A correlated ferromagnetic polar metal by design.

Polar metals have recently garnered increasing interest because of their promising functionalities. Here we report the experimental realization of an intrinsic coexisting ferromagnetism, polar distortion and metallicity in quasi-two-dimensional Ca3Co3O8. This material crystallizes with alternating stacking of oxygen tetrahedral CoO4 monolayers and octahedral CoO6 bilayers. The ferromagnetic metallic state is confined within the quasi-two-dimensional CoO6 layers, and the broken inversion symmetry arises simultaneously from the Co displacements. The breaking of both spatial-inversion and time-reversal symmetries, along with their strong coupling, gives rise to an intrinsic magnetochiral anisotropy with exotic magnetic field-free non-reciprocal electrical resistivity. An extraordinarily robust topological Hall effect persists over a broad temperature-magnetic field phase space, arising from dipole-induced Rashba spin-orbit coupling. Our work not only provides a rich platform to explore the coupling between polarity and magnetism in a metallic system, with extensive potential applications, but also defines a novel design strategy to access exotic correlated electronic states.

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films.

The anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator. However, the origin of its intriguing AHE behaviors remains elusive. Here, we demonstrate the Berry curvature-dominated intrinsic AHE in wafer-scale MnBi2Te4 films. By applying back-gate voltages, we observe an ambipolar conduction and n-p transition in ∼7-layer MnBi2Te4, where a quadratic relation between the AHE resistance and longitudinal resistance suggests its intrinsic AHE nature. In particular, for ∼3-layer MnBi2Te4, the AHE sign can be tuned from pristine negative to positive. First-principles calculations unveil that such an AHE reversal originated from the competing Berry curvature between oppositely polarized spin-minority-dominated surface states and spin-majority-dominated inner bands. Our results shed light on the underlying physical mechanism of the intrinsic AHE and provide new perspectives for the unconventional sign-tunable AHE.

Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles.

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

Chiral-Bubble-Induced Topological Hall Effect in Ferromagnetic Topological Insulator Heterostructures.

We report compelling evidence of an emergent topological Hall effect (THE) from chiral bubbles in a two-dimensional uniaxial ferromagnet, V-doped Sb2Te3 heterostructure. The sign of THE signal is determined by the net curvature of domain walls in different domain configurations, and the strength of THE signal is correlated with the density of nucleation or pinned bubble domains. The experimental results are in good agreement with the integrated linear transport and Monte Carlo simulations, corroborating the emergent gauge field at chiral magnetic bubbles. Our findings not only reveal a general mechanism of THE in two-dimensional ferromagnets but also pave the way for the creation and manipulation of topological spin textures for spintronic applications.

Possible Topological Hall Effect above Room Temperature in Layered Cr1.2Te2 Ferromagnet.

Topological Hall effect (THE) has been used as a powerful tool to unlock spin chirality in novel magnetic materials. Recent focus has been widely paid to THE and possible chiral spin textures in two-dimensional (2D) layered magnetic materials. However, the room-temperature THE has been barely reported in 2D materials, which hinders its practical applications in 2D spintronics. In this paper, we report a possible THE signal featuring antisymmetric peaks in a wide temperature window up to 320 K in Cr1.2Te2, a new quasi-2D ferromagnetic material. The temperature, thickness, and magnetic field dependences of the THE lead to potential spin chirality origin that is associated with the spin canting under external magnetic fields. Our work holds promise for practical applications in future chiral spin-based vdW spintronic devices.

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures.

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

Quantum-Well Bound States in Graphene Heterostructure Interfaces.

We present experimental evidence of electronic and optical interlayer resonances in graphene van der Waals heterostructure interfaces. Using the spectroscopic mode of a low-energy electron microscope (LEEM), we characterized these interlayer resonant states up to 10 eV above the vacuum level. Compared with nontwisted, AB-stacked bilayer graphene (AB BLG), an ≈0.2 Å increase was found in the interlayer spacing of 30° twisted bilayer graphene (30°-tBLG). In addition, we used Raman spectroscopy to probe the inelastic light-matter interactions. A unique type of Fano resonance was found around the D and G modes of the graphene lattice vibrations. This anomalous, robust Fano resonance is a direct result of quantum confinement and the interplay between discrete phonon states and the excitonic continuum.

Erratum: Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque [Phys. Rev. Lett. 124, 127204 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.124.127204.

Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque.

