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We report measurements and calculations of the spin-polarization, induced by a parallel magnetic field, of interacting, dilute, two-dimensional electron systems confined to GaAs/AlGaAs heterostructures. The results reveal the crucial role the non-zero electron layer thickness plays: it causes a deformation of the energy surface in the presence of a parallel field, leading to enhanced values for the effective mass and g-factor and a non-linear spin-polarization with field.

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