Magnetoresistive sensors based on giant magnetoresistance (GMR) or tunnel magnetoresistance (TMR) play a major role towards the miniaturization in the industrial society. Typically, spin-valve-type magnetoresistive sensors are embedded in a Wheatstone bridge configuration with rectangular, meander-like or elliptically shaped thin film elements. Such elements usually switch via multi-domain, C- or S-shaped magnetization states and, therefore, often exhibit an open non-linear hysteresis curve. Linearity and hysteretic effects are key features in the improvement of such sensors.
We will present a different approach by using circularly shaped elements exhibiting a different magnetization state of a magnetic vortex . This is one of the fundamental magnetization ground states occurring in disk-shaped thin film elements and is characterized by minimization of the demagnetizing energy at the expense of exchange energy.
Experimental data were generated on electrically contacted GMR and TMR disks which were fabricated by optical lithography. The following advantages will be discussed and compared to standard elliptical sensor elements. (a) The vortex state shows essentially no hysteresis in the minor loop. (b) Since the vortex nucleation happens prior to the zero field, the M(H=0)=0 crossing is independent of history. (c) The critical fields can be easily controlled by the element geometry. (d) The noise is low.
All characteristic experimental values have been determined in dependence of free layer thickness, disk diameter and temperature. These findings are discussed in the frame of the semi-analytical rigid-vortex-model  and micromagnetic simulations.
The financial support by the Austrian Federal Ministry of Science, Research and Economy and the Christian Doppler Research Association in Austria is gratefully acknowledged.
 D. Suess, A. Bachleitner-Hofmann, A. Satz, H. Weitensfelder, C. Vogler, F. Bruckner, C. Abert, K. Prügl, J. Zimmer, C. Huber, S. Luber, W. Raberg, T. Schrefl, H. Brückl, „Topologically Protected Vortex Structures to Realize Low-Noise Magnetic Sensors with High Linear Range”, Nature Electronics 1, 362 (2018)
 K. Y. Guslienko et al., “Magnetization reversal due to vortex nucleation, displacement, and annihilation in submicron ferromagnetic dot arrays”, Phys. Rev. B 65 (2001)