Abstract Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 .
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Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets
Moiré superlattices of twisted nonmagnetic two-dimensional (2D) materials are highly controllable platforms for the engineering of exotic correlated and topological states. Here, we report emerging magnetic textures in small-angle twisted 2D magnet chromium triiodide (CrI 3 ). Using single-spin quantum magnetometry, we directly visualized nanoscale magnetic domains and periodic patterns, a signature of moiré magnetism, and measured domain size and magnetization. In twisted bilayer CrI 3 , we observed the coexistence of antiferromagnetic (AFM) and ferromagnetic (FM) domains with disorder-like spatial patterns. In twisted double-trilayer CrI 3 , AFM and FM domains with periodic patterns appear, which is in good agreement with the calculated spatial magnetic structures that arise from the local stacking-dependent interlayer exchange interactions in CrI 3 moiré superlattices. Our results highlight magnetic moiré superlattices as a platform for exploring nanomagnetism.
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- Award ID(s):
- 1719797
- NSF-PAR ID:
- 10322829
- Date Published:
- Journal Name:
- Science
- Volume:
- 374
- Issue:
- 6571
- ISSN:
- 0036-8075
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Moiré magnetism featured by stacking engineered atomic registry and lattice interactions has recently emerged as an appealing quantum state of matter at the forefront of condensed matter physics research. Nanoscale imaging of moiré magnets is highly desirable and serves as a prerequisite to investigate a broad range of intriguing physics underlying the interplay between topology, electronic correlations, and unconventional nanomagnetism. Here we report spin defect-based wide-field imaging of magnetic domains and spin fluctuations in twisted double trilayer (tDT) chromium triiodide CrI3. We explicitly show that intrinsic moiré domains of opposite magnetizations appear over arrays of moiré supercells in low-twist-angle tDT CrI3. In contrast, spin fluctuations measured in tDT CrI3manifest little spatial variations on the same mesoscopic length scale due to the dominant driving force of intralayer exchange interaction. Our results enrich the current understanding of exotic magnetic phases sustained by moiré magnetism and highlight the opportunities provided by quantum spin sensors in probing microscopic spin related phenomena on two-dimensional flatland.
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We apply the density-functional theory to study various phases (including non-magnetic (NM), anti-ferromagnetic (AFM), and ferromagnetic (FM)) in monolayer magnetic chromium triiodide (CrI 3 ), a recently fabricated 2D magnetic material. It is found that: (1) the introduction of magnetism in monolayer CrI 3 gives rise to metal-to-semiconductor transition; (2) the electronic band topologies as well as the nature of direct and indirect band gaps in either AFM or FM phases exhibit delicate dependence on the magnetic ordering and spin–orbit coupling; and (3) the phonon modes involving Cr atoms are particularly sensitive to the magnetic ordering, highlighting distinct spin–lattice and spin–phonon coupling in this magnet. First-principles simulations of the Raman spectra demonstrate that both frequencies and intensities of the Raman peaks strongly depend on the magnetic ordering. The polarization dependent A 1g modes at 77 cm −1 and 130 cm −1 along with the E g mode at about 50 cm −1 in the FM phase may offer a useful fingerprint to characterize this material. Our results not only provide a detailed guiding map for experimental characterization of CrI 3 , but also reveal how the evolution of magnetism can be tracked by its lattice dynamics and Raman response.more » « less
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Abstract The twist angle between a pair of stacked 2D materials has been recently shown to control remarkable phenomena, including the emergence of flat‐band superconductivity in twisted graphene bilayers, of higher‐order topological phases in twisted moiré superlattices, and of topological polaritons in twisted hyperbolic metasurfaces. These discoveries, at the foundations of the emergent field of twistronics, have so far been mostly limited to explorations in atomically thin condensed matter and photonic systems, with limitations on the degree of control over geometry and twist angle, and inherent challenges in the fabrication of carefully engineered stacked multilayers. Here, this work extends twistronics to widely reconfigurable macroscopic elastic metasurfaces consisting of LEGO pillar resonators. This work demonstrates highly tailored anisotropy over a single‐layer metasurface driven by variations in the twist angle between a pair of interleaved spatially modulated pillar lattices. The resulting quasi‐periodic moiré patterns support topological transitions in the isofrequency contours, leading to strong tunability of highly directional waves. The findings illustrate how the rich phenomena enabled by twistronics and moiré physics can be translated over a single‐layer metasurface platform, introducing a practical route toward the observation of extreme phenomena in a variety of wave systems, potentially applicable to both quantum and classical settings without multilayered fabrication requirements.
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A moiré photonic crystal is an optical analog of twisted graphene. A 3D moiré photonic crystal is a new nano-/microstructure that is distinguished from bilayer twisted photonic crystals. Holographic fabrication of a 3D moiré photonic crystal is very difficult due to the coexistence of the bright and dark regions, where the exposure threshold is suitable for one region but not for the other. In this paper, we study the holographic fabrication of 3D moiré photonic crystals using an integrated system of a single reflective optical element (ROE) and a spatial light modulator (SLM) where nine beams (four inner beams + four outer beams + central beam) are overlapped. By modifying the phase and amplitude of the interfering beams, the interference patterns of 3D moiré photonic crystals are systemically simulated and compared with the holographic structures to gain a comprehensive understanding of SLM-based holographic fabrication. We report the holographic fabrication of phase and beam intensity ratio-dependent 3D moiré photonic crystals and their structural characterization. Superlattices modulated in the z-direction of 3D moiré photonic crystals have been discovered. This comprehensive study provides guidance for future pixel-by-pixel phase engineering in SLM for complex holographic structures.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1126/science.abj7478
