Magnetic anisotropy is crucially important for the stabilization of two-dimensional (2D) magnetism, which is rare in nature but highly desirable in spintronics and for advancing fundamental knowledge. Recent works on CrI 3 and CrGeTe 3 monolayers not only led to observations of the long-time-sought 2D ferromagnetism, but also revealed distinct magnetic anisotropy in the two systems, namely Ising behavior for CrI 3 versus Heisenberg behavior for CrGeTe 3 . Such magnetic difference strongly contrasts with structural and electronic similarities of these two materials, and understanding it at a microscopic scale should be of large benefits. Here, first-principles calculations are performed and analyzed to develop a simple Hamiltonian, to investigate magnetic anisotropy of CrI 3 and CrGeTe 3 monolayers. The anisotropic exchange coupling in both systems is surprisingly determined to be of Kitaev-1 arXiv:1811.05413v1 [cond-mat.mtrl-sci] 13 Nov 2018 type. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the different magnetic behaviors of CrI 3 and CrGeTe 3 . Finally, both the Kitaev interaction and SIA are further found to be induced by spin-orbit coupling of the heavy ligands (I of CrI 3 or Te of CrGeTe 3 ) rather than the commonly believed 3d magnetic Cr ions.

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

Quantum spin liquids (QSLs) form an extremely unusual magnetic state in which the spins are highly correlated and fluctuate coherently down to the lowest temperatures, but without symmetry breaking and without the formation of any static long-range-ordered magnetism. Such intriguing phenomena are not only of great fundamental relevance in themselves, but also hold the promise for quantum computing and quantum information. Among different types of QSLs, the exactly solvable Kitaev model is attracting much attention, with most proposed candidate materials, e.g., RuCl3 and Na2IrO3, having an effective S=1/2 spin value. Here, via extensive first-principlebased simulations, we report the investigation of the Kitaev physics and possible Kitaev QSL state in epitaxially strained Cr-based monolayers, such as CrSiTe3, that rather possess a S=3/2 spin value. Our study thus extends the playground of Kitaev physics and QSLs to 3d transition metal compounds. :2002.12184v1 [cond-mat.mtrl-sci] arXiv

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