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Although many emerging new phenomena have been unraveled in two dimensional (2D) materials with long-range spin orderings, the usually low critical temperature in van der Waals (vdW) magnetic material has thus far hindered the related practical applications. Here, we show that ferromagnetism can hold above 300 K in a metallic phase of 1T-CrTe 2 down to the ultra-thin limit. It thus makes CrTe 2 so far the only known exfoliated ultra-thin vdW magnets with intrinsic long-range magnetic ordering above room temperature. An in-plane room-temperature negative anisotropic magnetoresistance (AMR) was obtained in ultra-thin CrTe 2 devices, with a sign change in the AMR at lower temperature, with −0.6% and +5% at 300 and 10 K, respectively. Our findings provide insights into magnetism in ultra-thin CrTe 2 , expanding the vdW crystals toolbox for future room-temperature spintronic applications.

Geometrical frustration in magnetic materials often gives rise to exotic, low-temperature states of matter, such as the ones observed in spin ices. Here we report the imaging of the magnetic states of a thermally active artificial magnetic ice that reveal the fingerprints of a spin fragmentation process. This fragmentation corresponds to a splitting of the magnetic degree of freedom into two channels and is evidenced in both real and reciprocal space. Furthermore, the internal organization of both channels is interpreted within the framework of a hybrid spin–charge model that directly emerges from the parent spin model of the kagome dipolar spin ice. Our experimental and theoretical results provide insights into the physics of frustrated magnets and deepen our understanding of emergent fields through the use of tailor-made magnetism. By nanofabricating arrays of dipolar-coupled bistable single-domain nanomagnets, artificial model systems exhibiting collective ordering may be realized. Here, the authors present signatures of spin fragmentation in low-energy states of an artificial kagome ice.

All of the characteristics of the square-ice model are observed in an artificial square-ice system in which the two sublattices of nanomagnets are slightly vertically separated. A 'square ice' model relevant to real materials Geometric frustration in atomic lattices, such as those in water ice and magnetic materials called spin ice, leads to rich physical behaviour. So-called artificial spin ice, consisting of two-dimensional lattices of nanomagnets, was developed as a means of modelling these systems. Magnetic ordering, where neighbouring magnets try to align such that one is spin-up and the other spin-down, cannot be optimized owing to geometric frustration in these systems, which can be directly imaged. Until now it has not been possible to realize a fundamental 'square ice' model in these artificial systems that is of direct relevance to real materials. Nicolas Rougemaille and colleagues have solved this problem by designing a square lattice in which one of the two sublattices of nanomagnets is slightly vertically displaced. This enables them to directly observe the predicted spin-liquid state. Artificial spin-ice systems are lithographically patterned arrangements of interacting magnetic nanostructures that were introduced as way of investigating the effects of geometric frustration in a controlled manner 1 , 2 , 3 , 4 . This approach has enabled unconventional states of matter to be visualized directly in real space 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , and has triggered research at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite efforts to create an artificial realization of the square-ice model—a two-dimensional geometrically frustrated spin-ice system defined on a square lattice—no simple geometry based on arrays of nanomagnets has successfully captured the macroscopically degenerate ground-state manifold of the model 19 . Instead, square lattices of nanomagnets are characterized by a magnetically ordered ground state that consists of local loop configurations with alternating chirality 1 , 20 , 21 , 22 , 23 , 24 , 25 , 26 . Here we show that all of the characteristics of the square-ice model are observed in an artificial square-ice system that consists of two sublattices of nanomagnets that are vertically separated by a small distance. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of a Coulomb phase and algebraic spin-spin correlations, which are characterized by the presence of ‘pinch’ points in the associated magnetic structure factor. Local excitations—the classical analogues of magnetic monopoles 27 —are free to evolve in an extensively degenerate, divergence-free vacuum. We thus provide a protocol that could be used to investigate collective magnetic phenomena, including Coulomb phases 28 and the physics of ice-like materials.

Pressure is a powerful tool for tuning the magnetic properties of van der Waals magnets owing to their weak interlayer bonding. However, local magnetometry measurements under high pressure still remain elusive for this important class of emerging materials. Here we demonstrate magnetic imaging of a van der Waals magnet under high pressure with sub-micron spatial resolution, using a two-dimensional (2D) quantum sensing platform based on boron-vacancy ( V B − ) centers in hexagonal boron nitride (hBN). We first analyze the performances of V B − centers in hBN for magnetic imaging under pressures up to few GPa, and we then use this 2D sensing platform to investigate the pressure-dependent magnetization in micrometer-sized flakes of 1 T -CrTe 2 . Besides providing a new path for studying pressure-induced phase transitions in van der Waals magnets, this work also opens up interesting perspectives for exploring the physics of 2D superconductors under pressure via local measurements of the Meissner effect. NV center-based quantum sensors integrated into diamond anvil cells have enabled magnetic imaging under high pressure but are less suited for studying magnetic van der Waals materials. Here, the authors demonstrate magnetic imaging of micrometer-sized flakes of 1T-CrTe2 under high pressure using spin-centers in a thin hBN layer.

