(untitled) (Journal of Atomic, Molecular, Condensed Matter and Nano Physics, 2017)
Loop induced interaction in a magnetized matter can make charge neutral fermions interact with photons. The matter or electromagnetic field induces an effective vertex and modifies the dispersion relation. In standard model of electroweak interaction, it has already been noted that in a medium neutrinos acquire an effective charge (from the vector type vertex of weak interaction). On the other hand in magnetized plasma, the axial vector part also start contributing to the effective charge of a neutrino. This contribution corresponding to the axial vector part in the interaction Lagrangian is denoted as the axial polarisation tensor. In an earlier paper the explicit form of the axial polarisation tensor to all odd orders in external magnetic field B was reported. In this note we complete that investigation by computing the same, to all even orders in external magnetic field. We further show its gauge invarience properties. Lastly, the zero external momentum limit of this axial polarisation tensor is reported.