A single Co atom adsorbed on Cu(111) or on ferromagnetic Co islands is contacted with nonmagnetic W or ferromagnetic Ni tips in a scanning tunneling microscope. When the Co atom bridges two non-magnetic electrodes conductances of 2 e 2 /h are found. With two ferromagnetic electrodes a conductance of e 2 /h is observed which may indicate fully spin-polarized transport.PACS numbers: 68.37. Ef,72.25.Ba,73.23.Ad,73.63.Rt The conductance of nanometer-sized contacts may be decomposed into contributions of transport eigenchannels according to G = G 0 n i=1 τ i , where G 0 = 2e 2 /h is the quantum of conductance (-e: electron charge, h: Planck's constant), and τ i is the transmission probability of the ith channel [1,2]. The factor 2 in the quantum of conductance is due to spin degeneracy. In contacts involving magnetic electrodes the spin degeneracy of transport channels may be lifted. Each spin-polarized channel then may contribute up to G 0 /2 to the total conductance.A quantized conductance of G 0 /2 is expected when a fully spin-polarized current is transmitted with a probability of 1 through a spin-polarized transport channel. These conditions appear difficult to fulfill. Nevertheless, experimental observations of conductance quantization in units of G 0 /2 have repeatedly been reported [3,4,5,6,7,8]. These conductances were observed with [4,6] or without [3,5,7,8] external magnetic fields, for ferromagnetic [3,4,5,6,7] and non-magnetic electrodes [7,8]. On the other hand, the absence of noninteger conductance quantization has also been inferred from experimental results [9,10]. Untiedt et al. showed that contaminants like H 2 or CO modify the conductance and could, in the case of CO adsorption on Pt electrodes, give rise to a conductance of G 0 /2 [10]. A considerable variety of model calculations [11,12,13,14,15] have been performed and support the notion that conductance quantization in units of G 0 /2 is not expected from the investigated ferromagnetic contacts. It should be noted, however, that the modeling performed so far did not include geometrical relaxations of the contacts although the importance of the detailed atomic arrangement has been emphasized [11,15,16,17].The contradictory conclusions reached from the various experiments may be related to a lack of characterisation of the atomic details of the junction. This problem may be reduced by using a cryogenic scanning tunneling microscope to probe the conductance of clean singleatom contacts in ultra-high vacuum. Here we apply this approach to investigate prototypical junctions. A single magnetic atom on a spin-polarized island or a nonmagnetic substrate is contacted with non-magnetic and ferromagnetic tips. We find that the conductance of a single Co atom is G 0 when two non-magnetic electrodes are used. With ferromagnetic electrodes the conductance is G 0 /2. Conductances of ≈ 0.9 G 0 are observed for a combination of a non-magnetic and a ferromagnetic electrode. In contrast to previous experiments, the contact geometry and chemistry are character...