Effective magnetization of rotating free ferromagnetic metal clusters

The deflection of free magnetic metal clusters in a Stern-Gerlach magnetic field is studied. In particular we investigate magnetic resonance effects resulting from lattice anisotropy and cluster rotation. In analogy to small suspended particles in an oscillating magnetic field the anisotropy field fixed to the rotating atomic lattice of the cluster acts on the cluster magnetization like an rf field in NMR experiments. In our calculation we have used the Bloch equations and assumed different anisotropy field symmetries (uniaxial, cubic). A minimum in the magnetization as a function of the Stern-Gerlach field and also of the cluster size, as observed recently, is obtained under certain conditions. However, such a resonance behavior occurs only if the distribution of the rotation frequency _rot is relatively narrow, while a broad distribution of _rot yields an almost superparamagnetic behavior. In addition, the strength of the anisotropy field and the relaxation time are important variables which determine the magnetic behavior of the clusters.     

Magnetization of ferromagnetic clusters

The magnetization and deflection profiles of magnetic clusters in a Stern-Gerlach magnet are calculated for conditions under which the magnetic moment is fixed in the intrinsic frame of the cluster, and the clusters enter the magnetic field adiabatically. The predicted magnetization is monotonic as a function of the ratio of magnetic energy ₀ B to the rotational thermal energyk _BT. In low field the average magnetization is 2/3 of the Langevin function. The high-field moment approaches saturation asymptotically asB ^–1/2 instead of theB ^–1 dependence in the Langevin function     

Structure and Magnetism of Hybrid Fe and Co Nanoclusters up to N?≤?7 Atoms

The structural and magnetic properties of small gas-phase Fe _m Co _n clusters with m?+?n ranging between 2 and 7 atoms are investigated using spin-polarized density functional theory. For a given cluster size possible compositions are subject to optimization using a variety of initial structures. The geometry, bond lengths, binding energies and magnetization are reported for the lowest energy structures. The results show that a magnetization peak occurs for Fe₄, while for hybrid clusters, switching a cobalt atom with an iron atom increases the cluster’s total magnetization by 1?μ _B . Our structural predictions are generally in agreement with other theoretical results; the origin of the discrepancies arising in some cases is discussed.     

Magnetic properties of free alkali and transition metal clusters

The Stern-Gerlach deflections of small alkali clusters (N<6) and iron clusters (10<N<500) show that the paramagnetic alkali clusters always have a non-deflecting component, while the iron clusters always deflect in the high field direction. Both of these effects appear to be related to spin relaxation however in the case of alkali clusters it is shown that they are in fact caused by avoided level crossing in the Zeeman diagram. For alkali clusters the relatively weak couplings cause reduced magnetic moments where levels cross. For iron clusters however the total spin is strongly coupled to the molecular framework. Consequently this coupling is responsible for avoided level crossings which ultimately cause the total energy of the cluster to decrease with increasing magnetic field so that the iron clusters will deflect in one direction when introduced in an inhomogeneous magnetic field. Experiment and theory are discussed for both cases.     

Rotational effects on the magnetic properties of an ensemble of free metal clusters

The magnetization of an ensemble of free magnetic metal clusters in an inhomogeneous external magnet field is calculated. In particular we have investigated the effects of the combined lattice anisotropy and cluster rotation on the magnetic properties. If weak anisotropy is present, almost superparamagnetic behavior is obtained. For stronger anisotropies deviations from this are calculated as a consequence of spin resonance due to the anisotropy field and the cluster rotation. This was proposed recently by de Heer et al. to explain his experimental data as generally expected, since a rotating cluster in a static magnetic field should behave similarly than a nonrotating one in an oscillating magnetic field. The magnetization depends also sensitively on the relaxation times.     

Magnetic properties of lanthanide organometallic sandwich complexes produced in a molecular beam

The magnetic properties of gas-phase terbium–cyclooctatetraene multi-decker sandwich complexes, Tb_n(C₈H₈)_n+1 were measured using a Stern-Gerlach type magnetic deflection approach. Beams of Tb_n(C₈H₈)_n+1 complexes displayed one-sided deflection toward high field – indicating that fast spin relaxation occurs within the complexes as they pass through the magnetic field. The magnetic moment for Tb_n(C₈H₈)_n+1 (n = 1−5) was evaluated using the Langevin model. Evolution of magnetic moment with the complex size is discussed with electronic structures for oxidation states of Tb^3+/2+ ions, implying the possibility of antiferromagnetic interaction of two adjacent Tb²⁺ ions.     

