Hopfion rings in a cubic chiral magnet.

Magnetic skyrmions and hopfions are topological solitons1-well-localized field configurations that have gained considerable attention over the past decade owing to their unique particle-like properties, which make them promising objects for spintronic applications. Skyrmions2,3 are two-dimensional solitons resembling vortex-like string structures that can penetrate an entire sample. Hopfions4-9 are three-dimensional solitons confined within a magnetic sample volume and can be considered as closed twisted skyrmion strings that take the shape of a ring in the simplest case. Despite extensive research on magnetic skyrmions, the direct observation of magnetic hopfions is challenging10 and has only been reported in a synthetic material11. Here we present direct observations of hopfions in crystals. In our experiment, we use transmission electron microscopy to observe hopfions forming coupled states with skyrmion strings in B20-type FeGe plates. We provide a protocol for nucleating such hopfion rings, which we verify using Lorentz imaging and electron holography. Our results are highly reproducible and in full agreement with micromagnetic simulations. We provide a unified skyrmion-hopfion homotopy classification and offer insight into the diversity of topological solitons in three-dimensional chiral magnets.

Geometry-Induced Spin Filtering in Photoemission Maps from WTe_{2} Surface States.

We demonstrate that an important quantum material WTe_{2} exhibits a new type of geometry-induced spin filtering effect in photoemission, stemming from low symmetry that is responsible for its exotic transport properties. Through the laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping, we showcase highly asymmetric spin textures of electrons photoemitted from the surface states of WTe_{2}. Such asymmetries are not present in the initial state spin textures, which are bound by the time-reversal and crystal lattice mirror plane symmetries. The findings are reproduced qualitatively by theoretical modeling within the one-step model photoemission formalism. The effect could be understood within the free-electron final state model as an interference due to emission from different atomic sites. The observed effect is a manifestation of time-reversal symmetry breaking of the initial state in the photoemission process, and as such it cannot be eliminated, but only its magnitude influenced, by special experimental geometries.

Long-Range Orbital Torque by Momentum-Space Hotspots.

While it is often assumed that the orbital response is suppressed and short ranged due to strong crystal field potential and orbital quenching, we show that the orbital response can be remarkably long ranged in ferromagnets. In a bilayer consisting of a nonmagnet and a ferromagnet, spin injection from the interface results in spin accumulation and torque in the ferromagnet, which rapidly oscillate and decay by spin dephasing. In contrast, even when an external electric field is applied only on the nonmagnet, we find substantially long-ranged induced orbital angular momentum in the ferromagnet, which can go far beyond the spin dephasing length. This unusual feature is attributed to nearly degenerate orbital characters imposed by the crystal symmetry, which form hotspots for the intrinsic orbital response. Because only the states near the hotspots contribute dominantly, the induced orbital angular momentum does not exhibit destructive interference among states with different momentum as in the case of the spin dephasing. This gives rise to a distinct type of orbital torque on the magnetization, increasing with the thickness of the ferromagnet. Such behavior may serve as critical long-sought evidence of orbital transport to be directly tested in experiments. Our findings open the possibility of using long-range orbital response in orbitronic device applications.

Fabrication and Imaging Monatomic Ni Kagome Lattice on Superconducting Pb(111).

Artificial fabrication of a monolayer Kagome material can offer a promising opportunity to explore exceptional quantum states and phenomena in low dimensionality. Here, we have systematically studied a monatomic Ni Kagome lattice grown on Pb(111) by scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT). Sawtooth edge structures with distinct heights due to subsurface Ni atoms have been revealed, leading to asymmetric edge scattering of surface electrons on Pb(111). In addition, a local maximum at about -0.2 eV in tunneling spectra represents a manifestation of characteristic phase-destructive flat bands. Although charge transfer from underlying Pb(111) substrate results in a vanishing magnetic moment of Ni atoms, the proximity-induced superconducting gap is slightly enhanced on the Ni Kagome lattice. In light of single-atomic-layer Ni Kagome lattice on superconducting Pb(111) substrate, it could serve as an ideal platform to investigate the interplay between Kagome physics and superconductivity down to the two-dimensional limit.

Fermi-Surface Origin of Skyrmion Lattices in Centrosymmetric Rare-Earth Intermetallics.

We show from first principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu_{2}Si_{2} and Gd_{2}PdSi_{3} give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-q spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line between the subtleties of the three-dimensional Fermi surface topology and the stabilization of a square skyrmion lattice in GdRu_{2}Si_{2} at applied magnetic fields as observed in experiment.

Noncollinear Spin Current for Switching of Chiral Magnetic Textures.

We propose a concept of noncollinear spin current, whose spin polarization varies in space even in nonmagnetic crystals. While it is commonly assumed that the spin polarization of the spin Hall current is uniform, asymmetric local crystal potential generally allows the spin polarization to be noncollinear in space. Based on microscopic considerations, we demonstrate that such noncollinear spin Hall currents can be observed, for example, in layered Kagome Mn_{3}X (X=Ge, Sn) compounds. Moreover, by referring to atomistic spin dynamics simulations we show that noncollinear spin currents can be used to switch the chiral spin texture of Mn_{3}X in a deterministic way even in the absence of an external magnetic field. Our theoretical prediction can be readily tested in experiments, which will open a novel route toward electric control of complex spin structures in noncollinear antiferromagnets.

