Magnetism in 4d-transition metal clusters

Size dependent structural, electronic, and magnetic properties of Sc(N) (N=2-14) clusters investigated by density functional theory

Structural, electronic, and magnetic properties of ScN (N=2-14) clusters have been investigated using density functional theory (DFT) calculations. Different spin states isomer for each cluster size has been optimized with symmetry relaxation. The structural stability, dissociation energy, binding energy, spin stability, vertical ionization energy, electron affinity, chemical hardness, and size dependent magnetic moment per atom are calculated for the energetically most stable spin isomer for each size. The structural stability for a specific size cluster has been explained in terms of atomic shell closing effect, close packed symmetric structure, and chemical bonding. Spin stability of each cluster size is determined by calculating the value of spin gaps. The maximum value for second-order energy difference is observed for the clusters of size N = 2, 6, 11, and 13, which implies that these clusters are relatively more stable. The magnetic moment per atom corresponding to lowest energy structure has also been calculated. The magnetic moment per atom corresponding to lowest energy structures has been calculated. The calculated values of magnetic moment per atom vary in an oscillatory fashion with cluster size. The calculated results are compared with the available experimental data.

Multiferroic rhodium clusters

Simultaneous magnetic and electric deflection measurements of rhodium clusters (Rh(N), 6 ≤ N ≤ 40) reveal ferromagnetism and ferroelectricity at low temperatures, while neither property exists in the bulk metal. Temperature-independent magnetic moments (up to 1 μ(B) per atom) are observed, and superparamagnetic blocking temperatures up to 20 K. Ferroelectric dipole moments on the order of 1D with transition temperatures up to 30 K are observed. Ferromagnetism and ferroelectricity coexist in rhodium clusters in the measured size range, with size-dependent variations in the transition temperatures that tend to be anticorrelated in the range n = 6-25. Both effects diminish with size and essentially vanish at N = 40. The ferroelectric properties suggest a Jahn-Teller ground state. These experiments represent the first example of multiferroic behavior in pure metal clusters.

Structural and electronic study of neutral, positive, and negative small rhodium clusters [Rh(n), Rh(n)(+), Rh(n)(-) ; n = 10-13]

We have carried out a systematic study for the determination of the structure and the fundamental state of neutral and ionic small rhodium clusters [Rhn, Rhn(+), Rhn(-); n = 10-13] using ab initio Hartree-Fock methods with a LANL2DZ basis set. A range of spin multiplicities is investigated for each cluster. We present the bond lengths, angles, and geometric configuration adopted by the clusters in its minimum energy conformation showing the differences when the clusters have different number of unpaired electrons. Also we report the vertical ionization potential and the adiabatic one calculated by the Koopmans' theorem.

Characterization of iron ferromagnetism by the local atomic volume: from three-dimensional structures to isolated atoms

We present a comprehensive study of the relationship between the ferromagnetism and the structural properties of Fe systems from three-dimensional ones to isolated atoms based on the spin-density functional theory. We have found a relation between the magnetic moment and the volume of the Voronoi polyhedron, determining, in most cases, the value of the total magnetic moment as a function of this volume with an average accuracy of ±0.28 μ(B) and of the 3d magnetic moment with an average accuracy of ±0.07 μ(B) when the atomic volume is larger than 22 ų. It is demonstrated that this approach is applicable for many three-dimensional systems, including high-symmetry structures of perfect body-centered cubic (bcc), face-centered cubic (fcc), hexagonal close-packed (hcp), double hexagonal close-packed (dhcp), and simple cubic (sc) crystals, as well as for lower-symmetry ones, for example atoms near a grain boundary (GB) or a surface, around a vacancy or in a linear chain (for low-dimensional cases, we provide a generalized definition of the Voronoi polyhedron). Also, we extend the validity of the Stoner model to low-dimensional structures, such as atomic chains, free-standing monolayers and surfaces, determining the Stoner parameter for these systems. The ratio of the 3d-exchange splitting to the magnetic moment, corresponding to the Stoner parameter, is found to be I(3d) = (0.998 ± 0.006) eV /μ(B) for magnetic moments up to 3.0 μ(B). Further, the 3d exchange splitting changes nearly linearly in the region of higher magnetic moments (3.0-4.0 μ(B)) and the corresponding Stoner exchange parameter equals I(h)(3d) = (0.272 ± 0.006) eV /μ(B). The existence of these two regions reflects the fact that, with increasing Voronoi volume, the 3d bands separate first and, consequently, the 3d magnetic moment increases. When the Voronoi volume is sufficiently large (≥22 ų), the separation of the 3d bands is complete and the magnetic moment reaches a value of 3.0 μ(B). Then, when the volume further increases, the 4s bands start to separate, increasing thus the 4s magnetic moment. Surprisingly, in the region of higher magnetic moments (≥3.0 μ(B)), there is also a linear relationship between the 4s exchange splitting and the total magnetic moment with a slope of I(h)(4s) = (1.053 ± 0.016) eV /μ(B), which is nearly identical to I(3d) for magnetic moments up to 3.0 μB. These linear relations can be considered as an extension of the Stoner model for low-dimensional systems.

