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Crystal lattices with tetragonal or hexagonal structure often exhibit structural transitions in response to external stimuli 1 . Similar behaviour is anticipated for the lattice forms of topological spin textures, such as lattices composed of merons and antimerons or skyrmions and antiskyrmions (types of vortex related to the distribution of electron spins in a magnetic field), but has yet to be verified experimentally 2 , 3 . Here we report real-space observations of spin textures in a thin plate of the chiral-lattice magnet Co 8 Zn 9 Mn 3 , which exhibits in-plane magnetic anisotropy. The observations demonstrate the emergence of a two-dimensional square lattice of merons and antimerons from a helical state, and its transformation into a hexagonal lattice of skyrmions in the presence of a magnetic field at room temperature. Sequential observations with decreasing temperature reveal that the topologically protected skyrmions remain robust to changes in temperature, whereas the square lattice of merons and antimerons relaxes to non-topological in-plane spin helices, highlighting the different topological stabilities of merons, antimerons and skyrmions. Our results demonstrate the rich variety of topological spin textures and their lattice forms, and should stimulate further investigation of emergent electromagnetic properties. A magnetically induced two-dimensional square lattice of merons and antimerons is observed in real space, along with its transformation into a hexagonal lattice of skyrmions at room temperature.

From magnetism, ferroelectricity and superconductivity to electrical and thermal properties, oxides show a broad range of phenomena of fundamental as well as practical relevance. Reviewed here are the emergent phenomena arising at the interface between oxide materials, which have attracted considerable interest based on advances in thin-film deposition techniques. Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

Electrical rectification is usually achieved by layering p-type and n-type materials, but experiments now demonstrate rectification in a bulk polar semiconductor that has inversion-symmetry breaking and strong Rashba spin–orbit coupling. Noncentrosymmetric conductors are an interesting material platform, with rich spintronic functionalities 1 , 2 and exotic superconducting properties 3 , 4 typically produced in polar systems with Rashba-type spin–orbit interactions 5 . Polar conductors should also exhibit inherent nonreciprocal transport 6 , 7 , 8 , in which the rightward and leftward currents differ from each other. But such a rectification is difficult to achieve in bulk materials because, unlike the translationally asymmetric p–n junctions, bulk materials are translationally symmetric, making this phenomenon highly nontrivial. Here we report a bulk rectification effect in a three-dimensional Rashba-type polar semiconductor BiTeBr. Experimentally observed nonreciprocal electric signals are quantitatively explained by theoretical calculations based on the Boltzmann equation considering the giant Rashba spin–orbit coupling. The present result offers a microscopic understanding of the bulk rectification effect intrinsic to polar conductors as well as a simple electrical means to estimate the spin–orbit parameter in a variety of noncentrosymmetric systems.

Photoexcitation in solids brings about transitions of electrons/holes between different electronic bands. If the solid lacks an inversion symmetry, these electronic transitions support spontaneous photocurrent due to the geometric phase of the constituting electronic bands: the Berry connection. This photocurrent, termed shift current, is expected to emerge on the timescale of primary photoexcitation process. We observe ultrafast evolution of the shift current in a prototypical ferroelectric semiconductor antimony sulfur iodide (SbSI) by detecting emitted terahertz electromagnetic waves. By sweeping the excitation photon energy across the bandgap, ultrafast electron dynamics as a source of terahertz emission abruptly changes its nature, reflecting a contribution of Berry connection on interband optical transition. The shift excitation carries a net charge flow and is followed by a swing over of the electron cloud on a subpicosecond timescale. Understanding these substantive characters of the shift current with the help of first-principles calculation will pave the way for its application to ultrafast sensors and solar cells.

Magnetoelectric skyrmions Skyrmions are stable topological textures with particle-like properties, a mathematical concept originally developed to describe nuclear particles, but which in the past decade has found application at all scales from microscopic to cosmological. Skyrmions have proved particularly useful to describe novel spin configurations in magnets, and last year the presence of skyrmions in the magnetic compounds MnSi and Fe 1− x Co x Si was confirmed in neutron scattering experiments. Now Yu et al . present striking real-space images, using transmission electron microscopy, of a two-dimensional skyrmion lattice for the latter compound, in the form of a hexagonal arrangement of swirling spin structures. The lattice is shown to be stable for a wide range of temperatures and magnetic fields. The authors speculate that the observed nanometre-scale spin topology may lead to interesting new magnetoelectric effects. Skyrmions are stable topological textures with particle-like properties — a mathematical concept that was originally used to describe nuclear particles but has since turned up at all scales. Last year, the presence of skyrmions in the magnetic compounds MnSi and Fe 1−x Co x Si was confirmed with neutron-scattering experiments. Here, real-space images are presented of a two-dimensional skyrmion lattice in a thin film of the latter compound. The observed nanometre-scale spin topology might reveal new magneto-transport effects. Crystal order is not restricted to the periodic atomic array, but can also be found in electronic systems such as the Wigner crystal 1 or in the form of orbital order 2 , stripe order 3 and magnetic order. In the case of magnetic order, spins align parallel to each other in ferromagnets and antiparallel in antiferromagnets. In other, less conventional, cases, spins can sometimes form highly nontrivial structures called spin textures 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 . Among them is the unusual, topologically stable skyrmion spin texture, in which the spins point in all the directions wrapping a sphere 4 , 5 , 6 , 7 . The skyrmion configuration in a magnetic solid is anticipated to produce unconventional spin–electronic phenomena such as the topological Hall effect 24 , 25 , 26 . The crystallization of skyrmions as driven by thermal fluctuations has recently been confirmed in a narrow region of the temperature/magnetic field ( T – B ) phase diagram in neutron scattering studies of the three-dimensional helical magnets MnSi (ref. 17 ) and Fe 1− x Co x Si (ref. 22 ). Here we report real-space imaging of a two-dimensional skyrmion lattice in a thin film of Fe 0.5 Co 0.5 Si using Lorentz transmission electron microscopy. With a magnetic field of 50–70 mT applied normal to the film, we observe skyrmions in the form of a hexagonal arrangement of swirling spin textures, with a lattice spacing of 90 nm. The related T – B phase diagram is found to be in good agreement with Monte Carlo simulations. In this two-dimensional case, the skyrmion crystal seems very stable and appears over a wide range of the phase diagram, including near zero temperature. Such a controlled nanometre-scale spin topology in a thin film may be useful in observing unconventional magneto-transport effects.

