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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.

 

After graphene was first exfoliated in 2004, research worldwide has focused on discovering and exploiting its distinctive electronic, mechanical, and structural properties. Application of the efficacious methodology used to fabricate graphene, mechanical exfoliation followed by optical microscopy inspection, to other analogous bulk materials has resulted in many more two-dimensional (2D) atomic crystals. Despite their fascinating physical properties, manual identification of 2D atomic crystals has the clear drawback of low-throughput and hence is impractical for any scale-up applications of 2D samples. To combat this, recent integration of high-performance machine-learning techniques, usually deep learning algorithms because of their impressive object recognition abilities, with optical microscopy have been used to accelerate and automate this traditional flake identification process. However, deep learning methods require immense datasets and rely on uninterpretable and complicated algorithms for predictions. Conversely, tree-based machine-learning algorithms represent highly transparent and accessible models. We investigate these tree-based algorithms, with features that mimic color contrast, for automating the manual inspection process of exfoliated 2D materials (e.g., MoSe₂). We examine their performance in comparison to ResNet, a famous Convolutional Neural Network (CNN), in terms of accuracy and the physical nature of their decision-making process. We find that the decision trees, gradient boosted decision trees, and random forests utilize physical aspects of the images to successfully identify 2D atomic crystals without suffering from extreme overfitting and high training dataset demands. We also employ a post-hoc study that identifies the sub-regions CNNs rely on for classification and find that they regularly utilize physically insignificant image attributes when correctly identifying thin materials.

 

Abstract As described in the Introduction, we became interested in the existing literature for the crystallization behavior of (±)-[Co(en) 3 ]I 3 ·H 2 O and the absolute configuration of its enantiomers because of our project on the historical sequence of chemical studies leading Werner to formulate his Theory of Coordination Chemistry. In so doing, we discovered a number of interesting facts, including the possibility that the published “ Pbca ” structure of the (±)-[Co(en) 3 ]I 3 ·H 2 O was incorrect, and that it really crystallizes as a kryptoracemate in space group P 2 1 2 1 2 1 . Other equally interesting facts concerning the crystallization behavior of [Co(en) 3 ]I 3 ·H 2 O are detailed below, together with an explanation why P laton incorrectly selects, in this case, the space group Pbca instead of the correct choice, P 2 1 2 1 2 1 . As for the Flack parameter, (±)-[Co(en) 3 ]I 3 ·H 2 O provides an example long sought by Flack himself – a challenging case, differing from the norm. For that purpose, data sets (for the pure enantiomer and for the racemate) were collected at 100 K with R -factors of 4.24 and 2.82%, respectively, which are ideal for such a test. The fact that Pbca is unacceptable in this case is documented by the results of Second-Harmonic Generation experiments. CCDC nos: 1562401 for compound (I) and 1562403 for compound (II). 

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 . 

Abstract Compelling evidence suggests distinct correlated electron behavior may exist only in clean 2D materials such as 1T-TaS 2 . Unfortunately, experiment and theory suggest that extrinsic disorder in free standing 2D layers disrupts correlation-driven quantum behavior. Here we demonstrate a route to realizing fragile 2D quantum states through endotaxial polytype engineering of van der Waals materials. The true isolation of 2D charge density waves (CDWs) between metallic layers stabilizes commensurate long-range order and lifts the coupling between neighboring CDW layers to restore mirror symmetries via interlayer CDW twinning. The twinned-commensurate charge density wave (tC-CDW) reported herein has a single metal–insulator phase transition at ~350 K as measured structurally and electronically. Fast in-situ transmission electron microscopy and scanned nanobeam diffraction map the formation of tC-CDWs. This work introduces endotaxial polytype engineering of van der Waals materials to access latent 2D ground states distinct from conventional 2D fabrication. 

Abstract While the anomalous Hall effect can manifest even without an external magnetic field, time reversal symmetry is nonetheless still broken by the internal magnetization of the sample. Recently, it has been shown that certain materials without an inversion center allow for a nonlinear type of anomalous Hall effect whilst retaining time reversal symmetry. The effect may arise from either Berry curvature or through various asymmetric scattering mechanisms. Here, we report the observation of an extremely large c -axis nonlinear anomalous Hall effect in the non-centrosymmetric T d phase of MoTe 2 and WTe 2 without intrinsic magnetic order. We find that the effect is dominated by skew-scattering at higher temperatures combined with another scattering process active at low temperatures. Application of higher bias yields an extremely large Hall ratio of E ⊥ / E ||  = 2.47 and corresponding anomalous Hall conductivity of order 8 × 10 7  S/m.