Topological phase transition in magnon bands in a honeycomb ferromagnet driven by sublattice symmetry breaking

Stacking-dependent topological magnons in bilayer CrI$_3$

“…Similarly, in magnetic honeycomb bilayers, a DMI-induced topological behavior of magnons is predicted, 20,[23][24][25] including the formation of Dirac magnon nodal-line loops, 23 and the opening of a topological bandgap, which contributes to a magnon Hall-and a spin Nernst effect. 20,24,25 Several recent works [26][27][28][29] attempted to characterize the magnonics of monolayer CrI 3 using ab initio calculations, and demonstrated the appearance of a small, possibly topological, bandgap caused by the spin-orbit coupling (SOC), suggesting that the material is a TMI. However, more work is required before full understanding of the magnonics in CrI 3 is achieved.…”

“…In section S.V of the supplementary material, 33 we show that by artificially reducing ∆J zz in our simulations, which also decreases the size of the bandgap at the K-point and the K'-point, we can induce a topological phase transition to a state with non-zero Chern numbers of C 1⊕2 = +1, C 3 = −1 and C 4 = 0, which confirms the influence that sublattice symmetry can have on the topology of magnonic bands. 20 In bilayers with AFM interlayer order, the bands are two-by-two degenerate, meaning that one can only define composite Chern numbers. In the case of AA-stacking, there is no bandgap and, thus, the Chern number is undefined and the bands display no topological behavior.…”

“…Early theoretical work suggested that honeycomb ferromagnetic (FM) monolayers could be classified as either MDMs or TMIs depending on whether any NNN DMI is present in the material. [15][16][17][18][19][20] Nonetheless, recent work identified Kitaev interactions as an alternative mechanism potentially able to open a topological bandgap in FM honeycomb materials, 21,22 suggesting that the absence of DMI is not the sole criterion for predicting the topological properties of such materials. Similarly, in magnetic honeycomb bilayers, a DMI-induced topological behavior of magnons is predicted, 20,[23][24][25] including the formation of Dirac magnon nodal-line loops, 23 and the opening of a topological bandgap, which contributes to a magnon Hall-and a spin Nernst effect.…”

“…[15][16][17][18][19][20] Nonetheless, recent work identified Kitaev interactions as an alternative mechanism potentially able to open a topological bandgap in FM honeycomb materials, 21,22 suggesting that the absence of DMI is not the sole criterion for predicting the topological properties of such materials. Similarly, in magnetic honeycomb bilayers, a DMI-induced topological behavior of magnons is predicted, 20,[23][24][25] including the formation of Dirac magnon nodal-line loops, 23 and the opening of a topological bandgap, which contributes to a magnon Hall-and a spin Nernst effect. 20,24,25 Several recent works [26][27][28][29] attempted to characterize the magnonics of monolayer CrI 3 using ab initio calculations, and demonstrated the appearance of a small, possibly topological, bandgap caused by the spin-orbit coupling (SOC), suggesting that the material is a TMI.…”

“…Afterwards, in section IV, we consider bilayer CrI 3 in three different stacking orders, each exhibiting significantly different magnonic behavior. Specifically, we investigate the AA-stacking and AB-stacking (rhombohedral) discussed in literature, 20,23,24 as well as the experimentally very relevant AB'-stacking (monoclinic) of which the spin-waves have -to the best of our knowledge -not been theoretically investigated to date. We find that all three stacking versions of bilayer CrI 3 exhibit either FM or antiferromagnetic (AFM) interlayer ordering, with intralayer ferromagnetism.…”