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We study the amplification of weak magnetic field with Weak-value techniquebased on Faraday magneto-optic effect. By using a different scheme to performthe Sagnac interferometer with the probe in momentum space, we havedemonstrated the new weak measure protocol to detect the small weak magneticfield by amplifying the phase shift of Faraday magneto-optic effect. At thegiven the maximum incident intensity of the initial spectrum, the detectionlimit of the intensity of the spectrometer and the accuracy of detecting weakmagnetic field, we can theoretically give the appropriate pre-selection,post-selection and others optical structure before experiment. Our numericalresults show our scheme with Weak-value technique is effective and feasible todetect weak magnetic field with magnetic field intensity lower than $10^{-10}$T.

Weak-value technique for detecting weak magnetic field based on Faraday magneto-optic effect