Atomically thin chromium triiodide (CrI 3 ) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled 1,2 . This unusual magnetic structure naturally comprises a series of anti-aligned spin filters which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR) 3-6 . Here we report voltage control of TMR formed by four-layer CrI 3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device can be switched reversibly between bistable magnetic states with the same net magnetization but drastically different resistance (by a factor of ten or more). In addition, without switching the state, the TMR can be continuously modulated between 17,000% and 57,000%, due to the combination of spin-dependent tunnel barrier with changing carrier distributions in the graphene contacts. Our work demonstrates new kinds of magnetically moderated transistor action and opens up possibilities for voltage-controlled van der Waals spintronic devices. Main Text:Electrical manipulation of magnetism is central to spintronics 7-13 . Voltage-controlled switching between bistable magnetic states can be employed in energy efficient magnetic memory and logic technologies. In this regard, the recently discovered two-dimensional (2D) magnetic insulator chromium triiodide (CrI3) has several assets as a building block for van der Waals (vdW) spintronics 1,2,14 . First, the extreme thinness of few-layer CrI3 enhances the probability that the magnetism will be amenable to electrostatic control [15][16][17][18][19][20] . Second, the layered antiferromagnetic structure at zero field naturally forms a series of interlayer spin filters, and their relative alignment can be changed by a moderate magnetic field via spin-flip transitions. This unusual property underpins the recent demonstration of multiple-spin-filter magnetic tunnel junctions (sf-MTJs) that exhibit giant tunneling magnetoresistance (TMR) [3][4][5][6]21,22 .

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite this lack of control the resulting braids can be used to systematically construct entangling gates for two qubits encoded by Fibonacci anyons.Comment: 9 pages, 6 figure

ability to synthesize and characterize 2D materials with long-range magnetic order was notably absent. Such materials hold great promise for potential applications in spintronics, [6][7][8][9][10][11] topological superconductivity, [12,13] vdW heterostructures, [14,15] and memory storage. [16,17] Hypothetical 2D magnets defy the Mermin-Wagner theorem, [18] which states that long-range magnetic order cannot exist at finite temperature within the 2D isotropic Heisenberg model. [19] Hence, magnetic anisotropy is a necessary prerequisite to realizing stable 2D magnetism, and has been demonstrated to exist in several layered materials over the last few years. [3,4,[20][21][22][23][24][25][26] Among these, the chromium trihalides CrX 3 (X = Cl, Br, I) have been the most extensively studied, all of which display intralayer ferromagnetic (FM) order and either FM or antiferromagnetic (AFM) interlayer coupling depending on the choice of halide and crystal thickness. [27] Despite their extensive characterization, chromium trihalides suffer from a lack of air and moisture stability and possess relatively low transition temperatures, limiting their applications. On the other hand, CrSBr has emerged [28][29][30][31] as an air-stable layered magnetic material possessing A-type AFM ordering with a comparatively high Néel temperature (T N ≈ 132 K).A variety of analytical tools have been used to characterize CrSBr, including magnetometry, [32,33] magneto-transport, [32,33] 2D materials can host long-range magnetic order in the presence of underlying magnetic anisotropy. The ability to realize the full potential of 2D magnets necessitates systematic investigation of the role of individual atomic layers and nanoscale inhomogeneity (i.e., strain) on the emergence of stable magnetic phases. Here, spatially dependent magnetism in few-layer CrSBr is revealed using magnetic force microscopy (MFM) and Monte Carlo-based simulations. Nanoscale visualization of the magnetic sheet susceptibility is extracted from MFM data and force-distance curves, revealing a characteristic onset of both intra-and interlayer magnetic correlations as a function of temperature and layer-thickness. These results demonstrate that the presence of a single uncompensated layer in odd-layer terraces significantly reduces the stability of the low-temperature antiferromagnetic (AFM) phase and gives rise to multiple coexisting magnetic ground states at temperatures close to the bulk Néel temperature (T N ). Furthermore, the AFM phase can be reliably suppressed using modest fields (≈16 mT) from the MFM probe, behaving as a nanoscale magnetic switch. This prototypical study of few-layer CrSBr demonstrates the critical role of layer parity on field-tunable 2D magnetism and validates MFM for use in nanomagnetometry of 2D materials (despite the ubiquitous absence of bulk zero-field magnetism in magnetized sheets).The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adma.202201000.

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