Is There a Polaron Signature in Angle-Resolved Photoemission of CsPbBr_{3}?

The formation of large polarons has been proposed as reason for the high defect tolerance, low mobility, low charge carrier trapping, and low nonradiative recombination rates of lead halide perovskites. Recently, direct evidence for large-polaron formation has been reported from a 50% effective mass enhancement in angle-resolved photoemission of CsPbBr_{3} over theory for the orthorhombic structure. We present in-depth band dispersion measurements of CsPbBr_{3} and GW calculations, which lead to similar effective masses at the valence band maximum of 0.203±0.016 m_{0} in experiment and 0.226 m_{0} in orthorhombic theory. We argue that the effective mass can be explained solely on the basis of electron-electron correlation and large-polaron formation cannot be concluded from photoemission data.

Ordering of Oxygen Vacancies and Related Ferroelectric Properties in HfO_{2-δ}.

Using density functional theory combined with an evolutionary algorithm, we investigate ferroelectricity in substoichiometric HfO_{2-δ} with fixed composition δ=0.25. We find that oxygen vacancies tend to cluster in the form of two-dimensional extended defects, revealing several patterns of local relative arrangements within an energy range of 100 meV per Hf atom. Two lowest-energy patterns result in polar monoclinic structures with different transformation properties. The lowest one elastically transforms to the ferroelectric orthorhombic structure via a shear deformation, overcoming an energy barrier, which is more than twice lower than in the stoichiometric hafnia. The second-lowest structure transforms at smaller volumes to a nonpolar tetragonal one. We discuss the experimentally observed wake-up effect, fatigue, and imprint in HfO_{2}-based ferroelectrics in terms of different local ordering of oxygen-vacancy extended defects, which favor specific crystallographic phases.

Transverse Transport in Two-Dimensional Relativistic Systems with Nontrivial Spin Textures.

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary, the anomalous, and the topological Hall effect, is incomplete and must be amended by an additional term, the "noncollinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing us to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.

Atomistic Perspective of Long Lifetimes of Small Skyrmions at Room Temperature.

The current development to employ magnetic skyrmions in novel spintronic device designs has led to a demand for room-temperature-stable skyrmions of ever smaller size. We present extensive studies on skyrmion stability in atomistic magnetic systems in two- and three-dimensional geometries. We show that for materials described by the same micromagnetic parameters, the variation of the atomistic exchange between different neighbors, the stacking order, and the number of layers of the atomic lattice can significantly influence the rate of the thermally activated decay of a skyrmion. These factors alone are important considerations, but we show that their combination can open up novel avenues of materials design in the search for sub-10 nm skyrmions, as their lifetime can be extended by several orders of magnitude.

Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach.

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the reinterpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

Plumbene on a Magnetic Substrate: A Combined Scanning Tunneling Microscopy and Density Functional Theory Study.

As a heavy analog of graphene, plumbene is a two-dimensional material with strong spin-orbit coupling effects. Using scanning tunneling microscopy, we observe that Pb forms a flat honeycomb lattice on an Fe monolayer on Ir(111). In contrast, without the Fe layer, a c(2×4) structure of Pb on Ir(111) is found. We use density-functional theory calculations to rationalize these findings and analyze the impact of the hybridization on the plumbene band structure. In the unoccupied states the splitting of the Dirac cone by spin-orbit interaction is clearly observed, while the occupied Pb states are strongly hybridized with the substrate. In a freestanding plumbene we find a band inversion below the Fermi level that leads to the formation of a topologically nontrivial gap. Exchange splitting as mediated by the strong hybridization with the Fe layer drives a quantum spin Hall to quantum anomalous Hall state transition.

Ab initio phase diagrams of Hf-O, Zr-O and Y-O: a comparative study.

We present phase diagrams of binary oxides, Hf-O, Zr-O and Y-O, obtained by ab initio evolutionary simulations, in order to explore possible metastable crystalline suboxide structures which could be quenched during the electroforming processes within the conductive filaments in stoichiometric HfO2, ZrO2 and Y2O3 host materials, in resistive switching devices. We find that, in the range MO-MO2 (where M = Hf, Zr, Y), the most energetically favourable atomic configurations have properties which facilitate the ionic conduction of oxygen. Namely, the calculations reveal that oxygen vacancies tend to order in arrays of one-dimensional channels, along which the migration barrier of anions is much lower than for the stoichiometric hosts. We explore for Hf-O and Zr-O a new set of structural patterns, different from those of the host materials, for which a change of oxygen stoichiometry does not change the underlying structural frame. However, a sufficient change of oxygen stoichiometry drives metallic conductivity in oxygen-deficient compounds, whereas their oxygen-rich counterparts are insulating. In contrast to Hf-O and Zr-O, in the Y-O system we find an atomic structure with metallic conductivity, which has the same structural frame as the stoichiometric Y2O3 host. We believe that this property enables the forming-free resistive switching in Y2O3.

