Relativistic exchange interactions in CrX3 ( X=Cl , Br, I) monolayers

Abstract

It has been predicted theoretically and indirectly confirmed experimentally that single-layer CrX 3 (X = Cl, Br, I) might be the prototypes of topological magnetic insulators (TMI). In this work, by using first-principles calculations combined with atomistic spin dynamics, we provide a complete picture of the magnetic interactions and magnetic excitations in CrX 3. The focus is here on the two most important aspects for the actual realization of TMI, namely the relativistic magnetic interactions and the finite-size (edge) effects. We compute the full interaction tensor, which includes both Kitaev and Dzyaloshinskii-Moriya (DM) terms, which are considered as the most likely mechanisms for stabilizing topological magnons. First, we instigate the properties of bulk CrI 3 and compare the simulated magnon spectrum with the experimental data [Phys. Rev. X 8, 041028 (2018)]. Our results suggest that a large size of topological gap, seen in experiment (≈4 meV), cannot be explained by considering pair-wise spin interactions only. We identify several possible reasons for this disagreement. The magnetic interactions in the monolayers of CrX 3 are also investigated. The strength of the anisotropic interactions is shown to scale with the position of halide atom in the periodic table, the heavier the element the larger is the anisotropy, in agreement with prior studies. Comparing the magnons for the bulk and single-layer CrI 3 , we find that the size of the topological gap becomes smaller in the latter case. The obtained next nearest-neighbor DM vector is oriented primarily in-plane of the monolayer and has relatively small z component, which results in a small value of the topological gap. Finally, we investigate finite-size effects in monolayers and demonstrate that the anisotropic couplings between Cr atoms close to the edges are much stronger than those in ideal periodic structure. This should have impact on the dynamics of the magnon edge modes in Cr halides.

Electron correlation effects on exchange interactions and spin excitations in 2D van der Waals materials

“…In conclusion, we have demonstrated that an ab initio description of electron correlations beyond DFT can accurately describe the SW spectra and the stacking-dependent magnetism in a parameter-free fashion, and reveals the gap-opening mechanism in CrI 3 . An unexpected correlation-enhanced interlayer super-superexchange induces a gap along the Γ-K-M path in the absence of previously proposed relativistic exchanges or magnon-phonon interactions 23 . To experimentally verify the true physical mechanism of the gap opening and the nature of magnetic interactions, future INS experiments may be used to search for the bandcrossings off the high-symmetry line in bulk CrI 3 .…”

“…By far, except for a few studies 23,38,39 using the magnetic force theorem (MFT) 40 , most of the theoretical investigations of the magnetic interactions in m2Dv are based on mapping the total energies of various collinear spin configurations into the Heisenberg model (referred to hereafter as the energy-mapping method), often employed with DFT + U. However, the applicability and accuracy of such an approach in CrI 3 are not clear.…”

“…In principle, the MFT approach is more suitable to describe the small spin deviation from the ground state, such as the SW excitations; moreover, it also allows one to resolve coupling into orbital contributions and elucidate the underlying exchange mechanism 39,42 . However, the resulting values still vary and are inconclusive; even the opposite trend of exchange-coupling dependence on on-site Cr U-values have been obtained 23 . The discrepancy likely lies in the details of the constructions of the TB Hamiltonian and Green's function 43 , which are often assisted by the Wannier function approach 44 .…”

“…Recent inelastic neutron-scattering (INS) experiments have shown a gap opening along the high-symmetry lines in pristine CrI 3 16 , implying a sizable DMI or Kitaev interaction 19 may indeed exist in CrI 3 . In contrast, ab initio investigations show that both DMI [20][21][22][23] and Kitaev interactions 23,24 in pristine CrI 3 are insufficient to open up the sizable gap observed in experiments. The role of the relativistic magnetic interactions is still not fully understood.…”

Electronic structure of chromium trihalides beyond density functional theory

“…CrX 3 is a 2D FM insulator with FM originating from the Cr-X-Cr superexchange interaction [13,[23][24][25]. Six Cr 3+ ions * swagata.acharya@ru.nl form a honeycomb structure with D 3d point group symmetry, and each Cr is surrounded by six X in an octahedral geometry (see Fig.…”