Edge magnetism of Heisenberg model on honeycomb lattice

Abstract

Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.

Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edge boundaries

“…The energy gap between propagating and edge modes is larger for the nanoribbon with bearded edges boundaries. For the zigzag nanoribbon, our results for the edge mode in the isotropic case are identical to previous studies [25,33] based on the Holstein-Primakov quantum approach and the linear spin wave approximation.…”

“…Edge spin waves are obtained for both types of nanoribbons, with and without magnetic anisotropy. Our results for the edge modes of the magnetically isotropic zigzag edged nanoribbon are identical to the results of existing quantum studies [25,33], as the decay factors are found to be independent of the nanoribbon width. For the anisotropic zigzag edged nanoribbon, however, our results are significantly different.…”

“…Nonreciprocal spin waves have received intensive theoretical and experimental attention in view of their importance for technological applications [20][21][22][23][24]. The important recent discovery of magnetic properties in Dirac materials attracted substantial interest in their magnetic excitations [25][26][27][28][29][30][31][32][33][34][35][36][37]. The novel characteristics for magnetic excitations in Dirac materials is believed to open important new opportunities in the field of magnonics.…”

“…Solving the bulk equations of motion consistently with the boundary conditions yields the edge and discretized bulk exchange spin waves for both types of nanoribbons in the long wavelength part of the Brillouin zone. Unlike previous theoretical studies [25,33,34,37] where the boundary conditions are derived and solved on one edge of the nanoribbon, in our approach the derived boundary equations are solved simultaneously on both edges. Edge spin waves are obtained for both types of nanoribbons, with and without magnetic anisotropy.…”

A new class of nonreciprocal spin waves on the edges of 2D antiferromagnetic honeycomb nanoribbons

“…Bounded 2D magnetic materials present edge spin waves, considered as the 1D analogue of surface spin waves in magnetic thin films. The interest in surface spin waves is naturally extended to edge spin waves [26,39,40,48,51,52], as fundamental phenomena with potentials for pioneering applications. Despite the intensive research on magnetic excitations in 2D materials, the effects of the DMI and magnetic anisotropy on edge spin waves in bounded 2D antiferromagnets have not yet received the deserved attention and remain open to be discovered.…”