contrasting the results for different adatoms X and by systematically varying the distance between the adatom X and the Fe clusters. One observes that the adatoms trigger most significant DM couplings in Fe2X, often in the range of 10–30 meV. Thus, the consequences of breaking the inversion symmetry of the Fe dimer are quantified. Comparison between the symmetric and antisymmetric Fe-Fe couplings shows that the DM couplings are about two orders of magnitude weaker than the isotropic Heisenberg interactions. However, they are in general stronger than the anisotropy of the symmetric couplings. In Fe3X, alloying induces interesting changes in both the direction and strength of the DM couplings, which are the consequence of breaking the reflection symmetry of the Fe trimer and which depend significantly on the adatom-trimer distance. A local analysis of the chirality of the electronic energy shows that the DM interactions are dominated by the spin-orbit coupling at the adatoms and that the contribution of the Fe atoms is small but not negligible.

Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures

Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.

On the influence of exact exchange on transition metal superatoms

The electronic structure of A7C (A = Hg, Pd, V, Cr, Mn, Fe, Ni, Cu; C = 0, ±1, ±2) clusters has been determined using density functional theory methods. The A7C (A = Hg, Pd, Cr, Cu; C = 0, ±1, ±2) clusters all conform to the existing superatomic model, with a sufficiently stabilised local structure to prevent perturbation upon the introduction of exact exchange to the exchange correlation functional. For the A7C (A = Mn, Fe, Ni; C = 0, ±1, ±2) clusters the incorporation of exact exchange separates the atomic s- and d-electrons, leading to a net increase in the number of superatomic electrons. Conversely the incorporation of exact exchange into the exchange correlation functional decreases the number of superatomic electrons for the V7C (C = 0, ±1, ±2) clusters, owing to the radial extension of the d-orbitals influencing their ability to contribute into superatomic shells.

The Behavior of Magnetic Properties in the Clusters of 4d Transition Metals

The current focus of material science researchers is on the magnetic behavior of transition metal clusters due to its great hope for future technological applications. It is common knowledge that the 4d transition elements are not magnetic at their bulk size. However, studies indicate that their magnetic properties are strongly dependent on their cluster sizes. This study attempts to identify magnetic properties of 4d transition metal clusters. Using a tight-binding Friedel model for the density of d-electron states, we investigated the critical size for the magnetic-nonmagnetic transition of 4d transition-metal clusters. Approaching to the critical point, the density of states of the cluster near the Fermi level is higher than 1/J and the discrete energy levels form a quasi-continuous band. Where J is correlation integral. In order to determine the critical size, we considered a square shape band and fcc, bcc, icosahedral and cuboctahedral close-packed structures of the clusters. We also investigated this size dependent magnetic behavior using Heisenberg model. Taking some quantum mechanical approximations in to consideration, we determined magnetic behavior of the clusters. For practicality, we considered three clusters of transition metals (Ru, Rh and Pd) and the obtained results are in line with the results of previous studies.

Structural evolution, electronic and magnetic manners of small rhodium Rhn+/− (n = 2–8) clusters: a detailed density functional theory study

We have evaluated the stable electronic structure and magnetic properties of all neutral and ionic Rh_n (n = 2–8) clusters using density functional theory. This study reveals that Rh₄ is the magic cluster based on the calculated reactivity parameters.

Metastability of free cobalt and iron clusters: a possible precursor to bulk ferromagnetism

Homonuclear cobalt and iron clusters Co(N) and Fe(N) measured in a cryogenic molecular beam exist in two states with distinct magnetic moments (μ), polarizabilities, and ionization potentials, indicating distinct valences. The μ is approximately quantized: μ(N)∼2Nμ(B) in the ground states and μ(N)(*)∼Nμ(B) in the excited states for Co; μ(N)∼3Nμ(B) and μ(N)(*)∼Nμ(B) for Fe. At a large size, the average μ of the two states converges to the bulk value with diminishing ionization potential differences. The experiments suggest localized ferromagnetism in the two states and that itinerant ferromagnetism emerges from their superposition.

Ultrafine metallic Fe nanoparticles: synthesis, structure and magnetism

The results of the investigation of the structural and magnetic (static and dynamic) properties of an assembly of metallic Fe nanoparticles synthesized by an organometallic chemical method are described. These nanoparticles are embedded in a polymer, monodisperse, with a diameter below 2 nm, which corresponds to a number of around 200 atoms. The X-ray absorption near-edge structure and Mössbauer spectrum are characteristic of metallic Fe. The structural studies by wide angle X-ray scattering indicate an original polytetrahedral atomic arrangement similar to that of β-Mn, characterized by a short-range order. The average magnetic moment per Fe atom is raised to 2.59 µ(B) (for comparison, bulk value of metallic Fe: 2.2 µ(B)). Even if the spontaneous magnetization decreases rapidly as compared to bulk materials, it remains enhanced even up to room temperature. The gyromagnetic ratio measured by ferromagnetic resonance is of the same order as that of bulk Fe, which allows us to conclude that the orbital and spin contributions increase at the same rate. A large magnetic anisotropy for metallic Fe has been measured up to (3.7 ± 1.0)·10(5) J/m(3). Precise analysis of the low temperature Mössbauer spectra, show a broad distribution of large hyperfine fields. The largest hyperfine fields display the largest isomer shifts. This indicates a progressive increase of the magnetic moment inside the particle from the core to the outer shell. The components corresponding to the large hyperfine fields with large isomer shifts are indeed characteristic of surface atoms.

