Magnetic materials reduced to a single atom show unexpected magnetic properties that interact with the spin states of the transmitting electrons and modify the nature of the quantized conductance. This integration of quantized conductance and spin-dependent transport across a magnetic atom gives rise to a multichannel system across which the transmission of electron waves can be regulated by a domain wall acting as a 'valve'-a quantum spin-valve. Here we measure complete magnetoresistance loops across magnetic quantum point contacts as small as a single atom, using cobalt. 'Discrete' or quantum magnetoresistance loops are observed owing to the varying transmission probability from the available discrete conductance channels. A remarkable feature of these quantum contacts is the discovery of a rapid oscillatory decay in magnetoresistance with increasing contact size. The results provide an evolutionary trace of spin-dependent transport from a single atom to larger ensembles.