When monolayers of two-dimensional (2D) materials are stacked into van der Waals structures, interlayer electronic coupling can introduce entirely new properties, as exemplified by recent discoveries of moiré bands that host highly correlated electronic states and quantum dot-like interlayer exciton lattices. Here we show the magnetic control of interlayer electronic coupling, as manifested in tunable excitonic transitions, in an A-type

Exfoliated chromium triiodide (CrI3) is a layered van der Waals (vdW) magnetic insulator that consists of ferromagnetic layers coupled through antiferromagnetic interlayer exchange [1][2][3] . The resulting permutations of magnetic configurations combined with the underlying crystal symmetry produces tunable magneto-optical phenomena that is unique to the two-dimensional (2D) limit [4][5][6][7] . Here, we report the direct observation of 2D magnons through magneto-Raman spectroscopy with optical selection rules that are strictly determined by the honeycomb lattice and magnetic states of atomically thin CrI3. In monolayers, we observe an acoustic magnon mode of ~0.3 meV with cross-circularly polarized selection rules locked to the magnetization direction. These unique selection rules arise from the discrete conservation of angular momentum of photons and magnons dictated by threefold rotational symmetry in a rotational analogue to Umklapp scattering 8 . In bilayers, by tuning between the layered antiferromagnetic and ferromagnetic-like states, we observe the switching of two magnon modes. The bilayer structure also enables Raman activity from the optical magnon mode at ~17 meV (~4.2 THz) that is otherwise Raman-silent in the monolayer. From these measurements, we quantitatively extract the spin wave gap, magnetic anisotropy, intralayer and interlayer exchange constants, and establish 2D magnets as a new system for exploring magnon physics.

The coupling between spin and charge degrees of freedom in a crystal imparts strong optical signatures on scattered electromagnetic waves. This has led to magneto-optical effects with a host of applications, from the sensitive detection of local magnetic order to optical modulation and data storage technologies. Here, we demonstrate a new magnetooptical effect, namely, the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI3). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A1g phonon mode due to the emergence of ferromagnetic order. The linearly polarized, inelastically scattered light rotates by ~40⁰, more than two orders of magnitude larger than the rotation from MOKE under the same experimental conditions. In CrI3 bilayers, we show that the same A1g phonon mode becomes Davydov-split into two modes of opposite parity, exhibiting divergent selection rules that depend on inversion symmetry and the underlying magnetic order. By switching between the antiferromagnetic states and the fully spin-polarized states with applied magnetic and electric fields, we demonstrate the magnetoelectrical control over their selection rules. Our work underscores the unique opportunities provided by 2D magnets for controlling the combined time-reversal and inversion symmetries to manipulate Raman optical selection rules and for exploring emergent magneto-optical effects and spin-phonon coupled physics. Main text:Raman scattering measures light inelastically scattered from collective quasiparticle excitations. Since it is highly sensitive to material parameters such as crystal symmetry and local electronic states, Raman spectroscopy has provided a powerful probe of a broad range of condensed matter phenomena, such as charge density waves 1 , superconductivity 2 , ferroelectricity 3 , and topological physics 4 . In particular, Raman scattering from spin-phonon excitations has yielded incisive information on magnetic materials. For instance, in recently developed 2D van der Waals magnets, Raman scattering has been used to reveal magnetic order and phase transitions 5-7 down to a single layer [8][9][10] .Chromium triiodide (CrI3), a van der Waals magnet, was shown to be a layered antiferromagnet in its few-layer form: spins within each layer are ferromagnetically (FM) coupled with strong outof-plane anisotropy, while the interlayer exchange is antiferromagnetic (AFM) 11 . For bilayers, the system undergoes a spin-flip transition upon the application of a moderate magnetic field 11 , switching from a layered AFM state to a fully spin-polarized state. In addition, magneto-optical effects manifest strongly and in distinctly novel ways in CrI3. Examples include the very large magnetic-optical Kerr effect (MOKE) 11,12 and spontaneous helical light emission 13 from ferromagnetic monolayers, and electric-field induced Kerr rotation [14][15][16] and giant second-order nonreciprocal optical effects 17 in antiferromagnetic bilayers. Content:Extended Data...