Structures of medium-sized ruthenium clusters: the octahedral motif

We describe the first direct structural characterization of medium-sized ruthenium clusters (Ru19 (-) , Ru28 (-) , Ru38 (-) , and Ru44 (-) ) by using a combination of trapped ion electron diffraction and density functional theory. We find close-packed structures based on octahedral geometries: Ru19 (-) and Ru44 (-) are closed-shell octahedra whereas Ru28 (-) is a double octahedron. In the case of Ru38 (-) , instead of a truncated octahedron we obtain evidence for lower symmetry structures containing a reentrant surface.

Magnetism in nanoparticles: tuning properties with coatings

This paper reviews the effect of organic and inorganic coatings on magnetic nanoparticles. The ferromagnetic-like behaviour observed in nanoparticles constituted by materials which are non-magnetic in bulk is analysed for two cases: (a) Pd and Pt nanoparticles, formed by substances close to the onset of ferromagnetism, and (b) Au and ZnO nanoparticles, which were found to be surprisingly magnetic at the nanoscale when coated by organic surfactants. An overview of theories accounting for this unexpected magnetism, induced by the nanosize influence, is presented. In addition, the effect of coating magnetic nanoparticles with biocompatible metals, oxides or organic molecules is also reviewed, focusing on their applications.

Theoretical study for the adsorption of CO on neutral and charged Pd13 clusters

Adsorption of carbon monoxide, CO, on the surface of magnetic Pd13, Pd13–, and Pd13+ clusters, showing magnetic moments of 8, 7, and 7 Bohr magnetons (μB), respectively, was studied by means of density functional methods, allowing partial inclusion of relativistic effects. The favorable adsorption modes are on top, bridge, and threefold, with the binding energy of CO with Pd13– increasing in this same order as 39.4, 48.0 and 50.2 kcal/mol. In addition, the experimental results for the [Pdn–CO]–, n = 4–12, anions show a decrease of the vibrational frequency of CO along this triad of modes, 1940, 1800, and 1680 cm−1, with respect to the free CO value, 2143 cm−1, which conforms to our estimated frequencies, 1956, 1784, and 1679 cm−1, for CO in the [Pd13–CO]– complex. Also, the threefold mode shows a significantly longer bond length for CO, 1.210 Å, with respect to the free case, 1.139 Å. Then the bond of CO is considerably weakened in the negatively charged [Pd13CO]– cluster when the adsorption occurs in a threefold site. These results are mainly accounted for by charge transfer effects from the Pd13 cluster to the CO molecule. Smaller CO activation was found in neutral Pd13–CO and in [Pd13–CO]+, where hollow adsorption yields bigger structural and electronic changes on CO than the respective bridge and on-top modes. Overall, CO adsorption notably quenches the magnetization of neutral and charged Pd13 particles.

Stacking principle and magic sizes of transition metal nanoclusters based on generalized Wulff construction

Nanoclusters with extra stability at certain cluster sizes are known as magic clusters with exotic properties. The classic Wulff construction principle, which stipulates that the preferred structure of a cluster should minimize its total surface energy, is often invoked in determining the cluster magicity, resulting in close-shelled Mackay icosahedronal clusters with odd-numbered magic sizes of 13, 55, 147, etc. Here we use transition metal clusters around size 55 as prototypical examples to demonstrate that, in the nanometer regime, the classic Wulff construction principle needs to be generalized to primarily emphasize the edge atom effect instead of the surface energy. Specifically, our detailed calculations show that nanoclusters with much shorter total edge lengths but substantially enlarged total surface areas are energetically much more stable. As a consequence, a large majority of the nanoclusters within the 3d-, 4d-, and 5d-transition metal series are found to be fcc or hcp crystal fragments with much lower edge energies, and the widely perceived magic size of 55 is shifted to its nearby even numbers.