A Magnetic Study of Low Moment Nickel Clusters Formed from the Solid-State Decomposition Reaction of Nickel bis-1,5-Cyclooctadiene

Variable temperature SQUID magnetometry measurements were made on a sample of commercially available nickel bis-1,5-cyclooctadiene (Ni(COD)₂) is reported. The material is shown to be a mixed phase magnetic system where the Ni(COD)₂ behaves as a diamagnet containing a paramagnetic component at low temperatures which we believe consists of elemental Ni clusters arising from the decomposition of the material. The magnetic response of the Ni clusters can be described by the combination of two Langevin functions, which indicate cluster magnetic moments of 1.8 μ _B and 15 μ _B suggesting Ni _n clusters with n = 2–3 and n = 14–19. However, we demonstrate that these clusters appear to show a spin transition to an S = 0 state at low temperatures, which may be a consequence of interactions between the clusters and the surrounding organic medium. Nevertheless, our results suggest that Ni(COD)₂ is a novel material for the study of Ni clusters embedded in a diamagnetic background material.     

Photoelectron spectroscopy of jet-cooled aluminium cluster anions

Aluminium cluster anions (Al _n ^? ) are produced by laser vaporization without additional ionization and cooled by supersonic expansion. Photoelectrons from mass-identified anion bunches (n=2...25) are detached by laser light (hv=3.68 eV) and undergo energy analysis in a magnetic bottle-type time-of-flight spectrometer. The measurements provide information about the electronic excitation energies from ionic ground states to neutral states of the clusters. In contrast to bulk aluminium these cluster photoelectron spectra partially have well-resolved bands which originate from low-lying excited bands. For small clusters, especially the aluminium dimer and trimer, quantum-chemical calculations will be compared to the measurements. The electron affinity size dependence of larger clusters shows conclusive evidence for “shell” effects.     

Rotational coupling effects on the spin relaxation of free ferromagnetic clusters

A model based on resonant spin-rotation coupling is used to reproduce the magnetization of free iron clusters experimentally observed by Stern-Gerlach deflections. Due to the interaction with the rotating magnetocrystalline anisotropy field, the dynamics of the magnetic moment of the clusters cannot be explained only in terms of thermal relaxation. As in magnetic resonance experiments, modified Bloch equations can describe the interaction of the particle spin with the deflecting field and the rotating anisotropy field. The dependence of the magnetization on the rotational temperature of the clusters and the relaxation time is discussed.     

A density functional theory study on the Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>H (<Emphasis Type="Italic">n</Emphasis> = 1–10) clusters

Density functional GGA-PW91 method with DNP basis set is applied to optimize the geometries of Ag _n H (n = 1–10) clusters. For the lowest energy geometries of Ag _n H (n = 1–10) clusters, the hydrogen atom prefers to occupy the two-fold coordination bridge site except the occupation of single-fold coordination site in AgH cluster. After adsorption of hydrogen atom, most Ag _n structures are slightly perturbed and only the Ag₆ structure in Ag₆H cluster is distorted obviously. The Ag–Ag bond is strengthened and the strength of Ag–H bond exhibits a clear odd–even oscillation like the strength of Au–H bond in Au _n H clusters, indicating that the hydrogen atom is more favorable to be adsorbed by odd-numbered pure silver clusters. The adsorption strength of small silver cluster toward H atom is obviously weaker than that of small gold cluster toward H atom due to the strong scalar relativistic effect in small gold cluster. The pronounced odd–even alternation of the magnetic moments is observed in Ag _n H systems, indicating that the Ag _n H clusters possess tunable magnetic properties by adsorbing hydrogen atom onto odd-numbered or even-numbered small silver cluster.     

Magnetic and electronic properties of nanocrystalline Gd3Fe5O12 garnet

The Gd₃Fe₅O₁₂ nanocrystalline Gadolinium Iron Garnet (GdIG) obtained from a sintered block was milled in a high energy ball mill. We measured the magnetization at 5 K under applied fields up to 12 T. We report here our study of approach to saturation magnetization. The results have been interpreted within the framework of random anisotropy model. From an analysis of the approach to saturation magnetization some fundamental parameters have been extracted. We have determined the anisotropy field H_r and the local magnetic anisotropy constant K_L. In addition, first-principles spin-density functional calculations, using the Full potential Linear Augmented Plane Waves (FLAPW) method are performed to investigate electronic and magnetic structures. All computed parameters are discussed and compared to available experimental data.     

