The magnetic coupling between single Co atoms adsorbed on a copper surface is determined by probing the Kondo resonance using low-temperature scanning tunneling spectroscopy. The Kondo resonance, which is due to magnetic correlation effects between the spin of a magnetic adatom and the conduction electrons of the substrate, is modified in a characteristic way by the coupling of the neighboring adatom spins. Increasing the interatomic distance of a Cobalt dimer from 2.56 to 8.1 A we follow the oscillatory transition from ferromagnetic to antiferromagnetic coupling. Adding a third atom to the antiferromagnetically coupled dimer results in the formation of a collective correlated state.

The electronic structure of thin Co nanoislands on Cu(111) has been investigated below and above the Fermi level (E(F)) by scanning tunneling spectroscopy at low temperature. Two surface related electronic states are found: a strong localized peak 0.31 eV below E(F) and a mainly unoccupied dispersive state, giving rise to quantum interference patterns of standing electron waves on the Co surface. Ab initio calculations reveal that the electronic states are spin polarized, originating from d3(z(2)-r(2))-minority and sp-majority bands, respectively.

Quantum interference is a coherent quantum phenomenon that takes place in confined geometries. Using spin-polarized scanning tunneling microscopy, we found that quantum interference of electrons causes spatial modulation of spin polarization within a single magnetic nanostructure. We observed changes in both the sign and magnitude of the spin polarization on a subnanometer scale. A comparison of our experimental results with ab initio calculations shows that at a given energy, the modulation of the spin polarization can be ascribed to the difference between the spatially modulated local density of states of the majority spin and the nonmodulated minority spin contribution.

Single molecule magnets and single spin centres can be individually addressed when coupled to contacts forming an electrical junction. To control and engineer the magnetism of quantum devices, it is necessary to quantify how the structural and chemical environment of the junction affects the spin centre. Metrics such as coordination number or symmetry provide a simple method to quantify the local environment, but neglect the many-body interactions of an impurity spin coupled to contacts. Here, we utilize a highly corrugated hexagonal boron nitride monolayer to mediate the coupling between a cobalt spin in CoHx (x=1,2) complexes and the metal contact. While hydrogen controls the total effective spin, the corrugation smoothly tunes the Kondo exchange interaction between the spin and the underlying metal. Using scanning tunnelling microscopy and spectroscopy together with numerical simulations, we quantitatively demonstrate how the Kondo exchange interaction mimics chemical tailoring and changes the magnetic anisotropy.

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Let k be a positive integer and let G k denote the set of all joint distributions of k-tuples (a 1 , . . . , a k ) in a non-commutative probability space (A, ϕ) such that ϕ(a 1 ) = · · · = ϕ(a k ) = 1. G k is a group under the operation of free multiplicative convolution ⊠. We identify G k , ⊠ as the group of characters of a certain Hopf algebra Y (k) . Then, by using the log map from characters to infinitesimal characters of Y (k) , we introduce a transform LS µ for distributions µ ∈ G k . LS µ is a power series in k non-commuting indeterminates z 1 , . . . , z k ; its coefficients can be computed from the coefficients of the R-transform of µ by using summations over chains in the lattices N C(n) of non-crossing partitions. The LS-transform has the "linearizing" property thatIn the particular case k = 1 one has that Y (1) is naturally isomorphic to the Hopf algebra Sym of symmetric functions, and that the LS-transform is very closely related to the logarithm of the S-transform of Voiculescu, by the formulaIn this case the group (G 1 , ⊠) can be identified as the group of characters of Sym, in such a way that the S-transform, its reciprocal 1/S and its logarithm log S relate in a natural sense to the sequences of complete, elementary and respectively power sum symmetric functions.

One of the most promising candidates for the construction of ultrahigh-density storage media is low-dimensional atomic-scale magnetic nanostructures exhibiting magnetic bi- or multistability. Here we propose a novel route of locally controlling and switching magnetism in such nanostructures. Our ab initio studies reveal that externally applied electric field can be used for this purpose.

The state of the art ab initio calculations of quantum mirages, the spin polarization of surface-state electrons, and the exchange interaction between magnetic adatoms in Cu and Co corrals on Cu(111) are presented. We find that the spin polarization of the surface-state electrons caused by magnetic adatoms can be projected to a remote location and can be strongly enhanced in corrals, compared to an open surface. Our studies give clear evidence that quantum corrals could permit one to tailor the exchange interaction between magnetic adatoms at large separations.