  The existence of chiral edge states, corresponding to the nontrivial
bulk-band topology characterized by a non-vanishing topological invariant, and
the manipulation of topological transport via chiral edge states promise
topological electronic/spintronic device applications. Here we predict the
existence, practical realization, topological protection, and topological
switching of spin-gapless valley-filtered chiral edge states, representing a
novel topological Dirac spin-gapless/half-metal phase in antiferromagnetic
honeycomb structures terminated on zigzag edges. We demonstrate that this
phenomenon is realizable if a perpendicular (transverse) electric field is
applied in zigzag nanoribbons with an antiferromagnetic ordering on the
boundary (in the bulk), and the Weber-Fechner type nonlinear behavior is
optimizable by a transverse (perpendicular) electric field. The existence of
spin-gapless valley-filtered chiral edge states, their correspondence with
nontrivial topological character in the bulk, and electric-field-driven
switching of their spin-polarization that is accompanied by switching of
bulk-band topology promise a new strategy for topological spintronics without
spin-orbit interaction.
