Antichiral edge states in Heisenberg ferromagnet on a honeycomb lattice

We demonstrate the emergence of antichiral edge states in a Heisenberg ferromagnet with Dzyaloshinskii-Moriya interaction (DMI) on a honeycomb lattice with inequivalent sublattices, using both Schwinger-boson mean field theory and Holstein-Primakoff transformation. The DMI, which acts between atoms of the same species, differs in magnitude for the two sublattices, resulting in a shifting of the energy of the magnon bands (or bands in each spinon sector) in opposite directions at the two Dirac points. The chiral symmetry is broken and, for sufficiently strong asymmetry, the band shifting leads to antichiral edge states (in addition to the normal chiral edge states) in a rectangular strip where the magnon (or up or down spinon) current propagates in the same direction along the two edges. This is compensated by a counter propagating bulk current that is enabled by the broken chiral symmetry. We analyze the resulting magnon (spinon) current profile across the width of the system in details and suggest realistic experimental probes to detect them. Finally, we discuss possible materials that can potentially exhibit such antichiral edge states.