Magnetic properties of small nickel oxide clusters enclosed inY-zeolite

The magnetization of small nickel oxide clusters containing less than four nickel atoms (sample A) and about ten atoms (sample B), respectively, formed inside the supercages ofY-zeolite, was studied in the magnetic field below 50 kOe and in the temperature range of 2 to 600 K. The magnetic susceptibility of sample A obeyed a Curie-Weiss' (C-W) law above about 20 K with a C-W temperature of 12 K. A saturation behavior was observed in the magnetization versus field (M-H) curve below about 20 K. A hysteresis in the M-H curve and a remanent magnetization were found below about 7 K. A similar behavior was observed for sample B. The observed positive C-W temperature indicates a ferromagnetic interaction between nickel ions in each cluster, which is semiquantitatively consistent with nearest neighbor ferromagnetic interactions previously reported for antiferromagnetic NiO single crystals. The hysteresis suggests an enhanced magnetic anisotropy energy in the present clusters.     

Magnetic properties of 3d-transition-metal alloy clusters: (Fe x Cr1−x ) n

We present results for the magnetic properties of (Fe _x Cr_1?x ) _n alloy clusters obtained by using a tight-binding Hubbard Hamiltonian in the unrestricted Hartree-Fock approximation. The dependence of the average magnetic moment, local magnetic moments, magnetic order, and cohesive energy on the size and composition of the cluster were determined. In agreement with surface calculations, we find that the average magnetic moment of the alloy is larger than that of the cluster of one element. Forn=15 a transition from ferromagnetic to antiferromagnetic order is obtained forx≈0.4?0.53. We discuss the importance of the overlap interaction in the spin polarized charge distribution of the alloy (e.g., charge transfer, local magnetic moments). The characteristic properties of the mixed clusters are also discussed by comparison with available results for homogeneous clusters.     

Molecular dynamics calculation of half-lives for thermal decay of Lennard-Jones clusters

Molecular dynamics has been used with a Lennard-Jones (6–12) potential in order to study the decay behavior of neutral Argon clusters containing between 12 and 14 atoms. The clusters were heated to temperatures well above their melting points and then tracked in time via molecular dynamics until evaporation of one or more atoms was observed. In each simulation, the mode of evaporation, energy released during evaporation, and cluster lifetime were recorded. Results from roughly 2000 simulation histories were combined in order to compute statistically significant values of cluster half-lives and decay energies. It was found that cluster half-life decreases with increasing energy and that for a given value of excess energy (defined asE=(E _tot ?E _gnd)/n), the 13 atom cluster is more stable against decay than clusters containing either 12 or 14 atoms. The dominant decay mechanism for all clusters was determined to be single atom emission.     

Magnetic behaviour of the orthochromite La0.5Gd0.5CrO3

Magnetic behaviour of the perovskite La_0.5Gd_0.5CrO₃ has been studied. The orthochromite orders canted antiferromagnetically below Neel temperature T_N of ～225 K. Reversal of magnetization is observed in temperature dependence of magnetization measured in field cooled mode under external fields upto 500 Oe. In the field dependence of magnetization below T_N, a small hysteresis is observed with the magnetic anisotropy continuously increasing with lowering of temperature. Estimated values of Cr³⁺ moments, internal field due to sub-lattice of canted ordered Cr³⁺ and the paramagnetic Curie temperature of Gd³⁺ sub-lattice are found to be smaller than reported for GdCrO₃. Compared with Pr substituted analogue La_0.5Pr_0.5CrO₃, Cr³⁺ moment is about the same but the internal field at the Gd³⁺ sub-lattice is much smaller.     

Possible large magnetic moments in 4d transition metal clusters

The electronic structure and magnetism of 13 atom clusters of ruthenium, rhodium and palladium having face centered cubic(fcc) geometry has been studied using a Gaussian orbital basis and the local spin density approximation. Calculations were done for the lattice spacings relevant to the bulk crystal lattice. Using the fixed moment states as input potentials, as many as 3 self-consistent states were obtained for these clusters. The 3 converged states of Rh₁₃ cluster is found to have magnetic moments of 0.69 _μB , 1.00 _μB and 1.46 _μB . Out of these states, 0.69 _μB moment state is found to be the ground state. But the total energy difference between the 0.69 _μB and 1.00 _μB state is very small. The 1.46 _μB moment state coincides with the state reported previously by other authors which was obtained using the discrete variational method. The experimentally observed moment was around 0.47 _μB . Our calculated moment is closer to the experimentally observed moment than the previously reported moment, but is still a bit larger. Ru₁₃ cluster is also found to have large moments, and 3 self-consistent states are also obtained for this cluster. The 3 magnetic moments of the Ru₁₃ cluster are 0.46 _μB , 0.62 _μB and 1.08 _μB . Out of these states, 0.62 _μB moment state is found to be the ground state. For the Pd₁₃ cluster, in addition to the nonmagnetic state previously reported, a state with magnetic moment of 0.46 _μB is also found to exist indicating possible magnetism in cluster phase.     

