The local and average orbital moments of transition-metal (TM) clusters are determined bridging the gap between atomic Hund's rules and solid-state quenching. A remarkable enhancement of is revealed in agreement with recent measurements. In small Ni(N) (N< or =10), represents (20-40)% of the total magnetization and is therefore crucial for the comparison between theory and experiment. Larger clusters (N> or =150) show nearly bulklike quenching at the interior but retain a considerable surface enhancement. Trends for different TM's are discussed.

Magneto-resistance is a physical effect of great fundamental and industrial interest since it is the basis for the magnetic field sensors used in computer read-heads and Magnetic Random Access Memories. As device dimensions are reduced, some important physical length scales for magnetism and electrical transport will soon be attained. Ultimately, there is a strong need to know if the physical phenomena responsible for magneto-resistance still hold at the atomic scale. Here, we show that the anisotropy of magneto-resistance is greatly enhanced in atomic size constrictions. We explain this physical effect by a change in the electronic density of states in the junction when the magnetisation is rotated, as supported by our ab-initio calculations. This stems from the "spinorbit coupling" mechanism linking the shape of the orbitals with the spin direction. This sensitively affects the conductance of atomic contacts which is determined by the overlap of the valence orbitals.PACS numbers: PACS numbers: 75.70. Kw, 72.75.Gd The effect of an external field on the resistivity of pure ferromagnetic metals (the magnetoresistance-MR) was the subject of intense research work in the second half of the 20ieth century. The field has seen a renewed interest in the past fifteen years with the discovery of giant effects in systems combining magnetic and non-magnetic materials. This Giant Magneto-Resistance (GMR) has had a tremendous impact both through its industrial applications as read-heads and Magnetic Random Access Memories as well as for triggering the field of "spintronics" [1], aiming to use the spin of the charge carriers in electronic devices with higher functionalities. As the pressure towards miniaturization increases, it is important to understand how magnetoresistive effects are influenced by size reduction. In constrictions of dimensions close to the Fermi wavelength, boundary conditions enforce that transverse electronic modes are quantized which results in the discreteness of propagating electron modes. 2-D electron gases are archetypical systems in which the conductance is quantized in units of 2e 2 /h. In metals where the Fermi wavelength is typically 3Å, one needs to reach atomic dimensions in order to observe such effects [2]. But because even in the single atomic regime several orbitals overlap, one normally finds that several conduction channels are opened with imperfect transparency, i.e. each channel has a transmittance associated to it (a coefficient between 0 and 1). Calculations seem to indicate that 4 or 5 channels participate significantly to the conduction of 3d transition metal nanocontacts [3,4]. The magneto-resistance obtained when one side of the contact flips its magnetization is enhanced compared to that in the bulk [4,5] and values of the order of 20% have been reported in some careful experiments [6,7]. On the other hand, one could expect some dependence of the conductance to the direction of the magnetization because changing the spins' direction will affect the orbitals through a mechanism ...

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