On possible conical singularities in magneto-optics

The conditions for the appearance of conical singularities in a magnetically ordered crystal in the presence of dichroism, birefringence, and magneto-optical activity have been considered. The possibility of the existence of singularities such as a nodal point, cusp, and point of contact has been demonstrated. The relation of the topological index of the closed singular line to the indices of the C points lying inside the contour has been revealed. Estimates have been made for the YIG:Bi crystal.