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.

We investigate the magnetization reversal of individual Co islands on Cu(111) in the size range of N=700 to 18,000 atoms by spin-polarized scanning tunneling microscopy at 8 K. The switching field H(sw) changes with island size in a nonmonotonic manner: it increases with island size and reaches a maximum value of 2.4 T at N=5500 atoms, and it decreases for larger islands. We extract the energy barrier for magnetization reversal as a function of island size. The maximum H(sw) corresponds to an energy barrier of 1 eV. Our results elucidate a crossover of the magnetization reversal from an exchange-spring behavior to domain wall formation with increasing size at around 7500 atoms.

Spin-dependent scanning tunneling spectroscopy has been performed on single Co islands on Cu(111) at 7 K in fields of up to 4 T. The differential conductance shows a hysteretic behavior as a function of magnetic field. Symmetric hysteresis curves of the differential conductance are obtained which identify an abrupt switching of the Co island magnetization along the sample normal at fields around 1.5 T, and a reversible change of the spin orientation of the Cr-tip apex with increasing magnetic field. Our result allows a clear-cut assignment of the differential conductance curves in terms of parallel and antiparallel states of the spin orientation between tip and sample.

We propose a conclusive characterization of the magnetic configuration of tips for spin-polarized scanning tunneling microscopy studies. We show that both careful tip preparation and characterization by tunneling spectroscopy need to be augmented by in-field measurements to ensure a reliable analysis of a magnetic contrast in spin-polarized scanning tunneling microscopy studies.

We investigate the local tunnel magnetoresistance (TMR) effect within a single Co nanoisland using spin-polarized scanning tunneling microscopy. We observe a clear spatial modulation of the TMR ratio with an amplitude of ~20% and a spacing of ~1.3 nm between maxima and minima around the Fermi level. This result can be ascribed to a spatially modulated spin polarization within the Co island due to spin-dependent quantum interference. Our combined experimental and theoretical study reveals that spin-dependent electron confinement affects all transport properties such as differential conductance, conductance, and TMR. We demonstrate that the TMR within a nanostructured magnetic tunnel junction can be controlled on a length scale of 1 nm through spin-dependent quantum interference.

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Multiphoton photoemission, scanning tunneling spectroscopy, and first-principles electronic structure calculations have been applied to determine the dispersion of the occupied and unoccupied Shockley surface state of Cu(111). The dispersion deviates significantly from the paradigmatic parabolic behavior of quasi-free electrons with increasing energy above the Fermi level. Based on our calculations, we ascribe this deviation to the shift of the spectral weight of the surface state into the bulk, and of bulk states toward the surface, which leads to an enhanced hybridization between the states with increasing energy.

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm 2 .