Nanomagnetism & Oxides Laboratory
What is a magnetoresistive element?
Two ferromagnetic layer separated by a spacer - insulating for TMR and conductive for GMR. The resistance of the structure depends on the relative orientation of the electrodes magnteziation as depicted in the figure.
The performance of  the sensors is given by its: 
-sensitivity (variantion of resistance versus field - typically 3%/mT for GMR and 100%/mT for TMR)
-noise (electronic and magnetic fluctuations)
-detectivity (field limit for a signal of noise ratio larger than 1) - typically between nT and pT/sqrt(Hz)  
The interest of GMR and TMR is their high detetivity for a small size and room temperature operating.