Abstract
The search for topological spin excitations in recently discovered two-dimensional (2D) van der Waals (vdW) magnetic materials is important because of their potential applications in dissipation-less spintronics. In the 2D vdW ferromagnetic (FM) honeycomb lattice CrI$_3$(T$_C$= 61 K), acoustic and optical spin waves were found to be separated by a gap at the Dirac points. The presence of such a gap is a signature of topological spin excitations if it arises from the next nearest neighbor(NNN) Dzyaloshinskii-Moriya (DM) or bond-angle dependent Kitaev interactions within the Cr honeycomb lattice. Alternatively, the gap is suggested to arise from an electron correlation effect not associated with topological spin excitations. Here we use inelastic neutron scattering to conclusively demonstrate that the Kitaev interactions and electron correlation effects cannot describe spin waves, Dirac gap and their in-plane magnetic field dependence. Our results support the DM interactions being the microscopic origin of the observed Dirac gap. Moreover, we find that the nearest neighbor (NN) magnetic exchange interactions along the axis are antiferromagnetic (AF)and the NNN interactions are FM. Therefore, our results unveil the origin of the observedcaxisAF order in thin layers of CrI$_3$, firmly determine the microscopic spin interactions in bulk CrI$_3$, and provide a new understanding of topology-driven spin excitations in 2D vdW magnets.
Highlights
The discovery of robust two-dimensional (2D) ferromagnetic (FM) long-range order in monolayer van der Waals magnets [1,2,3] is important because these materials can provide a new platform to study fundamental physics without the influence of a substrate and can potentially be used to develop new spintronic devices [4,5]
The momentum transfer Q 1⁄4 Haà þ Kbà þ Lcà is denoted as ðH; K; LÞ in reciprocal lattice units (r.l.u.) with marked high-symmetry points [Figs. 2(a) and 2(b)]
Even in the bulk samples, the surface layers are reported to have AF monoclinic structure that can be tuned by a c-axis aligned magnetic field of a few Tesla [39]. While these results indicate minor energy differences in rhombohedral and monoclinic structures of CrI3, they suggest that the Cr honeycomb lattice may have subtle NN inversion symmetry-breaking structural distortions that are responsible for the observed Dirac spin gap [56]
Summary
The discovery of robust two-dimensional (2D) ferromagnetic (FM) long-range order in monolayer van der Waals (vdW) magnets [1,2,3] is important because these materials can provide a new platform to study fundamental physics without the influence of a substrate and can potentially be used to develop new spintronic devices [4,5]. The 3d electrons of Cr3þ do not provide large spin-orbit coupling (SOC), the heavier ligand atoms such as iodine may serve as a source of significant SOC This provides the thermal stability observed in vdW layered materials and enriches the physics of magnetism in the 2D limit [9,10,11,12,13,14]. It is proposed that the Kitaev interaction [15], known to be important for effective S 1⁄4 1=2 honeycomb lattice magnets near a Kitaev quantum spin liquid [16,17], may occur in S 1⁄4 3=2 CrI3 across the nearest bond with bonddependent anisotropic Ising-like exchange [Fig. 1(b)] This occurrence would be critical for the magnetic stability of monolayer CrI3 and spin dynamics in bulk CrI3 [18,19,20,21,22]. If the system has TRSB arising from a large SOC, one would expect to observe an energy gap at
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