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The Pauli exclusion principle combined with interactions between fermions is a basic mechanism across condensed-matter systems giving rise to a spontaneous breaking of the spin-space rotation symmetry of spin-ordered phases. Ferromagnetism is a conventional manifestation of spin ordering that leads to numerous applications (e.g., in spintronic information technologies). Altermagnetism, whose recent discovery was largely motivated by spintronics, stands apart from conventional magnetism in the sense that it spontaneously breaks not only spin-space but also real-space rotation symmetries, while it preserves a symmetry combining spin-space and real-space rotations. This is realized on crystals by a collinear compensated ordering of spins with a characteristic d-, g-, or i-wave symmetry. This perspective goes beyond the theory of spin arrangements on crystals by connecting altermagnetism to basic notions in condensed matter physics. Specifically, we reflect on the analogies and distinctions of altermagnetism as compared to superfluid 3He and theories of spin ordering in the momentum space generated by other higher-partial-wave instabilities of a Fermi liquid. On one hand, all these physical systems have in common the extraordinary combination of spontaneous breaking of spin-space and real-space rotation symmetries. On the other hand, we point out that there are key differences, both at the symmetry level and, particularly, at the level of microscopic mechanisms of ordering. These explain the comparatively large abundance, robustness, and utility of altermagnetism, as predicted by the symmetry classification of spin arrangements on crystals and ab initio calculations, and supported by initial experiments. 

Abstract Spin- and valley flavor polarization plays a central role in the many-body physics of flat band graphene, with Fermi surface reconstruction — often accompanied by quantized anomalous Hall and superconducting state — observed in a variety of experimental systems. Here we describe an optical technique that sensitively and selectively detects flavor textures via the exciton response of a proximal transition metal dichalcogenide layer. Through a systematic study of rhombohedral and rotationally faulted graphene bilayers and trilayers, we show that when the semiconducting dichalcogenide is in direct contact with the graphene, the exciton response is most sensitive to the large momentum rearrangement of the Fermi surface, providing information that is distinct from and complementary to electrical compressibility measurements. The wide-field imaging capability of optical probes allows us to obtain spatial maps of flavor order with high throughput, and with broad temperature and device compatibility. Our work helps pave the way for optical probing and imaging of flavor orders in flat band graphene systems. 

Abstract Effective control of magnetic phases in two-dimensional magnets would constitute crucial progress in spintronics, holding great potential for future computing technologies. Here, we report a new approach of leveraging tunneling current as a tool for controlling spin states in CrI₃. We reveal that a tunneling current can deterministically switch between spin-parallel and spin-antiparallel states in few-layer CrI₃, depending on the polarity and amplitude of the current. We propose a mechanism involving nonequilibrium spin accumulation in the graphene electrodes in contact with the CrI₃layers. We further demonstrate tunneling current-tunable stochastic switching between multiple spin states of the CrI₃tunnel devices, which goes beyond conventional bi-stable stochastic magnetic tunnel junctions and has not been documented in two-dimensional magnets. Our findings not only address the existing knowledge gap concerning the influence of tunneling currents in controlling the magnetism in two-dimensional magnets, but also unlock possibilities for energy-efficient probabilistic and neuromorphic computing. 

Abstract The intrinsic magnetic topological insulator, Mn(Bi_1−xSb_x)₂Te₄, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number,$$C$$ $C$. Previous reports in MnBi₂Te₄thin films have shown higher$$C$$ $C$states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependent$$C$$ $C$ = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi_1−xSb_x)₂Te₄dual-gated devices—consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi_1−xSb_x)₂Te₄films under strong magnetic fields can be interpreted by a theory of surface and bulk spin-polarised Landau level spectra in thin film magnetic topological insulators.