Ab initio random structure search for 13-atom clusters of fcc elements

The 13-atom metal clusters of fcc elements (Al, Rh, Ir, Ni, Pd, Pt, Cu, Ag, Au) were studied by density functional theory calculations. The global minima were searched for by the ab initio random structure searching method. In addition to some new lowest-energy structures for Pd13 and Au13, we found that the effective coordination numbers of the lowest-energy clusters would increase with the ratio of the dimer-to-bulk bond length. This correlation, together with the electronic structures of the lowest-energy clusters, divides the 13-atom clusters of these fcc elements into two groups (except for Au13, which prefers a two-dimensional structure due to the relativistic effect). Compact-like clusters that are composed exclusively of triangular motifs are preferred for elements without d-electrons (Al) or with (nearly) filled d-band electrons (Ni, Pd, Cu, Ag). Non-compact clusters composed mainly of square motifs connected by some triangular motifs (Rh, Ir, Pt) are favored for elements with unfilled d-band electrons.

Giant magnetic moments of B and C doped cuboctahedral Mn13 clusters

Using first-principles calculations based on gradient corrected density functional theory we show that an otherwise distorted icosahedric Mn(13) ferrimagnetic cluster, when doped with six B or C atoms, transforms into a ferromagnetic cuboctahedral cluster with a magnetic moment that is an order of magnitude larger than that of the pure Mn(13) cluster. The origin of this magnetic transition is attributed to the change in the Mn-Mn interatomic distance resulting from the structural transformation. These doped clusters remain ferromagnetic with giant moments even after the removal of a B or C atom. However, similar doping with N atom does not lead to ferromagnetic ordering and Mn(13)N(6) remains ferrimagnetic with a magnetic moment of only 3 μ(B), just as in its parent Mn(13) cluster.

Spin fluctuations of paramagnetic Rh clusters revealed by x-ray magnetic circular dichroism

The magnetic moment induced on Rh atoms, forming 1.6 nm average diameter clusters, embedded in an Al(2)O(3) matrix, has been determined using x-ray magnetic circular dichroism measurements. The magnetic moment varies linearly with the applied magnetic field. At 2.3 K and under 17 T, the spin magnetic moment amounts to 0.067(2) μ(B)/Rh atom. The orbital moment does not exceed 2% of the spin moment. The susceptibility is highly temperature dependent. This is in agreement with a prediction due to Moriya and Kawabata, that in itinerant electron systems, close to the onset of magnetism, the renormalization of the magnetic susceptibility by electron correlations, leads to a Curie-like behavior.

Magnetism in gold nanoparticles

Gold nanoparticles currently elicit an intense and very broad research activity because of their peculiar properties. Be it in catalysis, optics, electronics, sensing or theranostics, new applications are found daily for these materials. Approximately a decade ago a report was published with magnetometry data showing that gold nanoparticles, most surprisingly, could also be magnetic, with features that the usual rules of magnetism were unable to explain. Many ensuing experimental papers confirmed this observation, although the reported magnetic behaviours showed a great variability, for unclear reasons. In this review, most of the experimental facts pertaining to "magnetic gold" are summarized. The various theories put forth for explaining this unexpected magnetism are presented and discussed. We show that despite much effort, a satisfying explanation is still lacking and that the field of hypotheses should perhaps be widened.

Magnetic properties of Pd atomic chains formed during submonolayer deposition of 3d metals on Pd(110)

Recently, an unusual intermixing-driven scenario for the growth of atomic Pd chains on a Pd(110) surface during deposition of 3d metal atoms has been predicted (Stepanyuk 2009 Phys. Rev. B 79 155410) and confirmed by STM and STS experiments (Wie et al 2009 Phys. Rev. Lett. 103 225504). Performing ab initio calculations we demonstrate that Pd atomic chains grown above embedded Fe atoms exhibit magnetic properties which depend on the substrate mediated exchange interaction between the Fe atoms.

Local electronic structure and density of edge and facet atoms at Rh nanoclusters self-assembled on a graphene template

The chemical and physical properties of nanoclusters largely depend on their sizes and shapes. This is partly due to finite size effects influencing the local electronic structure of the nanocluster atoms which are located on the nanofacets and on their edges. Here we present a thorough study on graphene-supported Rh nanocluster assemblies and their geometry-dependent electronic structure obtained by combining high-energy resolution core level photoelectron spectroscopy, scanning tunneling microscopy, and density functional theory. We demonstrate the possibility to finely control the morphology and the degree of structural order of Rh clusters grown in register with the template surface of graphene/Ir(111). By comparing measured and calculated core electron binding energies, we identify edge, facet, and bulk atoms of the nanoclusters. We describe how small interatomic distance changes occur while varying the nanocluster size, substantially modifying the properties of surface atoms. The properties of under-coordinated Rh atoms are discussed in view of their importance in heterogeneous catalysis and magnetism.