Magnetic hopfion is a three-dimensional (3D) topological soliton with novel spin structure that would enable exotic dynamics. Here, we study the current-driven 3D dynamics of a magnetic hopfion with a unit Hopf index in a frustrated magnet. Attributed to the spin Berry phase and symmetry of the hopfion, the phase space entangles multiple collective coordinates, thus the hopfion exhibits rich dynamics including longitudinal motion along the current direction, transverse motion perpendicular to the current direction, rotational motion, and dilation. Furthermore, the characteristics of hopfion dynamics is determined by the ratio between the nonadiabatic spin transfer torque parameter and the damping parameter. Such peculiar 3D dynamics of magnetic hopfion could shed light on understanding the universal physics of hopfions in different systems and boost the prosperous development of 3D spintronics.

Planar Hall Effect in Antiferromagnetic MnTe Thin Films.

We show that the spin-orbit coupling (SOC) in α-MnTe impacts the transport behavior by generating an anisotropic valence-band splitting, resulting in four spin-polarized pockets near Γ. A minimal k·p model is constructed to capture this splitting by group theory analysis, a tight-binding model, and ab initio calculations. The model is shown to describe the rotation symmetry of the zero-field planer Hall effect (PHE). The PHE originates from the band anisotropy given by SOC, and is quantitatively estimated to be 25%-31% for an ideal thin film with a single antiferromagnetic domain.

Direct imaging of magnetic field-driven transitions of skyrmion cluster states in FeGe nanodisks.

Magnetic skyrmion is a nanosized magnetic whirl with nontrivial topology, which is highly relevant for applications on future memory devices. To enable the applications, theoretical efforts have been made to understand the dynamics of individual skyrmions in magnetic nanostructures. However, directly imaging the evolution of highly geometrically confined individual skyrmions is challenging. Here, we report the magnetic field-driven dynamics of individual skyrmions in FeGe nanodisks with diameters on the order of several skyrmion sizes by using Lorentz transmission electron microscopy. In contrast to the conventional skyrmion lattice in bulk, a series of skyrmion cluster states with different geometrical configurations and the field-driven cascading phase transitions are identified at temperatures far below the magnetic transition temperature. Furthermore, a dynamics, namely the intermittent jumps between the neighboring skyrmion cluster states, is found at elevated temperatures, at which the thermal energy competes with the energy barrier between the skyrmion cluster states.

Direct Imaging of a Zero-Field Target Skyrmion and Its Polarity Switch in a Chiral Magnetic Nanodisk.

A target Skyrmion is a flux-closed spin texture that has twofold degeneracy and is promising as a binary state in next generation universal memories. Although its formation in nanopatterned chiral magnets has been predicted, its observation has remained challenging. Here, we use off-axis electron holography to record images of target Skyrmions in a 160-nm-diameter nanodisk of the chiral magnet FeGe. We compare experimental measurements with numerical simulations, demonstrate switching between two stable degenerate target Skyrmion ground states that have opposite polarities and rotation senses, and discuss the observed switching mechanism.

Foreword to special issue.

This is an Editorial for the Special Issue on Solitons in Quantum Physics.

Dynamics of an insulating Skyrmion under a temperature gradient.

We study the Skyrmion dynamics in thin films under a temperature gradient. Our numerical simulations show that both single and multiple Skyrmions in a crystal move towards the high temperature region, which is contrary to particle diffusion. Noticing a similar effect in the domain wall motion, we employ a theory based on magnon dynamics to explain this counterintuitive phenomenon. Unlike the temperature driven domain wall motion, the Skyrmion's topological charge plays an important role, and a transverse Skyrmion motion is observed. Our theory turns out to be in agreement with numerical simulations, both qualitatively and quantitatively. Our calculation indicates that a very promising Skyrmion dynamic phenomenon can be observed in experiments.

Controlling Dzyaloshinskii-Moriya interaction in a centrosymmetric nonsymmorphic crystal.

Presence of the Dzyaloshinskii-Moriya (DM) interaction in limited noncentrosymmetric materials leads to novel spin textures and exotic chiral physics. The emergence of DM interaction in centrosymmetric crystals could greatly enrich material realization. Here we show that an itinerant centrosymmetric crystal respecting a nonsymmorphic space group is a new platform for the DM interaction. Taking the P4/nmm space group as an example, we demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction induces the DM interactions, in addition to the Heisenberg exchange and the Kaplan-Shekhtman-Entin-wohlman-Aharony (KSEA) interaction. The direction of DM vector depends on the positions of magnetic atoms in the real space, and the amplitude depends on the location of the Fermi surface in the reciprocal space. The diversity stems from the position-dependent site groups and the momentum-dependent electronic structures guaranteed by the nonsymmorphic symmetries. Our study unveils the role of the nonsymmorphic symmetries in affecting magnetism, and suggests that the nonsymmorphic crystals can be promising platforms to design magnetic interactions.

