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Description
Magnetism is a macroscopic phenomenon that at microscopic level occurs due to exchange interactions, whose typical range, or more simply length scale, is determined by the spatial extent of the quantum mechanical wavefunctions. Confinement of these wavefunctions by for example the presence of a surface leads to many unusual magnetic phenomena. A natural question, in light of these considerations, is what happens in a system smaller than the length scale of the bulk exchange field?
Here we follow, both experimentally and theoretically, the development of magnetism in very small particles, or clusters, of various materials, starting from the atomic limit and adding one atom at a time. A wealth of non-intuitive and instructive magnetic phenomena can be found. Thus, in rare-earth clusters the usual bulk RKKY exchange interaction is replaced with an oscillatory ferromagnetic double-exchange and antiferromagnetic superexchange [1], leading to irregular oscillations of magnetic order as a function of the cluster size.
The most unusual is the appearance of magnetism in the normally nonmagnetic materials, such as rhodium [2], or even vanadium and niobium [3]. Particularly striking is Rh, that presents an example of multiferroic behavior in metal clusters. The fact that it is observed in rhodium is even more surprising, since this metal is neither ferromagnetic nor ferroelectric in the bulk. From a broader perspective, the emergence of ferroelectricity in small metal clusters appears to be mediated by very low energy excitations, possibly involving a single vibronic mode that is associated with a broken symmetry ground state [2].
Another intriguing question is how a single dopant atom can modify the properties of a cluster? Magnetic deflection experiments on isolated Co doped Nb clusters demonstrate a strong size dependence of magnetic properties, with large magnetic moments in certain cluster sizes, and fully non-magnetic behavior of others. There are in principle two explanations for this behavior. Either the local moment at the Co site is absent or it is screened by the delocalized electrons of the cluster, i.e. the Kondo effect. In order to reveal the physical origin, first, we established the ground state geometry of the clusters by experimentally obtaining their vibrational spectra and comparing them with a density functional theory study. Then, we performed an analysis based on the Anderson impurity model. It appears that the non-magnetic clusters are due to the absence of the local Co moment and not due to the Kondo effect. In addition, the magnetic behavior of the clusters can be understood from an inspection of their electronic structure. Here magnetism is favored when the effective hybridization around the chemical potential is small, while the absence of magnetism is signalled by a large effective hybridization around the chemical potential.
As a final note, the isolation of the clusters from the environment makes them ideal objects to study a transition between quantum and classical behavior. Kramers degeneracy, onset of Kondo screening, etc, could be studied with exact control of the electronic and geometric structure.
The work was supported by de Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) and the European Research Council.
[1] L. Peters et al., Sci. Reports 6, 19676 (2016).
[2] L. Ma et al., Phys. Rev. Lett. 113, 157203 (2014).
[3] A. Diaz Bachs et al., to be published
