Georgia Tech Cluster Beam Lab
PI: Walt de Heer

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Metal Cluster Physics

Metal cluster physics approaches condensed matter physics in a unique way. It attempts to explain and organize metallic properties by tracing their evolution from the atom to the bulk. Cluster sources produce a broad distribution of cluster sizes ranging from two atom dimers all the way up to tens of thousands of atoms. This allows the properties of clusters to be measured as a function of cluster size. For example, the electric polarizability is measured for a series of clusters with chemical composition MN, where N varies from 1 to several hundred, typically. Examination of these trends provides information about the bulk evolution of this property and directly connects atomic and molecular properties with their bulk counterparts.

Discovery of Shell Structure in Alkali Clusters

The first, and still one of the most important investigations along these lines, is the discovery of an electronic shell structure by de Heer and coworkers when he was a graduate student at UC Berkeley 25 years ago. This discovery stands out as a prime example of the power of the technique and the information that can be obtained from it. Conside figure 1, which shows a typical mass spectrum for sodium clusters.


Figure 1: Abundance spectrum of Na clusters.
From Electronic Shell Structure and Abundances of Sodium Clusters
W. D. Knight, Keith Clemenger, Walt A. de Heer, Winston A. Saunders, M. Y. Chou and Marvin L. Cohen
Phys. Rev. Lett. 52, 2141 - 2143 (1984)

This spectrum was obtained by heating a sodium metal target in an enclosed source chamber equipped with a pinhole nozzle. The resulting sodium vapor is then mixed with cooled He gas and is ejected out of the nozzle. In the process, the metal vapor condenses into extremely small droplets, what we call clusters. The clusters then enter a high vacuum chamber where they are ultimately detected as follows: The clusters are ionized using a UV light source and the cluster ions MN+ are detected with mass sensitivity in a quadrupole mass analyzer that is supplied with a sensitive ion detector, resulting in a mass spectrum as shown in figure 1 above.

Despite the apparent simplicity of the experiment, this mass spectrum has become an icon in cluster physics (for a review of earlier work, see W. A. de Heer, Review of Modern Physics 65, 611 (1993)). Note that there are abundance maxima at N= 2, 8, 20, 40, 58, and 92. This experiment has led to the realization that these numbers result from quantum confinement of electrons in a spherical well. That is, it demonstrated that alkali metal clusters have electronic shell structures: they resemble superatoms. Subsequent measurements verified that essentially all of the structures, including the small intensity variations in the mass spectrum, are explained in terms of an ellipsoidal shell model. Electronic shell structure now serves as the foundation of much of cluster physics, and in fact actually addresses a much deeper problem of the emergence of the metallic state. However, the fundamental question of how the metallic state develops remains only partly answered. It is perhaps interesting to note that these very early cluster experiments and the discovery of superatoms have recently come to the forefront of chemistry and physics. It is pleasing to see that 25 years after their discovery, the electronic shell concept in metal clusters is providing a foundation for a new chemistry.

Ferromagnetism from Atom to Bulk in Iron, Cobalt, and Nickel Clusters

Another advance in the cluster field was the measurement of the magnetic moments of Fe, Co, and Ni clusters. Producing a beam of these clusters required new innovation in cluster sources. These metals have very high melting temperatures, so their cluster forms cannot be produced with the same gas aggregation methods used to produce beams of Na clusters. Instead of thermal evaporation, a laser pulse can be used to produce the metal vapor by ablation. A nanosecond pulse of light from a Q-switched laser is focused onto a tiny spot of a metal target rod. The focused laser pulse has high enough intensity to instantly vaporize the metal at the focal point. If this vapor is quenched by a stream of cooled, inert gas, then the metal will condense into clusters. The development of this method enabled the production of beams of Fe, Co, and Ni clusters, to name a few.


Figure 2: Magnetic moments per atom of Co clusters.
From Magnetism from the Atom to the Bulk in Iron Cobalt and Nickel Clusters
Isabelle M. L. Billas, A. Châtelain, and Walt A. de Heer
Science Vol. 265 No. 5179 p. 1682 (1994)

In the bulk, the magnetization of these metals is due to spin polarization of the conduction electrons. They also have fractional moments per atom. Cobalt, for example, shows a magnetization of ~1.7 Bohr magnetons (μB) per atom. Clusters provide an ideal system to investigate how these fractional moments arise from electron spin, which comes in units of 1 μB. Recent results from our lab have found that for all cobalt clusters there are two magnetic states - one with 1 μB and another with 2 μB. These states become degenerate in the bulk limit and mix to produce the observed fractional moments.

Ferroelectricity in free Niobium Clusters

One of the defining properties of a metal is the screening of electric fields. Because of these screening properties, the internal electric field of a metal is exactly zero, and thus there is no electric dipole moment. At low temperatures (~30 - 50 K), however, it has been observed that Nb, V, and Ta clusters acquire large electric dipole moments. The fact that these dipole moments vanish at such a low transition temperature suggests a mechanism that acts at a very low energy scale.


Figure 3. Ferroelectric fraction of Nb Clusters at XX K.
See Ramiro Moro, Xiaoshan Xu, Shuangye Yin and Walt A. de Heer.
Ferroelectricity in Free Nb Clusters
Science Vol. 300 No. 5623 p. 1265 (2003)

These materials are good conductors in the bulk, so their screening must be inhibited when they are formed into clusters. Deflection experiments reveal that the ferroelectric polarization is weakly coupled to the cluster body. The most curious effect of all is the strong odd-even alternation of the ferroelectric fraction which begins around N = 20, and persists consistently until N = 100 (see figure 3). The even-N clusters show a larger ferroelectric fraction than the odd-N clusters. This odd-even alternation depends only on the total number of valence electrons in the cluster. The electronic origin of this effect has been demonstrated by a series of experiments where Nb clusters were doped with an impurity - impurities which donate or oxidize an odd number of valence electrons invert the odd-even effect, while impurities such as oxygen which oxidize an even number of valence electrons leave the odd-even effect unchanged. Doping a cluster with a magnetic impurity like manganese quenches the dipole moment.


Copyright © 2013 W.A. de Heer