MAGNETISM OF SMALL TRANSITION-METAL CLUSTERS AND EFFECTS OF ISOMERIZATION

We investigate the magnetic properties of small transition-metal clusters using a simple statistical model, which requires some input data from ab-initio spin-density-functional calculations. In our study, we consider a thermodynamically equilibrated ensemble of clusters with different structures, spin multiplicities, and ground-state energies. We calculate the physical properties of this system by weighting the individual configurations according to the Boltzmann statistics. We find that presence of isomers with very similar ground-state energies, yet very different magnetic properties, gives rise to a rich magnetic behavior of the system which differs significantly from what would be expected for single configurations. We apply the present model to determine the magnetic susceptibility of a cluster ensemble of Langevin paramagnets. Our results show that some of the anomalies in the magnetic behavior of transition-metal clusters might be understood in the framework of our model which is, of course, limited by the extremely high computational effort needed to obtain the input data.

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

Molecules ◽

10.3390/molecules23081896 ◽

2018 ◽

Vol 23 (8) ◽

pp. 1896 ◽

Cited By ~ 2

Author(s):

Habte Berry ◽

Baolin Wang ◽

Qinfang Zhang

Keyword(s):

Magnetic Properties ◽

Transition Metal ◽

Transition Metals ◽

Metal Clusters ◽

Critical Size ◽

Common Knowledge ◽

Magnetic Behavior ◽

Transition Metal Clusters ◽

Transition Elements ◽

Discrete Energy

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.

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MAGNETISM OF FREE TRANSITION METAL AND RARE EARTH CLUSTERS

International Journal of Modern Physics B ◽

10.1142/s0217979293002249 ◽

1993 ◽

Vol 07 (04) ◽

pp. 1079-1114 ◽

Cited By ~ 65

Author(s):

J.P. BUCHER ◽

L.A. BLOOMFIELD

Keyword(s):

Magnetic Field ◽

Magnetic Properties ◽

Transition Metal ◽

Magnetic Moment ◽

Effective Magnetic Moment ◽

Metal Clusters ◽

Vibrational Temperature ◽

Rotational Temperature ◽

Magnetic Behavior ◽

Transition Metal Clusters

When ferromagnetic (monodomain) transition metal clusters pass through a magnetic field gradient, they deflect towards increasing magnetic field. For transition metal clusters with a size between N=10 and N=400 atoms, the observable effective magnetic moment (similar to magnetization), measured from the cluster deflection, scales with magnetic field, cluster size and inverse of cluster vibrational temperature. The measurements are in quantitative agreement with a picture in which the cluster moments are subject to rapid orientational fluctuations and explore the whole distribution of magnetic moment projections on the field axis on the time scale of the experiment. Intrinsic magnetic moments per atom in excess of the bulk values are obtained. While transition metal clusters show a size independent behavior of the magnetic properties down to N=20, similar to what was observed previously for transition metal clusters in matrices, rare earth clusters are quite sensitive to symmetry (anisotropy) and exhibit dramatic variations in their magnetic behavior as a function of size. These size-specific variations of the magnetic behavior of clusters have never been seen before. Except for some “magic numbers”, for which the statistical interpretation still holds, an anomalous spreading of the deflection profile is observed. This spreading is due to a strong coupling of the magnetic moment with the cluster body. When the moment is locked to the lattice by strong crystal field anisotropies, the rotational temperature starts to play an important role in the interpretation of experimental data. This distinct behavior points to the fact that 3d and 4f ferromagnets react quite differently to a confined geometry. This dissimilarity is due in part to a different relative importance of magnetic anisotropy energy and exchange energy. It is found that Gd and Tb clusters retain their magnetic order for temperatures well above their bulk Curie temperatures. Three aspects of cluster magnetic properties can be determined by molecular beam experiments: (i) The effective magnetic moment of a cluster (equivalent to magnetization in a laboratory reference frame), (ii) the intrinsic quasi ground state properties in the reference frame of the particle, such as the magnetic moment per atom and the temperature dependence of the order parameter, and (iii) the dynamics of the cluster as a whole. While the vibrational temperature T vib is almost an experimental input, the rotational temperature T rot can be inferred in the case of strong anisotropy.

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