Size-dependent effects in exchange-biased planar Hall effect sensor crosses

Exchange-biased planar Hall effect magnetic field sensor crosses with arm width w have been studied as function of w. For large values of w, the magnetic behavior is hysteresis-free and follows the single domain Stoner–Wohlfarth model. When w is decreased, hysteresis is observed in the sensor response. For intermediate values of w, the magnetization reversal takes place in two steps, and for small values of w, the magnetization reversal takes place in a single step. Based on electrical measurements, magnetic force microscopy, and micromagnetic simulations, the observations are explained by an increasing magnetic shape anisotropy of the arms of the cross. We propose a simple analytical model that captures the essential physics of the observations and parameterizes the effects of the cross-shape on the central part of the cross.