Interface-engineered templates for molecular spin memory devices.

The use of molecular spin state as a quantum of information for storage, sensing and computing has generated considerable interest in the context of next-generation data storage and communication devices, opening avenues for developing multifunctional molecular spintronics. Such ideas have been researched extensively, using single-molecule magnets and molecules with a metal ion or nitrogen vacancy as localized spin-carrying centres for storage and for realizing logic operations. However, the electronic coupling between the spin centres of these molecules is rather weak, which makes construction of quantum memory registers a challenging task. In this regard, delocalized carbon-based radical species with unpaired spin, such as phenalenyl, have shown promise. These phenalenyl moieties, which can be regarded as graphene fragments, are formed by the fusion of three benzene rings and belong to the class of open-shell systems. The spin structure of these molecules responds to external stimuli (such as light, and electric and magnetic fields), which provides novel schemes for performing spin memory and logic operations. Here we construct a molecular device using such molecules as templates to engineer interfacial spin transfer resulting from hybridization and magnetic exchange interaction with the surface of a ferromagnet; the device shows an unexpected interfacial magnetoresistance of more than 20 per cent near room temperature. Moreover, we successfully demonstrate the formation of a nanoscale magnetic molecule with a well-defined magnetic hysteresis on ferromagnetic surfaces. Owing to strong magnetic coupling with the ferromagnet, such independent switching of an adsorbed magnetic molecule has been unsuccessful with single-molecule magnets. Our findings suggest the use of chemically amenable phenalenyl-based molecules as a viable and scalable platform for building molecular-scale quantum spin memory and processors for technological development.

Spin-Resolved Electronic Response to the Phase Transition in MoTe_{2}.

The semimetal MoTe_{2} is studied by spin- and angle-resolved photoemission spectroscopy across the centrosymmetry-breaking structural transition temperature of the bulk. A three-dimensional spin-texture is observed in the bulk Fermi surface in the low temperature, noncentrosymmetric phase that is consistent with first-principles calculations. The spin texture and two types of surface Fermi arc are not completely suppressed above the bulk transition temperature. The lifetimes of quasiparticles forming the Fermi arcs depend on thermal history and lengthen considerably upon cooling toward the bulk structural transition. The results indicate that a new form of polar instability exists near the surface when the bulk is largely in a centrosymmetric phase.

Duplication, Collapse, and Escape of Magnetic Skyrmions Revealed Using a Systematic Saddle Point Search Method.

Various transitions that a magnetic Skyrmion can undergo are found in calculations using a method for climbing up the energy surface and converging onto first order saddle points. In addition to collapse and escape through a boundary, the method identifies a transition where the Skyrmion divides and forms two Skyrmions. The activation energy for this duplication process can be similar to that of collapse and escape. A tilting of the external magnetic field for a certain time interval is found to induce the duplication process in a dynamical simulation. Such a process could turn out to be an important avenue for the creation of Skyrmions in future magnetic devices.

Magnetic Ground State Stabilized by Three-Site Interactions: Fe/Rh(111).

We report the direct observation of a theoretically predicted magnetic ground state in a monolayer Fe on Rh(111), which is referred to as an up-up-down-down (↑↑↓↓) double-row-wise antiferromagnetic spin structure, using spin-polarized scanning tunneling microscopy. This exotic phase, which exists in three orientational domains, is revealed by experiments with magnetic probe tips performed in external magnetic fields. It is shown that a hitherto unconsidered four-spin-three-site beyond-Heisenberg interaction distinctly contributes to the spin coupling of atoms with S≥1 spins. The observation of the ↑↑↓↓ order substantiates the presence of higher-order, in particular, three-site interactions, in thin magnetic films of itinerant magnets.

Interaction of Individual Skyrmions in a Nanostructured Cubic Chiral Magnet.

We report direct evidence of the field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high-resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of an external magnetic field the character of such long-range skyrmion interactions changes from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skyrmion-edge distances as a function of the applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. The important role of demagnetizing fields and the internal symmetry of three-dimensional magnetic skyrmions are discussed in detail.

Direct Observation of the Band Gap Transition in Atomically Thin ReS2.

ReS2 is considered as a promising candidate for novel electronic and sensor applications. The low crystal symmetry of this van der Waals compound leads to a highly anisotropic optical, vibrational, and transport behavior. However, the details of the electronic band structure of this fascinating material are still largely unexplored. We present a momentum-resolved study of the electronic structure of monolayer, bilayer, and bulk ReS2 using k-space photoemission microscopy in combination with first-principles calculations. We demonstrate that the valence electrons in bulk ReS2 are-contrary to assumptions in recent literature-significantly delocalized across the van der Waals gap. Furthermore, we directly observe the evolution of the valence band dispersion as a function of the number of layers, revealing the transition from an indirect band gap in bulk ReS2 to a direct gap in the bilayer and the monolayer. We also find a significantly increased effective hole mass in single-layer crystals. Our results establish bilayer ReS2 as an advantageous building block for two-dimensional devices and van der Waals heterostructures.