Metal magnetic memory testing technology has been effectively used in stress concentration areas and micro-cracks detection of ferromagnetic metal components. However, due to the lack of profound theoretical basis and effective experimental research, the magnetic memory signal characteristics and magnetism quantitative relationship has not yet been determined. In this study, the full electronic potential magneto-mechanical model is established which is using the norm conserving pseudo-potential algorithm based on the first-principle. The quantitative relationship is then calculated between the stress concentration and the magnetic memory signal. The calculation results show that the changes of the wave function, which result from the stress concentration in the solid band, are the fundamental cause of the magnetic memory phenomenon, and atomic magnetic moment, lattice constant and the magnetic flux leakage signal strength linearly changes as a function of stress trend. As the stress concentration reached the critical stress point, the lattice structure was damaged, and the magnetic memory signal had undergone mutation. In this study, the experimental results are consistent with the theoretical calculation results.