Topological spin texture in Janus monolayers of the chromium trihalides Cr(I, X)3

Abstract

Magnetic skyrmions are nano-scale spin structures that are promising for ultra-dense memory and logic devices. Recent progresses in two-dimensional magnets encourage the idea to realize skyrmionic states in freestanding monolayers. However, monolayers such as CrI 3 lack Dzyaloshinskii-Moriya interactions (DMI) and thus do not naturally exhibit skyrmions but rather a ferromagnetic state. Here we propose the fabrication of Cr(I,X) 3 Janus monolayers, in which the Cr atoms are covalently bonded to the underlying I ions and top-layer Br or Cl atoms. By performing first-principles calculations and Monte-Carlo simulations, we identify strong enough DMI, which leads to not only helical cycloid phases, but also to intrinsic skyrmionic states in Cr(I,Br) 3 and magnetic-field-induced skyrmions in Cr(I,Cl) 3 . 1 arXiv:1906.04336v2 [cond-mat.mtrl-sci] 28 Jun 2019Magnetic skyrmions are nano-scale spin clusters with topological stability, and are promising for advanced spintronics 1, 2 . One requirement toward such applications is that the hosting materials should be thin films, so that the nano size of skyrmions can be taken full advantage of.Besides previous studies on bulk MnSi 3-6 , recent works focused on ultrathin films, such as FeGe 7, 8 and rare-earth ion garnet 9, 10 , which both take advantage of the Dzyaloshinskii-Moriya interaction (DMI) arising from the heavy metal substrate. However, no skyrmionic state has ever been reported to intrinsically exist in free-standing monolayers, to the best of our knowledge, while two-dimensional (2D) semiconducting magnets, such as monolayer CrI 3 11 , are recently attracting much attention due to their novel physics and rich applications 12 . The ferromagnetic monolayer CrI 3 crystalizes in honeycomb lattice made of edge-sharing octahedra. Its ferromagnetic order is stabilized by an out-of-plane anisotropy 11 , which arises from single ion anisotropy (SIA) andKitaev-type exchange coupling that both result from the SOC of its heavy ligands 13,14 . However, the ingredient DMI is absent between the most strongly coupled first nearest neighbor (1st NN) Cr-Cr pairs, because the inversion center between the two Cr atoms prevents its existence 15 . Interestingly, very recent theoretical study proposed the application of electric field to break the inversion center and induce DMI in monolayer CrI 3 16 . Although this clever method leads to CrI 3 monolayers becoming closer to adopt a skyrmion phase, the weak effects of electric field in generating DMI, as well as the rather strong out-of-plane anisotropy, hinders the actual creation of skyrmions in this system.Here we propose a more effective approach that consists in fabricating Janus monolayers of chromium trihalides Cr(I,X) 3 (X = Br, Cl). One example of Janus monolayers is the transition

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

“…The D z component is relatively small, but it is the only one responsible for the gap opening at the K point. Our calculated magnitude of the next NN DM is in good agreement with the total-energy-based estimate [84,85]. The direction is not exactly the same though.…”

Spontaneous skyrmionic lattice from anisotropic symmetric exchange in a Ni-halide monolayer

“…Results remain qualitatively the same: the J 3iso /J 1iso , and J yz /J 1iso ratios (i.e., the quantities with relevant physical meaning, even more than the absolute values of the interactions) are almost unaffected, as shown in Table SII in Supplementary. We calculated the magnetic parameters reported in this paper via the four-state energy mapping method, which is explained in detail in the refs. 43,49,50 , performing noncollinear DFT calculations plus spin-orbit coupling (SOC) and constraints on magnetic moments direction. It is based on the use of large supercells, also allowing to exclude the coupling with unwanted distant neighbors.…”

Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2

“…The solid and dashed ellipses mark ferromagnetic and antiferromagnetic pairs, respectively. Note that our MC simulations are followed by a conjugate gradient algorithm, indicating that the spin patterns shown here are at global/local minima[35].FIG. 4.…”