Abstract:Electrons in 2-dimensional crystals with a honeycomb lattice structure possess a new valley degree of freedom (DOF) in addition to charge and spin. Each valley is predicted to exhibit a Hall effect in the absence of a magnetic field whose sign depends on the valley index, but to date this effect has not been observed. Here we report the first observation of this new valley Hall effect (VHE). Monolayer MoS 2 transistors are illuminated by circularly polarized light which preferentially excites electrons into a specific valley, and a finite anomalous Hall voltage is observed whose sign is controlled by the helicity of the light. Its magnitude is consistent with theoretical predictions of the VHE, and no anomalous Hall effect is observed in bilayer devices due to the restoration of crystal inversion symmetry. Our observation of VHE opens up new possibilities for using the valley DOF as an information carrier in next-generation electronics and optoelectronics.The charge and spin degrees of freedom (DOF) of electrons are at the heart of modern electronics. They form the basis for a wide range of applications such as transistors, photodetectors and magnetic memory devices. Interestingly, electrons in 2-dimensional (2D) crystals that have a honeycomb lattice structure possess an extra valley DOF (1) in addition to charge and spin. This new DOF has the potential to be used as an information carrier in nextgeneration electronics (2-6). Valley-dependent electronics and optoelectronics based on semimetallic graphene, a representative 2D crystal, have been theoretically proposed (2-5), but the presence of inversion symmetry in the crystal structure of pristine graphene makes both optical and electrical control of the valley DOF very difficult.In contrast, monolayer molybdenum disulfide (MoS 2 ), a 2D direct band gap semiconductor (7, 8) that possesses a staggered honeycomb lattice structure, is inversion asymmetric. Its fundamental direct energy gaps are located at the K and K' valleys of the Brillouin zone as illustrated in figure 1A. Due to the broken inversion symmetry in its crystal structure, electrons in the two valleys experience effective magnetic fields (proportional to the Berry curvature (4)) with equal magnitudes but opposite signs (figure 1A). Such a magnetic field not only defines the optical selection rules (6) that allow optical pumping of valley-polarized carriers by circularly polarized photons (9-13), but also generates an anomalous velocity for the charge carriers (6, 14). Namely, when the semiconductor channel is biased, electrons from different valleys move in opposite directions perpendicular to the drift current, a phenomenon called the valley Hall effect (VHE) (4)(5)(6) 15). The VHE originates from the coupling of the valley DOF to the orbital motion of electrons (4, 9). This is closely analogous to the spin Hall effect with the spin-polarized electrons replaced by valley-polarized carriers.Under time reversal symmetry, equal amounts of Hall current from each valley flow in opposite direc...

Abstract:Recent discoveries regarding current--induced spin--orbit torques produced by heavy--metal/ferromagnet and topological--insulator/ferromagnet bilayers provide the potential for dramatically--improved efficiency in the manipulation of magnetic devices. However, in experiments performed to date, spin--orbit torques have an important limitation -the component of torque that can compensate magnetic damping is required by symmetry to lie within the device plane. This means that spin--orbit torques can drive the most current--efficient type of magnetic reversal (antidamping switching) only for magnetic devices with in--plane anisotropy, not the devices with perpendicular magnetic anisotropy that are needed for high--density applications. Here we show experimentally that this state of affairs is not fundamental, but rather one can change the allowed symmetries of spin--orbit torques in spin--source/ferromagnet bilayer devices by using a spin source material with low crystalline symmetry. We use WTe 2 , a transition--metal dichalcogenide whose surface crystal structure has only one mirror plane and no two--fold rotational invariance. Consistent with these symmetries, we generate an out--of--plane antidamping torque when current is applied along a low--symmetry axis of WTe 2 /Permalloy bilayers, but not when current is applied along a high--symmetry axis. Controlling S--O torques by crystal symmetries in multilayer samples provides a new strategy for optimizing future magnetic technologies.2 Current--induced torques generated by materials with strong spin--orbit (S--O) interactions are a promising approach for energy--efficient manipulation of nonvolatile magnetic memory and logic technologies 1 . However, S--O torques observed to date are limited by their symmetry so that they cannot efficiently switch the nanoscale magnets with perpendicular magnetic anisotropy (PMA) that are required for high--density applications 2 . S--O torques generated either in conventional heavy metal/ferromagnet thin--film bilayers 3--13 or in topological insulator/ferromagnet bilayers 14,15 are restricted by symmetry to have a particular form 16 : an "antidamping--like" component oriented in the sample plane that is even upon reversal of the magnetization direction, m , plus an "effective field" component that is odd in m . The fact that the antidamping torque lies in--plane means that the most efficient mechanism of S--O--torque--driven magnetic reversal for small devices (antidamping switching) 17,18 is available only for magnetic samples with in--plane magnetic anisotropy 8,9 , and not PMA samples. S--O torques can also arise from broken crystalline inversion symmetry, even within single layers of ferromagnets 19--22 or antiferromagnets 23 , but the antidamping torques that have been measured to date are still limited to lie in the sample plane 21,22,24 . Here we demonstrate that the allowed symmetries of S--O torques in spin source/ferromagnet bilayer samples can be changed by using a spin source material with reduced crystalli...

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An array of micrometer-scale pixels of MoS2 works as a fluorescent “redox screen” to visualize redox molecule concentration.