Axion field induced topological magneto-electric response has attracted lots of attentions since it was first proposed by Qi et al. in 2008. Here we find a new type of anti-commutative magneto-electric response $beta^{xi}(omega)$, which can induce a dynamical magneto-electric current driven by a time-varying magnetic field. Unlike the Chern-Simons Axion term, this magneto-electric response term is gauge-independent, and manifests in the systems breaking the symmetries of the time-reversal, inversion and mirror. In particular, we predict Mn$_{2}$Bi$_{2}$Te$_{5}$ as a material candidate to observe dynamical magneto-electric current.
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