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A method is presented for measuring weak magnetic fields by applying a measurement principle known from fluxgate magnetometers to a magnetic tunnel junction. The fluxgate measurement principle based on second harmonic detection is transferred to magnetic tunnel junctions embedded in current lines. Based on Fourier analysis, we developed an analytical model to describe the response of a magnetic tunnel junction fluxgate sensor. The analytical result is compared to MATLAB simulations using Fast Fourier Transformation. Experimental results are obtained with a sensor prototype using lock-in amplification to detect the second harmonic component of the signal generated by the resistance change of the junction. A linear sensor characteristic with a sensitivity in the order of mV/mT is detected in an unshielded setup. Design improvements of the sensor layout as well as a low RA product of the magnetic tunnel junctions should make it possible in the future to detect pT-fields. A cheap sensing technology using magnetic tunnel junctions with the ability of measuring fields in the order of pT could promote novel diagnostic methods such as magnetocardiography into daily clinical routine.