A magnetoresistive magnetic field gradiometer sensor, comprising a magnetoresistive bridge, wherein the magnetoresistive bridge is a half-bridge, wherein the magnetoresistive bridge comprises: a multiplicity of magnetoresistive arms that each include one or more magnetoresistive elements, the magnetoresistive sensor elements being MTJ elements, the magnetoresistive elements having shape anisotropy, and the magnetoresistive elements being formed on the same substrate and having the same shape anisotropy, same resistance value and same magnetic field sensitivity, wherein each magnetoresistive element within the magnetoresistive bridge has a magnetic pinning layer with a magnetic moment aligned in the same direction, permanent magnets, wherein the magnetoresistive elements are each positioned between two permanent magnets, wherein the permanent magnets are set at an angle of orientation with respect to the sensitive axis of the gradiometer, wherein the permanent magnets are configured to provide a cross-bias field (H cross 27) perpendicular to the sensitive axis of the gradiometer, and wherein the thickness (t) of the permanent magnets, the direction (θ mag 37) of the magnetic moment of the permanent magnets and the angle of orientation (θ sns 44) of the permanent magnets are configured to generate a bias magnetic field (H off) to zero the offset (H o) of the transfer curve of each magnetoresistive element, a substrate on which the magnetoresistive bridge and the permanent magnets are deposited, and wire bond pads (28, 29, 30) used to electrically interconnect the magnetoresistive magnetic field gradiometer sensor to an ASIC chip or to a terminal of a package lead frame by bond wires. a multiplicity of magnetoresistive arms that each include one or more magnetoresistive elements, the magnetoresistive sensor elements being MTJ elements, the magnetoresistive elements having shape anisotropy, and the magnetoresistive elements being formed on the same substrate and having the same shape anisotropy, same resistance value and same magnetic field sensitivity, wherein each magnetoresistive element within the magnetoresistive bridge has a magnetic pinning layer with a magnetic moment aligned in the same direction, permanent magnets, wherein the magnetoresistive elements are each positioned between two permanent magnets, wherein the permanent magnets are set at an angle of orientation with respect to the sensitive axis of the gradiometer, wherein the permanent magnets are configured to provide a cross-bias field (H cross 27) perpendicular to the sensitive axis of the gradiometer, and wherein the thickness (t) of the permanent magnets, the direction (θ mag 37) of the magnetic moment of the permanent magnets and the angle of orientation (θ sns 44) of the permanent magnets are configured to generate a bias magnetic field (H off) to zero the offset (H o) of the transfer curve of each magnetoresistive element, a substrate on which the magnetoresistive bridge and the permanent magnets are deposited, and wire bond pads (28, 29, 30) used to electrically interconnect the magnetoresistive magnetic field gradiometer sensor to an ASIC chip or to a terminal of a package lead frame by bond wires.