Since the celebrated discovery of graphene 1,2 , the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors 3 , Ising superconductors 4-6 that can be tuned into a quantum metal 7 , possible Mott insulators with tunable charge-density waves 8 , and topological semi-metals with edge transport 9,10 . Despite this progress, there is still no 2D crystal with intrinsic magnetism [11][12][13][14][15][16] , which would be useful for many technologies such as sensing, information, and data storage 17 . Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem 18 . However, magnetic anisotropy removes this restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase transition, showcasing the hallmark thickness-dependent physical properties typical of van der Waals crystals 19-21 . Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect 22 , while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics 13,23 , and van der Waals engineering for novel interface phenomena 17 . 2 Main Text:Magnetic anisotropy is an important requirement for realizing 2D magnetism. In ultrathin metallic films, an easy-axis can originate from symmetry reduction at the interface/surface, which hinges on substrate properties and interface quality [24][25][26] . In contrast, most van der Waals magnets have an intrinsic magnetocrystalline anisotropy due to the reduced crystal symmetry of their layered structures. This offers the coveted possibility to retain a magnetic ground state in the monolayer limit. In addition to studying magnetism in naturally formed crystals in the true 2D limit, layered magnets provide a platform for studying the thickness dependence of magnetism in isolated single crystals where the interaction with the underlying substrate is weak. Namely, the covalently bonded van der Waals layers prevent complex magnetization reorientations induced by epitaxial lattice reconstruction and strain 23 . For layered materials, these advantages come at a low fabrication cost, since the micromechanical exfoliation technique 27 is much simpler than conventional approaches requiring sputtering or sophisticated molecular beam epitaxy.A variety of layered magnetic compounds have recently drawn increased interest due to the possibility of re...

We show that inversion symmetry breaking together with spin-orbit coupling leads to coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides, making possible controls of spin and valley in these 2D materials. The spin-valley coupling at the valence band edges suppresses spin and valley relaxation, as flip of each index alone is forbidden by the valley contrasting spin splitting. Valley Hall and spin Hall effects coexist in both electron-doped and hole-doped systems. Optical interband transitions have frequency-dependent polarization selection rules which allow selective photoexcitation of carriers with various combination of valley and spin indices. Photo-induced spin Hall and valley Hall effects can generate long lived spin and valley accumulations on sample boundaries. The physics discussed here provides a route towards the integration of valleytronics and spintronics in multi-valley materials with strong spin-orbit coupling and inversion symmetry breaking. 75.70.Tj, Since the celebrated discovery of graphene [1][2][3], there has been a growing interest in atomically thin two-dimensional (2D) crystals for potential applications in next-generation nano-electronic devices [4,5]. Layered transition-metal dichalcogenides represent another class of materials that can be shaped into monolayers [4], which display distinct physical properties from their bulk counterpart [6][7][8][9]. Recent experiments have demonstrated that MoS 2 , a prototypical group-VI dichalcogenide, crossovers from an indirect-gap semiconductor at multilayers to a direct band-gap one at monolayer [6,7]. The direct band-gap is in the visible frequency range, most favorable for optoelectronic applications. Monolayer MoS 2 transistor was also realized, demonstrating a room-temperature mobility over 200 cm 2 /(V·s) [8]. In monolayer MoS 2 , the conduction and valence band edges are located at the corners (K points) of the 2D hexagonal Brillouin zone [10][11][12]. Similar to graphene, the two inequivalent valleys constitute a binary index for low energy carriers. Because of the large valley separation in momentum space, the valley index is expected to be robust against scattering by smooth deformations and long wavelength phonons. The use of valley index as a potential information carrier was first suggested in the studies of conventional semiconductors such as AlAs and Si [13]. With the emergence of graphene, the concept of valleytronics based on manipulating the valley index has attracted great interests [14][15][16][17][18].MoS 2 monolayers have two important distinctions from graphene. First, inversion symmetry is explicitly broken in monolayer MoS 2 , which can give rise to the valley Hall effect where carriers in different valleys flow to opposite transverse edges when an in-plane electric field is applied [15]. Inversion symmetry breaking can also lead to valley-dependent optical selection rules for inter-band transitions at K points [16]. Second, MoS 2 has a strong spin-orbit coupling (SOC) originated from the...

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Monolayer group-VI transition metal dichalcogenides have recently emerged as semiconducting alternatives to graphene in which the true two-dimensionality is expected to illuminate new semiconducting physics. Here we investigate excitons and trions (their singly charged counterparts), which have thus far been challenging to generate and control in the ultimate two-dimensional limit. Utilizing high-quality monolayer molybdenum diselenide, we report the unambiguous observation and electrostatic tunability of charging effects in positively charged (X þ ), neutral (X o ) and negatively charged (X À ) excitons in field-effect transistors via photoluminescence. The trion charging energy is large (30 meV), enhanced by strong confinement and heavy effective masses, whereas the linewidth is narrow (5 meV) at temperatures o55 K. This is greater spectral contrast than in any known quasitwo-dimensional system. We also find the charging energies for X þ and X À to be nearly identical implying the same effective mass for electrons and holes.