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Controlling the crystal structure is a powerful approach for manipulating the fundamental properties of solids. In van der Waals materials, this control can be achieved by modifying the stacking order through rotation and translation between the layers. Here, we observed stacking-dependent interlayer magnetism in the two-dimensional (2D) magnetic semiconductor chromium tribromide (CrBr3), which was enabled by the successful growth of its monolayer and bilayer through molecular beam epitaxy. Using in situ spin-polarized scanning tunneling microscopy and spectroscopy, we directly correlate the atomic lattice structure with the observed magnetic order. Although the individual monolayer CrBr3 is ferromagnetic, the interlayer coupling in bilayer depends on the stacking order and can be either ferromagnetic or antiferromagnetic. Our observations pave the way for manipulating 2D magnetism with layer twist angle control.

\"Decolonization revolutionized the international order during the twentieth century. Yet standard histories that present the end of colonialism as an inevitable transition from a world of empires to one of nations--a world in which self-determination was synonymous with nation-building--obscure just how radical this change was. Drawing on the political thought of anticolonial intellectuals and statesmen such as Nnamdi Azikiwe, W.E.B Du Bois, George Padmore, Kwame Nkrumah, Eric Williams, Michael Manley, and Julius Nyerere, this important new account of decolonization reveals the full extent of their unprecedented ambition to remake not only nations but the world.Adom Getachew shows that African, African American, and Caribbean anticolonial nationalists were not solely or even primarily nation-builders. Responding to the experience of racialized sovereign inequality, dramatized by interwar Ethiopia and Liberia, Black Atlantic thinkers and politicians challenged international racial hierarchy and articulated alternative visions of worldmaking. Seeking to create an egalitarian postimperial world, they attempted to transcend legal, political, and economic hierarchies by securing a right to self-determination within the newly founded United Nations, constituting regional federations in Africa and the Caribbean, and creating the New International Economic Order.Using archival sources from Barbados, Trinidad, Ghana, Switzerland, and the United Kingdom, Worldmaking after Empire recasts the history of decolonization, reconsiders the failure of anticolonial nationalism, and offers a new perspective on debates about today's international order.\"--Jacket flap.

Topological phases, like the Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, nonlocal string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems owing to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of nonlocal spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique, which measures nonlocal order directly, can be readily extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.

Spin-triplet superconductors potentially host topological excitations that are of interest for quantum information processing. We report the discovery of spin-triplet superconductivity in UTe₂, featuring a transition temperature of 1.6 kelvin and a very large and anisotropic upper critical field exceeding 40 teslas. This superconducting phase stability suggests that UTe₂ is related to ferromagnetic superconductors such as UGe₂, URhGe, and UCoGe. However, the lack of magnetic order and the observation of quantum critical scaling place UTe₂ at the paramagnetic end of this ferromagnetic superconductor series. A large intrinsic zero-temperature reservoir of ungapped fermions indicates a highly unconventional type of superconducting pairing.

Intrinsic long-range ferromagnetic order is observed in few-layer Cr 2 Ge 2 Te 6 crystals, with a transition temperature that can be controlled using small magnetic fields. Magnetism in flatland The question of what happens to the properties of a material when it is thinned down to atomic-scale thickness has for a long time been a largely hypothetical one. In the past decade, new experimental methods have made it possible to isolate and measure a range of two-dimensional structures, enabling many theoretical predictions to be tested. But it has been a particular challenge to observe intrinsic magnetic effects, which could shed light on the longstanding fundamental question of whether intrinsic long-range magnetic order can robustly exist in two dimensions. In this issue of Nature , two groups address this challenge and report ferromagnetism in atomically thin crystals. Xiang Zhang and colleagues measured atomic layers of Cr 2 Ge 2 Te 6 and observed ferromagnetic ordering with a transition temperature that, unusually, can be controlled using small magnetic fields. Xiaodong Xu and colleagues measured atomic layers of CrI 3 and observed ferromagnetic ordering that, remarkably, was suppressed in double layers of CrI 3 , but restored in triple layers. The two studies demonstrate a platform with which to test fundamental properties of purely two-dimensional magnets. The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications 1 , 2 , 3 , 4 . In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin–Wagner theorem 5 ; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering 6 , 7 , 8 , 9 , 10 , or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr 2 Ge 2 Te 6 atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr 2 Ge 2 Te 6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.

