Coulomb-blockade spectroscopy measurements are made on a small GaAs/AlGaAs quantum dot in a magnetic field oriented parallel to the plane of the sample. Coulomb-blockade peak motion is observed which can be explained by changes in the spin of successive ground states as single electrons are added. The peak movement at low field is consistent with that expected from Zeeman coupling, from which it can be inferred that electrons are not added to the dot in a strictly alternating spin up/spin down manner.

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