Two simple textures of the magic neutrino mass matrix
The Tri-Bimaximal (TBM) mixing predicts a vanishing $θ_{13}$. This can be attributed to the inherited $μ-τ$ symmetry of TBM mixing. We break its $μ-τ$ symmetry by adding a complex magic matrix with one variable to TBM neutrino mass matrix with one vanishing eigenvalue. We present two such textures and study their phenomenological implications.