Size effect in the low temperature magnetoresistance of narrow GaAs/AlGaAs wires

We have measured the low temperature magnetoresistance of narrow wires formed as constrictions in the two-dimensional electron gas of a GaAs/AlGaAs heterojunction. In the quasi-ballistic regime, two relaxation times, at high and low magnetic fields, are observed in the amplitude analysis of the Shubnikov-de Haas oscillations. The boundary field which distinguishes these relaxation times is found to be determined by a simple relationship between the conducting width and the corresponding cyclotron radius. We discuss these features in terms of the effect of the magnetic field on sidewall scattering in a quasi-ballistic wire.