Magnetic nanostructures

Characteristic results of magnetism in small particles, thin films and tunnel junctions are presented. As a consequence of the reduced atomic coordination in small clusters and thin films the electronic states and density of states are modified. Thus, magnetic moments and magnetization are affected. Generally, in clusters and thin films magnetic anisotropy plays a special role. In tunnel junctions the interplay of magnetism, spin currents and superconductivity are of particular interest. In ring-like mesoscopic systems Aharonov-Bohm-induced currents are studied. Results are given for single transition metal clusters, cluster ensembles, thin films, mesoscopic structures and tunnel systems.

Towards a definition of inorganic nanoparticles from an environmental, health and safety perspective

The regulation of engineered nanoparticles requires a widely agreed definition of such particles. Nanoparticles are routinely defined as particles with sizes between about 1 and 100 nm that show properties that are not found in bulk samples of the same material. Here we argue that evidence for novel size-dependent properties alone, rather than particle size, should be the primary criterion in any definition of nanoparticles when making decisions about their regulation for environmental, health and safety reasons. We review the size-dependent properties of a variety of inorganic nanoparticles and find that particles larger than about 30 nm do not in general show properties that would require regulatory scrutiny beyond that required for their bulk counterparts.

Simulating functional magnetic materials on supercomputers

The recent passing of the petaflop per second landmark by the Roadrunner project at the Los Alamos National Laboratory marks a preliminary peak of an impressive world-wide development in the high-performance scientific computing sector. Also, purely academic state-of-the-art supercomputers such as the IBM Blue Gene/P at Forschungszentrum Jülich allow us nowadays to investigate large systems of the order of 10(3) spin polarized transition metal atoms by means of density functional theory. Three applications will be presented where large-scale ab initio calculations contribute to the understanding of key properties emerging from a close interrelation between structure and magnetism. The first two examples discuss the size dependent evolution of equilibrium structural motifs in elementary iron and binary Fe-Pt and Co-Pt transition metal nanoparticles, which are currently discussed as promising candidates for ultra-high-density magnetic data storage media. However, the preference for multiply twinned morphologies at smaller cluster sizes counteracts the formation of a single-crystalline L1(0) phase, which alone provides the required hard magnetic properties. The third application is concerned with the magnetic shape memory effect in the Ni-Mn-Ga Heusler alloy, which is a technologically relevant candidate for magnetomechanical actuators and sensors. In this material strains of up to 10% can be induced by external magnetic fields due to the field induced shifting of martensitic twin boundaries, requiring an extremely high mobility of the martensitic twin boundaries, but also the selection of the appropriate martensitic structure from the rich phase diagram.

Optimized Geometry of the Cluster Gd2O3 and Proposed Antiferromagnetic Alignment of f-Electron Magnetic Moment

There is currently experimental interest in assemblies of Gd2O3 clusters. This has motivated the present study in which a single such cluster in free space is examined quantitatively by spin-density functional theory, with appropriate relativistic corrections incorporated for Gd. First, the nuclear geometry of the cluster is optimized, and it is found to be such that the two Gd atoms lie in a symmetry axis perpendicular to the isosceles triangle formed by the O atoms. Then, a careful study is made of the magnetic arrangement of the localized f-electron moments on the two Gd atoms. The prediction of the present treatment is that the localized spins are aligned antiferromagnetically. An alternative picture using superexchange ideas leads to the same conclusion.

Magnetism and magnetic isomers in free chromium clusters

We have used the Stern-Gerlach deflection technique to study magnetism in chromium clusters of 20-133 atoms at temperatures between 60 and 100 K. We observe that these clusters have large magnetic moments and respond superparamagnetically to applied magnetic fields. Using superparamagnetic theory, we have determined the moment per atom for each cluster size and find that it often far exceeds the moment per atom present anywhere in the bulk antiferromagnetic lattice. Remarkably, our cluster beam contains two magnetically distinguishable forms of each cluster size with > or =34 atoms. We attribute this observation to structural isomers.

Green's function formalism coupled with Gaussian broadening of discrete states for quantum transport: application to atomic and molecular wires

A Green's function formalism incorporating broadened density of states (DOS) is proposed for the calculation of electrical conductance. In cluster-molecule-cluster systems, broadened DOS of the clusters are defined as continuous DOS of electrodes and used to calculate Green's function of electrodes. This approach combined with density functional theory is applied to the electrical transmission of gold atomic wires and molecular wires consisting of benzene-1,4-dithiolate, benzene-1,4-dimethanethiolate, 4,4(')-bipyridine, hexane dithiolate, and octane dithiolate. The B3LYP, B3PW91, MPW1PW91, SVWN, and BPW91 functionals with the LANL2DZ, CEP, and SDD basis sets are employed in the calculation of conductance. The width parameter was successfully determined to reproduce the quantum unit of conductance 2e(2)/h in gold atomic wires. The combination of the B3LYP hybrid functional and the CEP-31G basis set is excellent in reproducing measured conductances of molecular wires by Tao et al. [Science 301, 1221 (2003); J. Am. Chem. Soc. 125, 16164 (2003); Nano Lett. 4, 267 (2004)].

Evolution of magnetism in iron from the atom to the bulk

The evolution of the magnetic moment in iron clusters containing 20-400 atoms is investigated using first-principles numerical calculations based on density-functional theory and real-space pseudopotentials. Three families of clusters are studied, characterized by the arrangement of atoms: icosahedral, body-centered cubic centered on an atom site, and body-centered cubic centered on the bridge between two neighboring atoms. We find an overall decrease of magnetic moment as the clusters grow in size towards the bulk limit. Clusters with faceted surfaces are predicted to have magnetic moment lower than other clusters with similar size. As a result, the magnetic moment is observed to decrease as function of size in a nonmonotonic manner, which explains measurements performed at low temperatures.