Methods and apparatus are provided for sensing physical parameters. The apparatus comprises a magnetic tunnel junction (MTJ) and a magnetic field source whose magnetic field overlaps the MTJ and whose proximity to the MTJ varies in response to an input to the sensor. A magnetic shield is provided at least on a face of the MFS away from the MTJ. The MTJ comprises first and second magnetic electrodes separated by a dielectric configured to permit significant tunneling conduction therebetween. The first magnetic region has its spin axis pinned and the second magnetic electrode has its spin axis free. The magnetic field source is oriented closer to the second magnetic electrode than the first magnetic electrode. The overall sensor dynamic range is extended by providing multiple electrically coupled sensors receiving the same input but with different individual response curves and desirably but not essentially formed on the same substrate.