In recent years there has been considerable interest[1] in wire produced by subjecting cold-drawn Vicalloy to a schedule of stretching and twisting first developed by J. Wiegand[2]. Magnetization reversal in this wire occurs by a single giant Barkhausen jump, leading to a number of sensor-based applications. We show that the unusual switching behavior is due to a nearly perfect single magnetic domain running the length of the wire. This condition results from a doubly helical residual stress pattern (see figure) built into the wire by the twisting process. This stress is extremely large, causing a single-domain behavior first noted by Preisach[3] and Sixtus and Tonks[4] in externally stressed wires. The central region of the wire is frozen in axial tension (∼80 Kg/mm2) and twist, whereas the outer region is in compression and twist of opposite chirality. This model accounts for all of the observed properties of this wire[5].