Magnetoelectric (ME) effect, the phenomenon of inducing magnetization by application of an electric field or vice versa, holds great promise for magnetic sensing and switching applications 1 . Studies of the ME effect have so far focused on the control of the electron spin degree of freedom (DOF) in materials such as multiferroics 2 and conventional semiconductors 3 . Here, we report a new form of the ME effect based on the valley DOF in two-dimensional (2D) Dirac materials 4-6 . By breaking the three-fold rotational symmetry in single-layer MoS 2 via a uniaxial stress, we have demonstrated the pure electrical generation of valley magnetization in this material, and its direct imaging by Kerr rotation microscopy. The observed out-of-plane magnetization is independent of in-plane magnetic field, linearly proportional to the in-plane current density, and optimized when the current is orthogonal to the strain-induced piezoelectric field. These results are fully consistent with a theoretical model of valley magnetoelectricity driven by Berry curvature effects. Furthermore, the effect persists at room temperature, opening possibilities for practical valleytronic devices.Electrons in two-dimensional (2D) Dirac materials including gapped graphene and single-layer transition metal dichalcogenides (TMDs) possess a new two-fold valley degree of freedom (DOF) corresponding to the K and K' valleys of the Brillouin zone. The valley DOF carries orbital magnetic moment [4][5][6] . A net valley magnetization forms the basis for valley-based applications. Such magnetization can arise from either a finite population imbalance between the valleys (i.e. a net valley polarization) or a distribution difference between them without a population imbalance 5 . Whereas the former relaxes by intervalley scattering, the latter is largely limited by intravalley scattering. The presence of valley contrasting Berry curvatures in 2D Dirac materials, which can couple to external electromagnetic excitations, enables the control of valley magnetization [6][7][8][9][10][11][12][13][14][15][16][17] . Although the control of valley magnetization by circularly polarized light and by a vertical magnetic field has now become routine [6][7][8][10][11][12][13][14][15][16] , the development of practical valleytronic devices requires the pure electrical control of valley magnetization. The valley magnetoelectric (ME) effect is an attractive approach for this purpose.To realize the linear ME effect, a material has to possess broken time-reversal and spatial-inversion symmetries 1,18 . For an electrical conductor, time-reversal symmetry can be broken naturally by application of a bias voltage, under which dissipation through carrier scattering is caused by a charge current. The magnetoelectricity produced in this manner is known as the kinematic ME effect 19,20 . Single-layer TMDs such as MoS 2 , which are

Twist engineering, or the alignment of two-dimensional (2D) crystalline layers with desired orientations, has led to tremendous success in modulating the charge degree of freedom in heteroand homo-structures, in particular, in achieving novel correlated and topological electronic phases in moiré electronic crystals 1,2 . However, although pioneering theoretical efforts have predicted nontrivial magnetism 3,4 and magnons 5 out of twisting 2D magnets, experimental realization of twist engineering spin degree of freedom remains elusive. Here, we leverage the archetypal 2D Ising magnet chromium triiodide (CrI3) to fabricate twisted double bilayer homostructures with tunable twist angles and demonstrate the successful twist engineering of 2D magnetism in them. Using linear and circular polarization-resolved Raman spectroscopy, we identify magneto-Raman signatures of a new magnetic ground state that is sharply distinct from those in natural bilayer (2L) and four-layer (4L) CrI3. With careful magnetic field and twist angle dependence, we reveal that, for a very small twist angle (~ 0.5 o ), this emergent magnetism can be well-approximated by a weighted linear superposition of those of 2L and 4L CI3 whereas, for a relatively large twist angle (~ 5 o ), it mostly resembles that of isolated 2L CrI3. Remarkably, at an intermediate twist angle (~ 1.1 o ), its magnetism cannot be simply inferred from the 2L and 4L cases, because it lacks sharp spin-flip transitions that are present in 2L and 4L CrI3 and features a dramatic Raman circular dichroism that is absent in natural 2L and 4L ones. Our results demonstrate the possibility of designing and controlling the spin degree of freedom in 2D magnets using twist engineering.

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A moirésuperlattice formed by stacking two lattice mismatched transition metal dichalcogenide monolayers, functions as a diffusion barrier that affects the energy transport and dynamics of interlayer excitons (electron and hole spatially concentrated in different monolayers). In this work, we experimentally quantify the diffusion barrier experienced by interlayer excitons in hexagonal boron nitrideencapsulated molybdenum diselenide/tungsten diselenide (MoSe 2 / WSe 2 ) heterostructures with different twist angles. We observe the localization of interlayer excitons at low temperature and the temperature-activated diffusivity as a function of twist angle and hence attribute it to the deep periodic potentials arising from the moirésuperlattice. We further support the observations with theoretical calculations, Monte Carlo simulations, and a three-level model that represents the exciton dynamics at various temperatures.