Controlling magnetism via electric fields addresses fundamental questions of magnetic phenomena and phase transitions, and enables the development of electrically coupled spintronic devices, such as voltage-controlled magnetic memories with low operation energy. Previous studies on dilute magnetic semiconductors such as (Ga,Mn)As and (In,Mn)Sb have demonstrated large modulations of the Curie temperatures and coercive fields by altering the magnetic anisotropy and exchange interaction. Owing to their unique magnetic properties, the recently reported two-dimensional magnets provide a new system for studying these features. For instance, a bilayer of chromium triiodide (CrI) behaves as a layered antiferromagnet with a magnetic field-driven metamagnetic transition. Here, we demonstrate electrostatic gate control of magnetism in CrI bilayers, probed by magneto-optical Kerr effect (MOKE) microscopy. At fixed magnetic fields near the metamagnetic transition, we realize voltage-controlled switching between antiferromagnetic and ferromagnetic states. At zero magnetic field, we demonstrate a time-reversal pair of layered antiferromagnetic states that exhibit spin-layer locking, leading to a linear dependence of their MOKE signals on gate voltage with opposite slopes. Our results allow for the exploration of new magnetoelectric phenomena and van der Waals spintronics based on 2D materials.

Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises varied magnetic states, including ultrathin insulating multiferroics, spin liquids, and ferromagnets, but device-oriented characterization methods are needed to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and interlayer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI barriers, respectively. We further measure inelastic tunneling spectra for our junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI.

Using polarization-resolved photoluminescence spectroscopy, we investigate breaking of valley degeneracy by out-of-plane magnetic field in back-gated monolayer MoSe2 devices. We observe a linear splitting of −0.22 meV T between luminescence peak energies in σ+ and σ− emission for both neutral and charged excitons. The optical selection rules of monolayer MoSe2 couple photon handedness to the exciton valley degree of freedom, so this splitting demonstrates valley degeneracy breaking. In addition, we find that the luminescence handedness can be controlled with magnetic field, to a degree that depends on the back-gate voltage. An applied magnetic field therefore provides effective strategies for control over the valley degree of freedom.

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...

2The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field [1]. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants [2, 3]. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field [3]. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets [3][4][5][6][7][8]. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry.However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry [9]. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints [10][11][12]. Here, we report the observation of the nonlinear Hall effect (NLHE) [12] in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe 2 . Specifically, flowing an electrical current in bilayer WTe 2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I -V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of ∼ 90 • . We further show that the NLHE directly measures the "dipole moment" [12] of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe 2 . Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.In 1879 Edwin H. Hall observed that, when an electrical current passes through a gold film under a magnetic field, a transverse voltage develops [1]. This effect, known as the Hall effect, forms the basis of both fundamental research and practical applications such as magnetic field measurements and motion detectors. In contrast to the classical Hall effect where the Lorentz force bends the trajectory of the charge carriers, quantum mechanics describes the "bending" by the intrinsic geometry of the quantum electron wavefunctions under time-reversal symmetry breaking. This crucial theoretical understanding eventually led to the seminal discoveries of the Berry curvature and the topological Chern number, which have become pillars of modern condensed matter physics [2, 3]. One important cur-3 rent frontier is to identify AHE with quantized or topological character in unconventional magnetic quantum materials, where spin-orbit coupling (SOC), geometrical frustration and electronic correlations coexist [3][4][5][6][7][8]. These extensive studies [1,[3][4][5][6][7][8] have established a paradigm for the electrical Hall effect: (1) A non-vanishing Hall conductivity arises from the momentum-integrated Berry curva...