  A local flexomagnetoelectric (A.P. Pyatakov, A.K. Zvezdin, 2009) effect in
the magnetic domain walls (DWs) of the cubic hexoctahedral crystal has been
investigated on the basis of a symmetry analysis. The strong connection between
magnetic symmetry of the DW and the type of the distribution of the electric
polarization was shown. Results were systemized in the scope of the DW
chirality. It was shown, that new type of the local flexomagnetoelectric
coupling can be experimentally detected using the external homogeneous electric
field.
