Intrinsic Magnetism of Grain Boundaries in Two-Dimensional Metal Dichalcogenides

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1 Supporting Information for Intrinsic Magnetism of Grain Boundaries in Two-Dimensional Metal Dichalcogenides Zhuhua Zhang,1 Xiaolong Zou,1 Vincent H. Crespi,2 Boris I. Yakobson1* 1 Department of Mechanical Engineering and Materials Science, Department of Chemistry, and the Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, TX 77005, USA. 2Department of Physics and Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania , USA. * biy@rice.edu Models Figure S1. Two types of models used in this work for simulating grain boundaries (GBs) in 2D MoS2. (a) A nanoribbon model for a Mo-rich 9 GB. The spacing between the GB and ribbon edges exceeds 2 nm. The nanoribbon edges are left in an unreconstructed state. (b) A 2D periodic boundary condition (PBC) model including a pair of opposite 9 GBs which are spaced by ~2 nm. (c) Atomic structures of simulated GBs composed of Mo-rich dislocations of various tilt angles and also (d) GBs containing substantial numbers of 4 8 dislocations. 1

2 Figure S2. (a) Magnetization density for a GB loop composed of three Mo-rich dislocations in a 8 8 MoS2 supercell. The total magnetic moment of the loop is 2 μb. (b) Magnetization density distributions on a Mo-rich 5 7 dislocation in a 22 GB, calculated using GGA of the PBE and HSE06 functionals. The iso-value is e/å3. The total magnetic moment obtained within HSE06 functional is 1.06 μb, close to the value obtained within GGA, but the spin-polarization energy reaches ~160 mev per dislocation, an increase over four-fold from the GGA value, as supported by much enhanced local moments. Figure S3. Isosurface plots (at 4.26 ev) of local electrostatic potential near (a) a Mo-rich dislocation and (b) a S-rich dislocation. Figure S4. Isosurface plots of the magnetization density (at e/å3) for a GB composed of dislocations, a structure observed in recent experiments by van der Zande et al.40 2

3 Figure S5. Carrier-tunable magnetism in dislocations of 2D MoS 2. (a) Magnetic moment of 4 6 and 6 8 dislocations in a 22 GB in a 2D periodic model, as a function of doping level. The inset gives isosurfaces (at e/å 3 ) of magnetization density on the 4 6 and 6 8 dislocations at a doping level of 0.2 e/supercell. (b) Magnetic moment of and dislocations in a 22 GB (for the 2D periodic model) as a function of the doping level. In each case, the placement of the Fermi level relative to the spin-split levels controls the net magnetization. Figure S6. Half-metallic nature in the GBs constructed by 2D periodic model, wherein GB dipoles are present. Spin-polarized total density of states projected of the (a) 22 and (b) 32 GBs. Solid and dashed lines are the DOS projected onto those atoms forming S-rich and Morich GBs, respectively, and the grey shaded regions are total DOS of the systems. Suggestions of band-edge van Hove singularities are visible for the bands associated with the quasi-1d grain boundaries. The 22 case has two nearly degenerate partially filled spin-down bands (blue) near the Fermi level. The 32 case has two spin-down bands in the vicinity of the Fermi energy. In both cases, these band structures yield self-doped metallic spinpolarized systems: generically, spin polarization should survive into the isolated single-gb limit, with experimental control of the doping level. 3

4 Figure S7. Isosurface plots of magnetization densities (at e/å 3 ) of 22 GBs in 2D (left) MoSe 2, (middle) WS 2 and (right) WSe 2. The top and bottom panels correspond to the M-rich and X-rich GBs, respectively. The local magnetic moment per dislocation is ~1.0 μ B in all the materials, the same as that in MoS 2. Figure S8. (a) Plane-averaged charge densities of dislocation-induced defect states along the direction perpendicular to the 22 GB in 2D MoS 2 (top), BN (middle) and graphene (bottom) sheet, respectively. (b) Energy levels of near-gap defect states, δ and δ *, induced by dislocations in 2D BN, graphene and MoS 2 sheets. Insets show electron localization functions around the corresponding dislocations, at an iso-surface value of 0.8. A comparison of dislocations in different 2D materials helps gain a deeper insight into the origin of magnetic GBs in MoS 2. Dislocations in graphene and h-bn sheets are nonmagnetic. The distributions of charge densities corresponding to dislocation-induced defect states show striking difference between zero-gap graphene and the semiconducting sheets. The electronic states at dislocations in graphene are delocalized, while those in h-bn and MoS 2 are well localized (Figure S8a). Strong localization of defect states can facilitate spin-polarization. 4

5 GBs in the metallic 1T phase of MoS 2 are nonmagnetic, consistent with this trend. Taking the dislocation as a perturbation, the static susceptibility of a 2D semiconducting system can be expressed as r -2 exp(- r/ l), where l 2E g m eff is the decay constant, with m eff the effective electron mass and E g the band gap. 62 This rough formula yields l = 2.1 Å for MoS 2 and l = 1.9 Å for the h-bn, which is reasonably consistent with the spatial dependence of Figure S8a. Beyond localization, a high density of states at the Fermi level is also helpful in the induction of magnetism, via a Stoner-like mechanism. The self-doping within the current models (or intentional doping in experiment) can then induce partial occupation and facilitate the advent of spontaneous magnetization. We also analyze the bonding character of dislocations in these 2D materials, as shown in Figure S8b. The Mo-Mo and S-S bonds in dislocations of MoS2 show weaker bonding/ antibonding splitting than do analogous bonds in dislocations within graphene or BN. The Mo-rich dislocation appears to be electron-deficient compared to the bulk, whereas the S- rich dislocation is electron-rich, thus yielding partial occupation of the δ and δ * states respectively within the nanoribbon or periodic models (see electron localization functions, 63 inserts of Figure S8b). This description accords with the two-level model in Figure 3 and the electrostatic potential distribution around the dislocations in Figure S3. (62) Bloembergen, N.; Rowland, T. Nuclear Spin Exchange in Solids: Tl 203 and Tl 205 Magnetic Resonance in Thallium and Thallic Oxide. Phys. Rev. 1955, 97, (63) Becke, A. D.; Edgecombe, K. E. A Simple Measure of Electron Localization in Atomic and Molecular Systems. J. Chem. Phys. 1990, 92,