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Noncoplanar magnets are excellent candidates for spintronics. However, such materials are difficult to find, and even more so to intentionally design. Here, we report a chemical design strategy that allows us to find a series of noncoplanar magnets-Ln 3 Sn 7 (Ln = Dy, Tb)-by targeting layered materials that have decoupled magnetic sublattices with dissimilar single-ion anisotropies and combining those with a square-net topological semimetal sublattice. Ln 3 Sn 7 shows high carrier mobilities upwards of 17,000 cm 2  ⋅ V -1  ⋅ s -1 , and hosts noncoplanar magnetic order. This results in a giant Hall response with an anomalous Hall angle of 0.17 and Hall conductivity of over 42,000 Ω -1  ⋅ cm -1 -a value over an order of magnitude larger than the established benchmarks in Co 3 Sn 2 S 2 and Fe thin films., Competing Interests: Competing interests: The authors declare no competing interests., (© 2024. The Author(s).)

Van-der-Waals magnetic materials can be exfoliated to realize ultrathin sheets or interfaces with highly controllable optical or spintronics responses. In majority, these are collinear ferro-, ferri-, or antiferromagnets, with a particular scarcity of lattice-incommensurate helimagnets of defined left- or right-handed rotation sense, or helicity. Here, we report polarized neutron scattering experiments on DyTe 3 , whose layered structure has highly metallic tellurium layers separated by double-slabs of dysprosium square nets. We reveal cycloidal (conical) magnetic textures, with coupled commensurate and incommensurate order parameters, and probe the evolution of this ground state in a magnetic field. The observations are well explained by a one-dimensional spin model, with an off-diagonal on-site term that is spatially modulated by DyTe 3 's unconventional charge density wave (CDW) order. The CDW-driven term couples to antiferromagnetism, or to the net magnetization in an applied magnetic field, and creates a complex magnetic phase diagram indicative of competing interactions in this easily cleavable van-der-Waals helimagnet., (© 2024. The Author(s).)

The magnetic skyrmion is a spin-swirling topological object characterized by its nontrivial winding number, holding potential for next-generation spintronic devices. While optical readout has become increasingly important towards the high integration and ultrafast operation of those devices, the optical response of skyrmions has remained elusive. Here, we show the magneto-optical Kerr effect (MOKE) induced by the skyrmion formation, i.e., topological MOKE, in Gd 2 PdSi 3 . The significantly enhanced optical rotation found in the skyrmion phase demonstrates the emergence of topological MOKE, exemplifying the light-skyrmion interaction arising from the emergent gauge field. This gauge field in momentum space causes a dramatic reconstruction of the electronic band structure, giving rise to magneto-optical activity ranging up to the sub-eV region. The present findings pave a way for photonic technology based on skyrmionics., (© 2023. Springer Nature Limited.)

The honeycomb magnet α-RuCl 3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κ xy of Majorana fermions is predicted to be half-quantized. Half-quantization of κ xy /T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κ xy on α-RuCl 3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κ xy /T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κ xy /T., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Magnetic skyrmions are topologically stable spin swirls with a particle-like character and are potentially suitable for the design of high-density information bits. Although most known skyrmion systems arise in non-centrosymmetric systems with a Dzyaloshinskii-Moriya interaction, centrosymmetric magnets with a triangular lattice can also give rise to skyrmion formation, with a geometrically frustrated lattice being considered essential in this case. Until now, it remains an open question if skyrmions can also exist in the absence of both geometrically frustrated lattice and inversion symmetry breaking. Here we discover a square skyrmion lattice state with 1.9 nm diameter skyrmions in the centrosymmetric tetragonal magnet GdRu 2 Si 2 without a geometrically frustrated lattice by means of resonant X-ray scattering and Lorentz transmission electron microscopy experiments. A plausible origin of the observed skyrmion formation is four-spin interactions mediated by itinerant electrons in the presence of easy-axis anisotropy. Our results suggest that rare-earth intermetallics with highly symmetric crystal lattices may ubiquitously host nanometric skyrmions of exotic origins.

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity/vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd 3 Ru 4 Al 12 , which materializes a breathing kagomé lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz-transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields.

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z 2 topological insulators by time-reversal symmetry 1-3 . Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials 4-12 . In particular, KHgSb is predicted to exhibit double quantum spin Hall states 10 . Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in Na 3 Bi (ref. ) and in TaAs (ref. ). An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function α xx of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.

Topological surface states protected by mirror symmetry are of interest for spintronic applications. Such states were predicted to exist in the rocksalt IV-VI semiconductors, and several groups have observed the surface states in (Pb,Sn)Te, (Pb,Sn)Se and SnTe using photoemission. An underlying assumption in the theory is that the surface states arise from bulk states describable as massive Dirac states, but this assumption is untested. Here we show that the thermoelectric response of the bulk states displays features specific to the Dirac spectrum. By relating the carrier density to the peaks in the quantum oscillations, we show that the first (N=0) Landau level is non-degenerate. This finding provides robust evidence that the bulk states are indeed massive Dirac states. In the lowest Landau level, Sxx displays a striking linear increase versus magnetic field characteristic of massive Dirac fermions. In addition, the Nernst signal displays a sign anomaly in the gap-inverted phase at low temperatures.