Electronic structure and bonding in clusters: Theoretical studies

The electronic structures of small Al _n ,n=5, 9, 13, clusters with bulk geometry are studied using the ab initio Hartree-Fock-LCAO method. The cluster ground states have always multiplicity higher than the lowest possible value. However, the energy difference between ground and lowest low spin state decreases with increasing cluster size. The energy range of the Al _n cluster valence levels is comparable with the width of the occupied part of the 3sp band in bulk Al. The different binding mechanisms that arise when a CO molecule interacts with Al _n clusters in different coordination sites are analyzed in detail with the constrained space orbital variation (CSOV) method. Electrostatic and polarization contributions to the interaction are found to be important. Among charge transfer (donation) contributions π electron transfer from Al _n to CO corresponding to π backbonding is energetically more important than σ electron transfer from CO to Al _n characterizing the σ bond.     

Distribution of interatomic distances in large metallic clusters

Spherically averaged pseudopotential (SAPS) calculations have been done for Mg _n clusters, withn up to 250 within the framework of density functional theory. The electronic structure is computed resorting to the Thomas-Fermi-Dirac-Weizsäcker (TFDW) approximation for the kinetic energy. The equilibrium geometries have been obtained by minimizing the total cluster energy with respect to the atomic positions using the steepest-descent method. The ground state geometries obtained in this way are formed by spherical atomic shells, the number of them increasing with cluster size, up to a number of four for the biggest sizes considered here. An analysis of the distribution of the interatomic distances shows that the more internal is the shell, the more contracted are the interatomic distances. This effect diminishes progressively with increasing cluster size. For the purpose of comparison, similar calculations have been done with Cs _n clusters in the same size range, allowing us to reproduce previous results obtained using a more elaborated density functional technique (Kohn-Sham method). The inhomogeneous contraction of interatomic distances then appears as a general fact for simple metallic clusters and not only for alkaline ones.     

Theory for the atomic shell structure of the cluster magnetic moment and magnetoresistance of a cluster ensemble

We present a simple theory for the cluster size dependence of the average cluster magnetic moment of transition metal clusters. Assuming a local environmental dependence of the atomic magnetic moments, the cluster magnetization exhibits a magnetic shell structure, reflecting the atomic structure of the cluster. Thus, the observed oscillations of the average cluster magnet moment may serve as a fingerprint of the cluster geometry. We also discuss the giant magnetoresistance (GMR) exhibited by an ensemble of magnetic clusters embedded in a metallic matrix. It is shown that the magnetic anisotropy affects strongly the magnetization of the cluster ensemble under certain conditions. Since the GMR depends on the cluster ensemble magnetization, it can be used to determine the cluster magnetic anisotropy energy.     

Theoretical Study of Hydrogen Adsorption on Ruthenium Clusters

The geometries, stabilities, electronic, and magnetic properties of hydrogen adsorption on Ru _n clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The result indicates the absorbed species does not lead to a rearrangement of the basic cluster. For n > 2, three different adsorption patterns are found for the Ru _n H₂ complexes: One H atom binds to the Ru top site, and another H binds to the bridge site for n = 3, 5, 6, 8; bridge site adsorption for n = 4; hollow site and top site adsorption for n = 7. The adsorption energies display oscillation and reach the peak at n = 2, 4, 7, implying their high chemical reactivity. The small electron transferred number between H atoms and Ru _n clusters indicates that the interaction between H atoms and Ru _n clusters is small. When H₂ is absorbed on the Ru _n clusters, the chemical activity of corresponding clusters is dramatically increased. The absorbed H₂ can lead to an oscillatory behavior of the magnetic moments, and this behavior is rooted in the electronic structure of the preceding cluster and the changes in the magnetic moment are indicative of the relative ordering of the majority and minority LUMO’s. The second order difference indicates 5 is magic number in Ru _n H₂ and Ru _n clusters.