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Axion insulator state in ferromagnetically ordered CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructures

Ferromagnetic (FM) axion insulators may greatly simplify experimental explorations of the topological magnetoelectric effect, as the FM ordering can be stable in a broad range of magnetic field. Through density functional theory calculations and four-band model studies, we find that two-dimensional van der Waals FM CrI 3 and MnBi 2 Se 4 overlayers induce opposite-sign exchange fields in the topological surface states of Bi 2 Se 3 film when they are ferromagnetically ordered. As a consequence, the CrI 3 /Bi 2 Se 3 /MnBi 2 Se 4 heterostructure is a robust FM axion insulator, according to surface-resolved Berry curvature calculations. Our work opens up opportunities for the design of materials with the topological magnetoelectric effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spin-Forbidden Excitations in the Magneto-optical Spectra of CrI 3 Tuned by Covalency

Spin-forbidden (Δ⁢𝑆 ≠0) multiplet excitations and their coupling to magnetic properties are of increasing importance for magneto-optical studies of correlated materials. Nonetheless, the mechanisms for optically brightening these transitions and their generality remain poorly understood. Here, we report magnetic circular dichroism (MCD) spectroscopy on the van der Waals ferromagnet (FM) CrI 3 . Previously unreported spin-forbidden (Δ⁢𝑆 =1) 4 𝐴 2⁢g → 2 𝐸 g / 2 𝑇 1⁢g Cr 3+ 𝑑⁢𝑑 excitations are observed near the ligand-to-metal charge-transfer excitation threshold. The assignment of these excitations and their Cr 3+ multiplet character is established through complementary Cr 𝐿 3 -edge resonant inelastic x-ray scattering measurements along with charge-transfer multiplet calculations and chemical trends in the chromium trihalide series (Cr⁢𝑋 3 , 𝑋 = Cl, Br, I). We utilize the high sensitivity of MCD spectroscopy to study the thickness-dependent optical response. The spin-forbidden excitations remain robust down to the monolayer limit, and we observe a significant magnetic-field dependence of the MCD spectrum across the antiferromagnetic-to-FM transition in few-layer samples. We preliminarily attribute this behavior to changes in the metal-ligand covalency with magnetic state. Our results clarify the magneto-optical response of CrI 3 and identify covalency as a central mechanism for the brightening and field tunability of spin-forbidden multiplet excitations.

36 MATERIALS SCIENCE↗

Direct observation of twisted stacking domains in the van der Waals magnet CrI 3

Van der Waals (vdW) stacking is a powerful technique to achieve desired properties in condensed matter systems through layer-by-layer crystal engineering. A remarkable example is the control over the twist angle between artificially-stacked vdW crystals, enabling the realization of unconventional phenomena in moiré structures ranging from superconductivity to strongly correlated magnetism. Here, we report the appearance of unusual 120° twisted faults in vdW magnet CrI 3 crystals. In exfoliated samples, we observe vertical twisted domains with a thickness below 10 nm. The size and distribution of twisted domains strongly depend on the sample preparation methods, with as-synthesized unexfoliated samples showing tenfold thicker domains than exfoliated samples. Cooling induces changes in the relative populations among different twisting domains, rather than the previously assumed structural phase transition to the rhombohedral stacking. The stacking disorder induced by sample fabrication processes may explain the unresolved thickness-dependent magnetic coupling observed in CrI 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electronic structure of van der Waals ferromagnet CrI 3 from self-consistent vertex corrected GW approaches

Electronic structure of the layered van der Waals ferromagnet CrI 3 is studied with self consistent diagrammatic approaches beyond the GW approximation. Considerable improvement in the calculated band gap as compared to the non-self-consistent G0W0 results has been found. Certain spectral features in the valence bands discovered recently by the angle resolved photoemission spectroscopy, are reproduced better when we use full frequency dependent self energy. Density functional theory and the quasiparticle self-consistent GW method which are based on the frequency-independent self energy are unable to resolve these features. The non-locality effects in the diagrams beyond the GW approximation are large for both polarizability and self energy. This finding can potentially have an impact on the development of methods like the GW+DMFT (dynamical mean field theory).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Creating a three-dimensional intrinsic electric dipole on rotated CrI 3 bilayers