Magneto-structural properties and magnetic anisotropy of small transition-metal clusters: a first-principles study

Ab initio density-functional calculations including spin-orbit coupling (SOC) have been performed for Ni and Pd clusters with three to six atoms and for 13-atom clusters of Ni, Pd, and Pt, extending earlier calculations for Pt clusters with up to six atoms (2011 J. Chem. Phys. 134 034107). The geometric and magnetic structures have been optimized for different orientations of the magnetization with respect to the crystallographic axes of the cluster. The magnetic anisotropy energies (MAE) and the anisotropies of spin and orbital moments have been determined. Particular attention has been paid to the correlation between the geometric and magnetic structures. The magnetic point group symmetry of the clusters varies with the direction of the magnetization. Even for a 3d metal such as Ni, the change in the magnetic symmetry leads to small geometric distortions of the cluster structure, which are even more pronounced for the 4d metal Pd. For a 5d metal the SOC is strong enough to change the energetic ordering of the structural isomers. SOC leads to a mixing of the spin states corresponding to the low-energy spin isomers identified in the scalar-relativistic calculations. Spin moments are isotropic only for Ni clusters, but anisotropic for Pd and Pt clusters, orbital moments are anisotropic for the clusters of all three elements. The magnetic anisotropy energies have been calculated. The comparison between MAE and orbital anisotropy invalidates a perturbation analysis of magnetic anisotropy for these small clusters.

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.

Interface exchange coupling in Co nanoparticles dispersed in a Mn matrix

The structural and magnetic properties of 1.8 nm Co particles dispersed in a Mn matrix by co-depositing pre-formed mass-selected Co clusters with an atomic vapour of Mn onto a common substrate have been studied by using EXAFS (extended x-ray absorption fine structure), XMCD (x-ray magnetic circular dichroism), magnetometry, and theoretical modelling. At low Co volume fraction (5%) Co@Mn shows a significant degree of alloying and the well-defined particles originally deposited become centres of high Co concentration CoMn alloy that evolves from pure Co at the nanoparticle centre to the pure Mn matrix within a few nm. Each inhomogeneity is a core-shell particle with a Co-rich ferromagnetic core in contact with a Co-depleted antiferromagnetic shell. The XMCD reveals that the Co moment localized on the Co atoms within the Co-rich cores is much smaller than the ferromagnetic moment of the Co nanoparticles deposited at the same volume fraction in Ag. Electronic structure calculations indicate that the small magnitude of the core Co moment can be understood only if significant alloying occurs. Monte Carlo modelling replicates the exchange bias (EB) behaviour observed at low temperature from magnetometry measurements. We ascribe EB to the interaction between the ferromagnetic Co-rich cores and the antiferromagnetic Mn-rich shells.

Magnetic surface nanostructures

Recent trends in the emerging field of surface-supported magnetic nanostructures are reviewed. Current strategies for nanostructure synthesis are summarized, followed by a predominantly theoretical description of magnetic phenomena in surface magnetic structures and a review of experimental research in this field. Emphasis is on Fe- or Co-based nanostructures in various low-dimensional geometries, which are studied as model systems to explore the effects of dimensionality, atomic coordination, chemical bonds, alloying and, most importantly, interactions with the supporting substrate on the magnetism. This review also includes a discussion of closely related systems, such as 3d element impurities integrated into organic networks, surface-supported Fe-based molecular magnets, Kondo systems or 4d element nanostructures that exhibit emergent magnetism, thereby bridging the traditional areas of surface science, molecular physics and nanomagnetism.

