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We study the interaction between a ferromagnetically ordered medium and thesurface states of a topological insulator with a general surface termination.This interaction is strongly crystal face dependent and can generate chiralstates along edges between crystal facets even for a uniform magnetization.While magnetization parallel to quintuple layers shifts the momentum of Diracpoint, perpendicular magnetization lifts the Kramers degeneracy at any Diracpoints except on the side face where the spectrum remains gapless and the Hallconductivity switches sign. Chiral states can be found at any edge thatreverses the projection of surface normal to the stacking direction ofquintuple layers. Magnetization also weakly hybridizes non cleavage surfaces.

Surface State Magnetization and Chiral Edge States on Topological Insulators