A magnetic field sensor for sensing an external magnetic field is disclosed. The magnetic field sensor includes at least two magnetic tunneling junction (MTJ) elements disposed on an underlying electrode. Each of the MTJ elements is formed by a synthetic antiferromagnetic layer, a barrier layer and a free layer sequentially stacked together. A top electrode is then connected to the free layers. The free layer can be a single free layer, a composite free layer, a synthetic antiferromagnetic free layer or an alloy free layer. When a current is applied to a metal circuit passing over or below the MTJ elements, free magnetic moments generated by the MTJ elements are anti-parallel to each other along a reference axis, and the angles between the magnetic moments created by the MTJ elements and the reference axis are 40 to 50 degrees and 130 to 140 degrees, respectively.