Large perpendicular magnetic anisotropy of ultrathin Ru and Rh films on a NiAl(001) surface

Using the full potential linearized augmented plane wave (FLAPW) method, the magnetic properties of two-dimensional Ru and Rh monolayers (MLs) on a NiAl(001) surface have been investigated. It has been found that free standing one monolayer Ru and Rh films have ferromagnetic ground state with magnetic moments of 2.21 and 1.48 μ(B), respectively. The ferromagnetism is still observed even on a Ni terminated NiAl(001) surface, while no magnetic state is found on an Al terminated surface. The calculated magnetic moments of Ru and Rh atoms are 1.56 and 0.88 μ(B), respectively. In addition, an induced magnetic moment in surface Ni is observed. It has been found that the free standing Ru film has perpendicular magnetization to the film surface with a magnetocrystalline anisotropy (MCA) energy of 0.66 meV/atom, while an in-plane MCA energy of 0.37 meV/atom is achieved in Rh film. Very interestingly, we find that both Ru/NiAl(001) and Rh/NiAl(001) films have perpendicular magnetic anisotropy and the calculated MCA energies are 0.66 and 1.11 meV in Ru/NiAl(001) and Rh/NiAl(001), respectively. Along with the magnetic anisotropy, we have presented theoretically calculated x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) results.

Dominance of broken bonds and nonbonding electrons at the nanoscale

Although they exist ubiquitously in human bodies and our surroundings, the impact of nonbonding lone electrons and lone electron pairs has long been underestimated. Recent progress demonstrates that: (i) in addition to the shorter and stronger bonds between under-coordinated atoms that initiate the size trends of the otherwise constant bulk properties when a substance turns into the nanoscale, the presence of lone electrons near to broken bonds generates fascinating phenomena that bulk materials do not demonstrate; (ii) the lone electron pairs and the lone pair-induced dipoles associated with C, N, O, and F tetrahedral coordination bonding form functional groups in biological, organic, and inorganic specimens. By taking examples of surface vacancy, atomic chain end and terrace edge states, catalytic enhancement, conducting-insulating transitions of metal clusters, defect magnetism, Coulomb repulsion at nanoscale contacts, Cu(3)C(2)H(2) and Cu(3)O(2) surface dipole formation, lone pair neutralized interface stress, etc, this article will focus on the development and applications of theory regarding the energetics and dynamics of nonbonding electrons, aiming to raise the awareness of their revolutionary impact to the society. Discussion will also extend to the prospective impacts of nonbonding electrons on mysteries such as catalytic enhancement and catalysts design, the density anomalies of ice and negative thermal expansion, high critical temperature superconductivity induced by B, C, N, O, and F, the molecular structures and functionalities of CF(4) in anti-coagulation of synthetic blood, NO signaling, and enzyme telomeres, etc. Meanwhile, an emphasis is placed on the necessity and effectiveness of understanding the properties of substances from the perspective of bond and nonbond formation, dissociation, relaxation and vibration, and the associated energetics and dynamics of charge repopulation, polarization, densification, and localization. Finding and grasping the factors controlling the nonbonding states and making them of use in functional materials design and identifying their limitations will form, in the near future, a subject area of "nonbonding electronics and energetics", which could be even more challenging, fascinating, promising, and rewarding than dealing with core or valence electrons alone.

Enhanced magnetic moment in Fe-doped Pd(n) clusters (n = 1-13): a density functional study

Here we report a systematic theoretical study of the equilibrium structures, electronic and magnetic properties of FePd(n-1) clusters with n = 1-13, within the framework of density functional theory. The results show that the doping of a single Fe impurity enhances the binding energies as well as the magnetic moment of the Pd(n) clusters. Interestingly, in the mid-size region (n = 5-7), Fe substitution in Pd(n) clusters results in a three fold enhancement in the magnetic moment. We find that the geometries of the host clusters do not change significantly after the addition of an Fe atom, except for n = 6, 7, 11, 12. In the lowest energy configurations, the Fe atom tries to increase its coordination number by moving from the convex to the interior site as the number of Pd atoms varies from 2 to 12.

Ti2Rh6B – a new boride with a double perovskite-like structure containing octahedral Rh6 clusters

Single crystals of Ti2Rh6B were synthesized by arc-melting the elements in a water-cooled copper crucible under an argon atmosphere. The new silver-like compound with metallic luster crystallizes in space group Fm-3m (no. 225) with a = 7.8191(5) Å, V = 478.05(5) Å3, and Z = 4. The refinement converged to R 1 = 0.0169 and wR 2 = 0.0486 for all 96 unique reflections and 7 parameters. The structure can be described as a defect double perovskite, A2BB'O6, where the A site is occupied by titanium, the B site by boron, the O site by rhodium but the B' site is vacant leading to the formation of perfectly octahedral Rh6 clusters and BRh6 units. Rh—B, Rh—Ti, and Rh—Rh interactions are observed. According to density-functional (LMTO) electronic structure calculations, the strongest bonding occurs for the Rh—B contacts, and the Rh—Rh bonding within the clusters is more than two times stronger than in the BRh6 units.