The physical properties of two-dimensional van der Waals crystals can be sensitive to interlayer coupling. For two-dimensional magnets1–3, theory suggests that interlayer exchange coupling is strongly dependent on layer separation while the stacking arrangement can even change the sign of the interlayer magnetic exchange, thus drastically modifying the ground state4–10. Here, we demonstrate pressure tuning of magnetic order in the two-dimensional magnet CrI3. We probe the magnetic states using tunnelling8,11–13 and scanning magnetic circular dichroism microscopy measurements2. We find that interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phase. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities.

The spin Hall effect (SHE) 1 – 5 achieves coupling between charge currents and collective spin dynamics in magnetically ordered systems and is a key element of modern spintronics 6 – 9 . However, previous research has focused mainly on non-magnetic materials, so the magnetic contribution to the SHE is not well understood. Here we show that antiferromagnets have richer spin Hall properties than do non-magnetic materials. We find that in the non-collinear antiferromagnet 10 Mn 3 Sn, the SHE has an anomalous sign change when its triangularly ordered moments switch orientation. We observe contributions to the SHE (which we call the magnetic SHE) and the inverse SHE (the magnetic inverse SHE) that are absent in non-magnetic materials and that can be dominant in some magnetic materials, including antiferromagnets. We attribute the dominance of this magnetic mechanism in Mn 3 Sn to the momentum-dependent spin splitting that is produced by non-collinear magnetic order. This discovery expands the horizons of antiferromagnet spintronics and spin–charge coupling mechanisms. A magnetic contribution to the spin Hall effect is observed in the non-collinear antiferromagnet Mn 3 Sn, which is attributed to momentum-dependent spin splitting produced by non-collinear magnetic order.

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order 1 . Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics 1 , such as the quantum anomalous Hall effect 2 and chiral Majorana fermions 3 . So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3 d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic 4 and electronic 5 properties of these materials, restricting the observation of important effects to very low temperatures 2 , 3 . An intrinsic magnetic topological insulator—a stoichiometric well ordered magnetic compound—could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi 2 Te 4 . The antiferromagnetic ordering  that MnBi 2 Te 4  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ 2 topological classification; ℤ 2  = 1 for MnBi 2 Te 4 , confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi 2 Te 4 exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling 6 – 8 and axion electrodynamics 9 , 10 . Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect 2 and chiral Majorana fermions 3 . An intrinsic antiferromagnetic topological insulator, MnBi 2 Te 4 , is theoretically predicted and then realized experimentally, with implications for the study of exotic quantum phenomena.

Magnetism typically arises from the joint effect of Fermi statistics and repulsive Coulomb interactions, which favours ground states with non-zero electron spin. As a result, controlling spin magnetism with electric fields—a longstanding technological goal in spintronics and multiferroics 1 , 2 —can be achieved only indirectly. Here we experimentally demonstrate direct electric-field control of magnetic states in an orbital Chern insulator 3 – 6 , a magnetic system in which non-trivial band topology favours long-range order of orbital angular momentum but the spins are thought to remain disordered 7 – 14 . We use van der Waals heterostructures consisting of a graphene monolayer rotationally faulted with respect to a Bernal-stacked bilayer to realize narrow and topologically non-trivial valley-projected moiré minibands 15 – 17 . At fillings of one and three electrons per moiré unit cell within these bands, we observe quantized anomalous Hall effects 18 with transverse resistance approximately equal to h /2 e 2 (where h is Planck’s constant and e is the charge on the electron), which is indicative of spontaneous polarization of the system into a single-valley-projected band with a Chern number equal to two. At a filling of three electrons per moiré unit cell, we find that the sign of the quantum anomalous Hall effect can be reversed via field-effect control of the chemical potential; moreover, this transition is hysteretic, which we use to demonstrate non-volatile electric-field-induced reversal of the magnetic state. A theoretical analysis 19 indicates that the effect arises from the topological edge states, which drive a change in sign of the magnetization and thus a reversal in the favoured magnetic state. Voltage control of magnetic states can be used to electrically pattern non-volatile magnetic-domain structures hosting chiral edge states, with applications ranging from reconfigurable microwave circuit elements to ultralow-power magnetic memories. Non-volatile electrical switching of magnetic order in an orbital Chern insulator is experimentally demonstrated using a moiré heterostructure and analysis shows that the effect is driven by topological edge states.