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research and became in the past years the subject of intense works, mainly focused on controlling, manipulating and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1 mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.

The square ice is a two-dimensional spin liquid hosting a Coulomb phase physics. When constrained under specific boundary conditions, the so-called domain-wall boundary conditions, a phase separation occurs that leads to the formation of a spin liquid confined within a disk surrounded by magnetically ordered regions. Here, we numerically characterize the ground-state properties of this spin liquid, coined the arctic square ice in reference to a phenomenon known in statistical mechanics. Our results reveal that both the vertex distributions and the magnetic correlations are inhomogeneous within the liquid region, and they exhibit a radial dependence. If these properties resemble those of the conventional square ice close to the center of the disk, they evolve continuously as the disk perimeter is approached. There, the spin liquid orders. As a result, pinch points, signaling the presence of algebraic spin correlations, coexist with magnetic Bragg peaks in the magnetic structure factor computed within the disk. The arctic square ice thus appears as an unconventional Coulomb phase sharing common features with a fragmented spin liquid, albeit on a charge-neutral vacuum.

Two-dimensional (2D) materials naturally form moir\\'{e} patterns with other crystalline layers, such as other 2D material or the surface of a substrate. These patterns add a nanoscale characteristic length in the form of a superlattice: the moir\\'{e} wavelength. Understanding the origin and characteristics of these patterns is crucial to design/interpret moir\\'{e}-induced physical properties. Here, we use a mixed continuum mechanics + atomistic modeling to study two experimentally relevant epitaxial 2D materials -- graphene on Ir(111) and MoS\\(_2\\) on Au(111) -- under extrinsic and intrinsic strain. We consider three different scenarios affecting substantially the lattice constant of the 2D materials, the wavelength and corrugation of the moir\\'{e} pattern. (i) Under the influence of the interaction with the substrate, bending energy produces non trivial variations of the moir\\'{e} properties, even when the strain is small; (ii) When locked on a progressively strained substrate via the valleys of the moir\\'{e}, the membranes' nanorippling amplitude goes through several jumps related to relatively smaller jumps in the interatomic distance of the 2D materials; (iii) Finally, increasing the zero-deformation value of this interatomic distance (possibly controlable with temperature or illumination in experiments) the moir\\'{e} wavelength can either increase or decrease.

The square ice is a canonical example of a Coulomb phase in two dimensions: Its ground state is extensively degenerate and satisfies a local constraint on the spin arrangement (the so-called ice rule). In this paper, we use a loop flip algorithm to explore the properties of this ground state that we analyze not in terms of a spin texture, but rather in terms of a spatial distribution of ice-rule satisfying vertices. More specifically, we determine for various lattice sizes the average vertex populations characterizing the ice manifold, the pairwise vertex correlations, and the size distribution of vertex clusters. Comparing these results to those obtained from random, constraint-free vertex tilings, the square ice manifold is found to resemble an almost ideal vertex gas, and the cluster size distribution of ice-rule satisfying vertices is well approximated by percolation theory. Remarkably, this description remains reasonably accurate when monopoles are present in a dilute amount, allowing a direct comparison with experiments. Revising former experimental results on two artificial square ice systems, we illustrate the interest of our approach to spot the presence of a Coulomb phase from a vertex analysis.

Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\\'{e} patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a continuous+atomistic theory treating 2D materials as crystalline elastic membranes, we abandon the flat-membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and MoS\\(_2\\) on metals and reveal that compression/expansion and bending energies stored in the membrane can compete with adhesion energy, leading to a subtle moir\\'{e} wavelength selection and the formation of wrinkles.

We investigate numerically the micromagnetic properties and the low-energy physics of an artificial square spin system in which the nanomagnets are physically connected at the lattice vertices. Micromagnetic simulations reveal that the energy stored at the vertex sites strongly depends on the type of magnetic domain wall formed by the four connected nanomagnets. As a consequence, the energy gap between the vertex types can be partially modified by varying the geometrical parameters of the nanomagnets, such as their width and thickness. Based on the energy levels given by the micromagnetic simulations, we compute the thermodynamic properties of the corresponding spin models using Monte Carlo simulations. We found two regimes, both being characterized by an extensive ground state manifold, in sharp contrast with similar lattices with disconnected nanomagnets. For narrow and thin nanomagnets, low-energy spin configurations consist of independent ferromagnetic straight lines crossing the whole lattice. The ground state manifold is thus highly degenerate, although this degeneracy is subdominant. In the limit of thick and wide nanomagnets, our findings suggest that the celebrated square ice model may be fabricated experimentally from a simple square lattice of connected elements. These results show that the micromagnetic nature of artificial spin systems involves another degree of freedom that can be finely tuned to explore strongly correlated disordered magnetic states of matter.