Manipulating topological spin textures is a key for exploring unprecedented emergent electromagnetic phenomena. Whereas switching control of magnetic skyrmions, e.g., the transitions between a skyrmion-lattice phase and conventional magnetic orders, is intensively studied towards development of future memory device concepts, transitions among spin textures with different topological orders remain largely unexplored. Here we develop a series of chiral magnets MnSi 1− x Ge x , serving as a platform for transitions among skyrmion- and hedgehog-lattice states. By neutron scattering, Lorentz transmission electron microscopy and high-field transport measurements, we observe three different topological spin textures with variation of the lattice constant controlled by Si/Ge substitution: two-dimensional skyrmion lattice in x = 0–0.25 and two distinct three-dimensional hedgehog lattices in x = 0.3–0.6 and x = 0.7–1. The emergence of various topological spin states in the chemical-pressure-controlled materials suggests a new route for direct manipulation of the spin-texture topology by facile mechanical methods.

The Weyl semimetal (WSM), which hosts pairs of Weyl points and accompanying Berry curvature in momentum space near Fermi level, is expected to exhibit novel electromagnetic phenomena. Although the large optical/electronic responses such as nonlinear optical effects and intrinsic anomalous Hall effect (AHE) have recently been demonstrated indeed, the conclusive evidence for their topological origins has remained elusive. Here, we report the gigantic magneto-optical (MO) response arising from the topological electronic structure with intense Berry curvature in magnetic WSM Co3Sn2S2. The low-energy MO spectroscopy and the first-principles calculation reveal that the interband transitions on the nodal rings connected to the Weyl points show the resonance of the optical Hall conductivity and give rise to the giant intrinsic AHE in dc limit. The terahertz Faraday and infrared Kerr rotations are found to be remarkably enhanced by these resonances with topological electronic structures, demonstrating the novel low-energy optical response inherent to the magnetic WSM.

Spin structures with a non-trivial topology can emerge through the complex interplay of underlying magnetic interactions. Representative examples are magnetic skyrmions and hedgehogs observed in various materials. Although the most typical size of a skyrmion is 10–100 nm, there has been remarkable progress in the discovery of ultra-small (<3 nm) skyrmions and hedgehogs in the last few years. The dense topological spin crystals not only hold promise for technological applications but also provide a good arena to explore gigantic responses from emergent electromagnetic fields or Berry curvature. Here, we review design principles as well as electronic functions of versatile topological spin crystals, highlighting the distinct properties between skyrmion- and hedgehog-lattice states. Among them, unconventional outcomes from hedgehog-lattice states, such as their formation mechanisms and transport properties induced by the emergent magnetic monopoles, are discussed. The manipulation of such topological spin crystals, based on the strong couplings between topology and spin-charge-lattice degrees of freedom, may pave the way for electronics emerging in the near future.

Magnetic Weyl semimetals attract considerable interest not only for their topological quantum phenomena but also as an emerging materials class for realizing quantum anomalous Hall effect in the two-dimensional limit. A shandite compound Co3Sn2S2 with layered Kagome-lattices is one such material, where vigorous efforts have been devoted to synthesize the two-dimensional crystal. Here we report a synthesis of Co3Sn2S2 thin flakes with a thickness of 250 nm by chemical vapor transport method. We find that this facile bottom-up approach allows the formation of large-sized Co3Sn2S2 thin flakes of high-quality, where we identify the largest electron mobility (~2,600 cm 2 V -1 s -1 ) among magnetic topological semimetals, as well as the large anomalous Hall conductivity (~1,400  -1 cm -1 ) and anomalous Hall angle (~32 %) arising from the Berry curvature. Our study provides a viable platform for studying high-quality thin flakes of magnetic Weyl semimetal and stimulate further research on unexplored topological phenomena in the twodimensional limit.Magnetic Weyl semimetals (WSMs) with broken time-reversal symmetry exhibit unique physical properties arising from the interplay between magnetism and band topology [1][2][3][4][5]. In addition to the large magnetoresistance and high carrier mobility often observed in topological semimetals [6-8], the large anomalous Hall conductivity and anomalous Hall angle at zero magnetic field are known to be the hallmarks of diverging Berry curvature at the Weyl points in the presence of intrinsic magnetism [1,[9][10][11][12]. One other emerging aspect of the magnetic WSMs is that they are a new class of materials that can potentially realize the quantum anomalous Hall effect (QAHE) [13,14] in the two-dimensional (2D) limit. Since the Weyl fermions are only defined in the three-

The electrical Hall effect can be significantly enhanced through the interplay of the conduction electrons with magnetism, which is known as the anomalous Hall effect (AHE). Whereas the mechanism related to band topology has been intensively studied towards energy efficient electronics, those related to electron scattering have received limited attention. Here we report the observation of giant AHE of electron-scattering origin in a chiral magnet MnGe thin film. The Hall conductivity and Hall angle, respectively, reach $$40,000$$ 40 , 000  Ω−1 cm−1 and $$18$$ 18 % in the ferromagnetic region, exceeding the conventional limits of AHE of intrinsic and extrinsic origins, respectively. A possible origin of the large AHE is attributed to a new type of skew-scattering via thermally excited spin-clusters with scalar spin chirality, which is corroborated by the temperature–magnetic-field profile of the AHE being sensitive to the film-thickness or magneto-crystalline anisotropy. Our results may open up a new platform to explore giant AHE responses in various systems, including frustrated magnets and thin-film heterostructures.