These authors contributed equally: Tingxin Li, Shengwei Jiang.Stacking order can significantly influence the physical properties of two-dimensional (2D) van der Waals materials 1 . The recent isolation of atomically thin magnetic materials 2-22 opens the door for control and design of magnetism via stacking order. Here we apply hydrostatic pressure up to 2 GPa to modify the stacking order in a prototype van der Waals magnetic insulator CrI3. We observe an irreversible interlayer antiferromagnetic (AF) to ferromagnetic (FM) transition in atomically thin CrI3 by magnetic circular dichroism and electron tunneling measurements. The effect is accompanied by a monoclinic to a rhombohedral stacking order change characterized by polarized Raman spectroscopy. Before the structural change, the interlayer AF coupling energy can be tuned up by nearly 100% by pressure. Our experiment reveals interlayer FM coupling, which is the established ground state in bulk CrI3, but never observed in native exfoliated thin films. The observed correlation between the magnetic ground state and the stacking order is in good agreement with first principles calculations 23-27 and suggests a route towards nanoscale magnetic textures by moiré engineering 28 .Intrinsic magnetism in 2D van der Waals materials has received growing attention 2-22 . Of particular interest is the thickness-dependent magnetic ground state in atomically thin CrI3. In these exfoliated thin films, the magnetic moments are aligned (in the out-of-plane direction) in each layer, but anti-aligned in adjacent layers 3,12-22 . They are FM (or AF) depending on whether there is (or isn't) an uncompensated layer. The relatively weak interlayer coupling compared to the intralayer coupling allows effective ways to control the interlayer magnetism, which have led to interesting spintronics applications including voltage switching 12-14 , spin filtering 16-20 and spin transistors 21 . The origin of interlayer AF coupling is, however, not well understood since interlayer FM order is the ground state in the bulk crystals. Recent ab initio calculations 23-27 and experiments 22,29,30 have suggested that stacking order could provide an explanation but a direct correlation between stacking order and interlayer magnetism is lacking.In bulk CrI3, the Cr atoms in each layer form a honeycomb structure, and each Cr atom is surrounded by six I atoms in an octahedral coordination (Fig. 1a). The bulk crystals undergo a structural phase transition from a monoclinic phase (space group C2/m) at room temperature to a

The Hall effect occurs only in systems with broken time-reversal symmetry, such as solids under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE) 1 . Here we show a new Hall effect in a nonmagnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current 2-6 . We observe the effect (referred to as nonlinear AHE) in two-dimensional Td-WTe2, a semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage changes sign when the bias current reverses direction; it maximizes (vanishes) when the bias current is perpendicular (parallel) to the mirror line. The observed effect can be understood as an AHE induced by the bias current which generates an out-of-plane magnetization. The temperature dependence of the Hall conductivity further suggests that both intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE. Our results open the possibility of exploring the intrinsic Berry curvature effect in nonlinear electrical transport in solids 3-7 .Unlike the linear Hall effect that has to vanish to satisfy the Onsager's reciprocity relation in a time-reversal invariant system, in principle, the nonlinear Hall effect does not have to vanish 8 . On the other hand, a second-order nonlinear effect occurs only in systems with broken inversion symmetry 9 . Atomically thin Td-WTe2 possesses all the right symmetries to realize the second-order nonlinear anomalous Hall effect (AHE) with an in-plane Hall conductivity under an in-plane bias current. Monolayer WTe2 of the Td/T' polytype consists of a layer of W atoms sandwiched between two layers of Te atoms in a distorted octahedral coordination 10 ( Fig. 1a). It is centrosymmetric with one mirror line (dashed line, Fig. 1a) along the crystal b-axis. Multilayer Td-WTe2 is formed by stacking monolayers with rotated alternating layers by 180 degrees 10 ( Fig. 1a). It is non-centrosymmetric and has point group (Ref. 11 ). In contrast to the bulk (point group 2 1 ) 10 , the screw-axis and glide plane symmetries are broken at the surfaces to allow an in-plane polar axis along the mirror line. Pristine Td-WTe2 is a semimetal with nearly compensated electron and hole densities down to a thickness of three layers [12][13][14][15] . An array of quantum revelations has been recently reported in this system including a two-dimensional (2D) topological insulator in the monolayer limit [16][17][18][19] , superconductivity induced by electrostatic doping in monolayers 20, 21 , and a switchable ferroelectric metal 2 in two-and three-layers 22 . Here we investigate the nonlinear electrical properties of atomically thin Td-WTe2.In our experiment, Td-WTe2 samples with a thickness of 4 -8 layers have been studied. They were fabricated by mechanical exfoliation from bulk crystals (HQ Graphene) and were capped by hexagonal boron nitride th...

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Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show surprisingly that the newly discovered QAH state in AB-stacked MoTe2/WSe2 moiré bilayers is not valley-polarized but valley-coherent. The layer- and helicity-resolved optical spectroscopy measurement reveals that the QAH ground state possesses spontaneous spin (valley) polarization aligned (anti-aligned) in two TMD layers. In addition, saturation of the out-of-plane spin polarization in both layers occurs only under high magnetic fields, supporting a canted spin texture. Our results call for a new mechanism for the QAH effect and highlight the potential of TMD moiré materials with strong electronic correlations and spin-orbit interactions for exotic topological states.

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The spin Hall effect (SHE), in which electrical current generates transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons 1–7. The phenomenon originates from spin-orbit coupling. In general, stronger spin-orbit coupling favors larger SHEs but shorter spin relaxation times and diffusion lengths 1,4–7. To achieve both large SHEs and long-range spin transport in a single material has remained a challenge. Here we demonstrate a giant intrinsic SHE in AB-stacked MoTe2/WSe2 moiré bilayers by direct magneto optical imaging. Under moderate electrical currents with density < 1 A/m, we observe spin accumulation on transverse sample edges that nearly saturates the spin density. We also demonstrate long-range spin Hall transport and efficient non-local spin accumulation limited only by the device size (about 10 µm). The gate dependence shows that the giant SHE occurs only near the Chern insulating state, and at low temperatures, it emerges after the quantum anomalous Hall breakdown. Our results demonstrate moiré engineering of Berry curvature and large SHEs for potential spintronics applications.