Two intriguing manifestations of Hall physics are reported in a topologically insulating heterostructure: a sign-reversal of the anomalous Hall effect and the emergence of a topological Hall effect. Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric effects such as the anomalous 1 , spin 2 and topological Hall effects 3 , 4 , 5 , 6 . Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall effect, and the emergence of a topological Hall effect in magnetic/non-magnetic topological insulator heterostructures, Cr x (Bi 1− y Sb y ) 2− x Te 3 /(Bi 1− y Sb y ) 2 Te 3 . The sign-reversal in the anomalous Hall effect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall effect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii–Moriya interaction.

Uniaxial strain as small as 0.3% in FeGe thin films can induce large anisotropic deformation of magnetic skyrmions and their crystal lattice hosted in the material. Mechanical control of magnetism is an important and promising approach in spintronics. To date, strain control has mostly been demonstrated in ferromagnetic structures by exploiting a change in magnetocrystalline anisotropy. It would be desirable to achieve large strain effects on magnetic nanostructures. Here, using in situ Lorentz transmission electron microscopy, we demonstrate that anisotropic strain as small as 0.3% in a chiral magnet of FeGe induces very large deformations in magnetic skyrmions 1 , 2 , as well as distortions of the skyrmion crystal lattice on the order of 20%. Skyrmions are stabilized by the Dzyaloshinskii–Moriya interaction 3 , 4 , originating from a chiral crystal structure. Our results show that the change in the modulation of the strength of this interaction is amplified by two orders of magnitude with respect to changes in the crystal lattice due to an applied strain. Our findings may provide a mechanism to achieve strain control of topological magnetic structures based on the Dzyaloshinskii–Moriya interaction.

The motion of electrons in a solid has a profound effect on its topological properties and may result in a nonzero Berry's phase, a geometric quantum phase encoded in the system's electronic wave function. Despite its ubiquity, there are few experimental observations of Berry's phase of bulk states. Here, we report detection of a nontrivial π Berry's phase in the bulk Rashba semiconductor BiTel via analysis of the Shubnikov-de Haas (SdH) effect. The extremely large Rashba splitting in this material enables the separation of SdH oscillations, stemming from the spin-split inner and outer Fermi surfaces. For both Fermi surfaces, we observe a systematic π-phase shift in SdH oscillations, consistent with the theoretically predicted nontrivial π Berry's phase in Rashba systems.

Second-order continuous phase transitions are characterized by symmetry breaking with order parameters. Topological orders of electrons, characterized by the topological index defined in momentum space, provide a distinct perspective for phase transitions, which are categorized as quantum phase transitions not being accompanied by symmetry breaking. However, there are still limited observations of counterparts in real space. Here we show a real-space topological phase transition in a chiral magnet MnGe, hosting a periodic array of hedgehog and antihedgehog topological spin singularities. This transition is driven by the pair annihilation of the hedgehogs and antihedgehogs acting as monopoles and antimonopoles of the emergent electromagnetic field. Observed anomalies in the magnetoresistivity and phonon softening are consistent with the theoretical prediction of critical phenomena associated with enhanced fluctuations of emergent field near the transition. This finding reveals a vital role of topology of the spins in strongly correlated systems. Phase transitions in topologically non-trivial systems are characterized by changes of topological invariants, rather than conventional order parameters. Here, the authors propose a real-space topological phase transition upon pair annihilation of emergent monopoles inherent in chiral magnet MnGe.

A three-dimensional (3D) topological insulator features a 2D surface state consisting of a single linearly dispersive Dirac cone 1 – 3 . Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory 1 – 9 . However, despite various observations of quantization phenomena 10 – 15 , the half-integer quantization has not been observed because most experiments simultaneously measure a pair of equivalent Dirac cones 16 on two opposing surfaces. Here we demonstrate the half-integer quantization of Hall conductance in a synthetic heterostructure termed a semi-magnetic topological insulator, where only one surface state is gapped by magnetic doping and the opposite one is non-magnetic and gapless. We observe half-quantized Faraday and Kerr rotations with terahertz magneto-optical spectroscopy and half-quantized Hall conductance in transport at zero magnetic field. Our results suggest a condensed-matter realization of the parity anomaly 4 – 9 and open a way for studying the physics enabled by a single Dirac fermion. An electron with a linear dispersion relation should contribute half of a quantum of Hall conductance and thereby manifest the parity anomaly. This is demonstrated in a heterostructure of topological insulator materials.