The development of Spin-transfer torque magnetic RAM (STT-MRAM) mass production requires high-quality dedicated test solutions, for which understanding and modeling of manufacturing defects of the magnetic tunnel junction (MTJ) is crucial. This paper introduces and characterizes a new defect called Back-Hopping (BH); it also provides its fault models and test solutions. The BH defect causes MTJ state to oscillate during write operations, leading to write failures. The characterization of the defect is carried out based on manufactured MTJ devices. Due to the observed non-linear characteristics, the BH defect cannot be modelled with a linear resistance. Hence, device-aware defect modeling is applied by considering the intrinsic physical mechanisms; the model is then calibrated based on measurement data. Thereafter, the fault modeling and analysis is performed based on circuit-level simulations; new fault primitives/models are derived. These accurately describe the way the STT-MRAM behaves in the presence of BH defect. Finally, dedicated march test and a Design-for-Test solutions are proposed.