A sensor including a measuring assembly integrating at least one magnetoresistive element having a stack of two conductive magnetic layers, respectively reference and sensitive, the reference layer having magnetic anisotropy in the direction X and the sensitive layer having a direction Y, a polarization permanent magnet having a surface extending in a plane of directions X and Y and having a symmetry plane of directions X and Z, the measuring assembly being disposed with respect to the symmetry plane of the polarization magnet so that the layers of the magnetoresistive element are disposed in a plane parallel to the surface while being offset from said plane in the direction Y by a distance (Δy) that is arranged so that the magnetic field of the polarization magnet orients the magnetisation of the sensitive layer in the direction Y.