Topological Magnon Insulator in NonCoplanar Kagom\'e Antiferromagnets: Supplemental Material of arXiv:1608.04561

TL;DR

This paper demonstrates that noncoplanar spin textures induced by magnetic fields in Kagomé antiferromagnets can host topological magnon bands without Dzyaloshinskii-Moriya interaction, unlike coplanar textures which are topologically trivial.

Contribution

It reveals that field-induced noncoplanar spin textures in Kagomé antiferromagnets can produce topological magnon bands independently of DMI, expanding understanding of topological phases in frustrated magnets.

Findings

Topological magnon bands are absent in coplanar spin textures.

Out-of-plane magnetic fields induce noncoplanar spin textures with nonzero scalar chirality.

Field-induced spin chirality enables topological magnon bands in Kagomé antiferromagnets.

Abstract

Topological magnon insulators in insulating Kagom\'e ferromagnets have been extensively studied in a series of papers. It has been established that Dzyaloshinskii-Moriya interaction (DMI) is the key ingredient to observe a nontrivial topological magnon with edge modes. However, insulating antiferromagnets on the Kagom\'e lattice are frustrated systems considered as a playground for studying quantum spin liquid physics. In these systems the DMI can induce a coplanar but noncollinear magnetic orders with a $\mathbf{q}=0$ propagating wavevector. We show that topological magnon bands are absent in this coplanar spin texture in sharp contrast to collinear ferromagnets with DMI. Hence, geometrically frustrated Kagom\'e antiferromagnets can be deemed topologically trivial. The presence of an out-of-plane magnetic field in these frustrated magnets induces noncoplanar spin textures exhibiting a nonzero spin scalar chirality. We show that the field-induced spin chirality provides topological magnon bands in Kagom\'e antiferromagnets without the need of DMI and survives in the chiral spin liquid phase of frustrated magnets. Possible experimentally material includes iron jarosite KFe$_3$(OH)$_{6}$(SO$_{4}$)$_2$.