Here two-dimensional (2D) materials are being explored as a novel multiferroic platform. One of the most studied magnetoelectric multiferroic 2D materials are antiferromagnetically coupled (AFM) CrI 3 bilayers. Neglecting magnetism, those bilayers possess a crystalline point of inversion, which is only removed by the antiparallel spin configuration among its two constituent monolayers. The resulting intrinsic electric dipole on those bilayers has a magnitude no larger than 0.04 pC/m, it points out of plane, and it reverts direction when the Ising-like-chromium spins are flipped (toward opposite layers versus away from opposite layers). The combined presence of antiferromagnetism and a weak intrinsic electric dipole makes this material a two-dimensional magnetoelectric multiferroic. Here, we remove the crystalline center of inversion of the bilayer by a relative 60° rotation of its constituent monolayers. This process enhances the out-of-plane intrinsic electric dipole tenfold with respect to its magnitude in the nonrotated AFM bilayer and also creates an even stronger and switchable in-plane intrinsic electric dipole. The ability to create a three-dimensional electric dipole is important because it enhances the magnetoelectric coupling on this experimentally accessible 2D material, which is explicitly calculated here as well.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Iodine orbital moment and chromium anisotropy contributions to CrI 3 magnetism

The recent discovery of two-dimensional (2D) magnets, with a number of interesting magnetic properties, has drawn much interest due to their potential for future 2D spintronic device applications. CrI 3 , a van der Waals magnet, exhibits two-dimensional ferromagnetism even in monolayer form, stabilized by strong magnetic anisotropy. Its interlayer magnetic ordering is coupled to structural layer stacking, implying that the charge density distribution mediating van der Waals interactions plays a key role in the magnetic interaction between the layers. Using polarization-dependent x-ray spectroscopy, we investigated the response of the electronic environment around Cr and I sites to structural changes of layer stacking order. The highly anisotropic nature of the Cr local environment is significantly enhanced and is accompanied by changes in the valence band, in the rhombohedral phase. Magnetic spectroscopy measurements reveal a sizable iodine orbital moment, indicating the iodine contribution to magnetic anisotropy. Finally, our results uncover an important role for the extended nature of anisotropic Cr orbital states in dictating interlayer magnetic interactions and the iodine contribution to magnetic anisotropy.

36 MATERIALS SCIENCE↗

Dispersive Dark Excitons in van der Waals Ferromagnet CrI 3

Spin-flip dark excitons are optical-dipole-forbidden quasiparticles with remarkable potential in optoelectronics, especially when they are realized within cleavable van der Waals materials. Despite this potential, dark excitons have not yet been definitively identified in ferromagnetic van der Waals materials. Here, we report two dark excitons in a model ferromagnetic material CrI 3 using high-resolution resonant inelastic x-ray scattering and show that they feature narrower linewidths compared to the bright excitons previously reported in this material. These excitons are shown to have spin-flip character, to disperse as a function of momentum, and to change through the ferromagnetic transition temperature. Given the versatility of van der Waals materials, these excitons hold promise for new types of magneto-optical functionality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct observation of two-dimensional magnons in atomically thin CrI 3

Magnons are collective spin excitations in crystals with long-range magnetic order. The emergent van der Waals magnets provide a highly tunable platform to explore magnetic excitations in the two-dimensional limit with intriguing properties, manifesting from their honeycomb lattice structure and switchable magnetic configurations. Here, we report the direct observation of two-dimensional magnons through magneto-Raman spectroscopy with optical selection rules determined by the interplay between crystal symmetry, layer number and magnetic states in atomically thin CrI 3 . In monolayers, we observe an acoustic magnon mode at ~0.3 meV. It has strict cross-circularly polarized selection rules locked to the magnetization direction that originates from the conservation of angular momentum of photons and magnons dictated by three-fold rotational symmetry. Additionally, we reveal optical magnon modes at ~17 meV. This mode is Raman silent in monolayers, but optically active in bilayers and bulk due to a relaxation of the parity criterion resulting from the layer index. In the layered antiferromagnetic states, we directly resolve two degenerate optical magnon modes with opposite angular momentum and conjugate optical selection rules. From these measurements, we quantitatively extract the spin-wave gap, magnetic anisotropy and intralayer and interlayer exchange constants, and establish two-dimensional magnets as a new platform for exploring magnon physics.

36 MATERIALS SCIENCE↗

Role of nonlocality in exchange correlation for magnetic two-dimensional van der Waals materials

To obtain accurate independent-particle descriptions for ferromagnetic two-dimensional van der Waals materials, we apply the quasiparticle self-consistent G W (QSGW) method to VI 3 , CrI 3 , CrGeTe 3 , and Fe 3 GeTe 2 . QSGW provides a description of the nonlocal exchange-correlation term in the one-particle Hamiltonian. The nonlocal term is important not only as the U of density functional theory ( DFT ) + U but also for differentiating occupied and unoccupied states in semiconductors. Finally, we show the limitations of DFT + U in mimicking QSGW.

36 MATERIALS SCIENCE↗