Widely Tunable Berry Curvature in the Magnetic Semimetal Cr1+ δ Te2.

Magnetic semimetals have increasingly emerged as lucrative platforms hosting spin-based topological phenomena in real and momentum spaces. Cr1+ δ Te2 is a self-intercalated magnetic transition metal dichalcogenide (TMD), which exhibits topological magnetism and tunable electron filling. While recent studies have explored real-space Berry curvature effects, similar considerations of momentum-space Berry curvature are lacking. Here, the electronic structure and transport properties of epitaxial Cr1+ δ Te2 thin films are systematically investigated over a range of doping, δ (0.33 - 0.71). Spectroscopic experiments reveal the presence of a characteristic semi-metallic band region, which shows a rigid like energy shift with δ. Transport experiments show that the intrinsic component of the anomalous Hall effect (AHE) is sizable and undergoes a sign flip across δ. Finally, density functional theory calculations establish a link between the doping evolution of the band structure and AHE: the AHE sign flip is shown to emerge from the sign change of the Berry curvature, as the semi-metallic band region crosses the Fermi energy. These findings underscore the increasing relevance of momentum-space Berry curvature in magnetic TMDs and provide a unique platform for intertwining topological physics in real and momentum spaces.

Electrical manipulation of skyrmions in a chiral magnet.

Writing, erasing and computing are three fundamental operations required by any working electronic device. Magnetic skyrmions could be essential bits in promising in emerging topological spintronic devices. In particular, skyrmions in chiral magnets have outstanding properties like compact texture, uniform size, and high mobility. However, creating, deleting, and driving isolated skyrmions, as prototypes of aforementioned basic operations, have been a grand challenge in chiral magnets ever since the discovery of skyrmions, and achieving all these three operations in a single device is even more challenging. Here, by engineering chiral magnet Co8Zn10Mn2 into the customized micro-devices for in-situ Lorentz transmission electron microscopy observations, we implement these three operations of skyrmions using nanosecond current pulses with a low current density of about 1010 A·m-2 at room temperature. A notched structure can create or delete magnetic skyrmions depending on the direction and magnitude of current pulses. We further show that the magnetic skyrmions can be deterministically shifted step-by-step by current pulses, allowing the establishment of the universal current-velocity relationship. These experimental results have immediate significance towards the skyrmion-based memory or logic devices.

Dynamics of Skyrmion crystals in metallic thin films.

We study the collective dynamics of the Skyrmion crystal in thin films of ferromagnetic metals resulting from the nontrivial Skyrmion topology. It is shown that the current-driven motion of the crystal reduces the topological Hall effect and the Skyrmion trajectories bend away from the direction of the electric current (the Skyrmion Hall effect). We find a new dissipation mechanism in noncollinear spin textures that can lead to a much faster spin relaxation than Gilbert damping, calculate the dispersion of phonons in the Skyrmion crystal, and discuss the effects of impurity pinning of Skyrmions.

Magnetic skyrmion bundles and their current-driven dynamics.

Topological charge Q classifies non-trivial spin textures and determines many of their characteristics. Most abundant are topological textures with |Q| ≤ 1, such as (anti)skyrmions, (anti)merons or (anti)vortices. In this study we created and imaged in real space magnetic skyrmion bundles, that is, multi-Q three-dimensional skyrmionic textures. These textures consist of a circular spin spiral that ties together a discrete number of skyrmion tubes. We observed skyrmion bundles with integer Q values up to 55. We show here that electric currents drive the collective motion of these particle-like textures similar to skyrmions. Bundles with Q ≠ 0 exhibit a skyrmion Hall effect with a Hall angle of ~62°, whereas Q = 0 bundles, the so-called skyrmioniums, propagate collinearly with respect to the current flow, that is, with a skyrmion Hall angle of ~0°. The experimental observation of multi-Q spin textures adds another member to the family of magnetic topological textures, which may serve in future spintronic devices.

Kondo physics in antiferromagnetic Weyl semimetal Mn3+x Sn1-x films.

Topology and strong electron correlations are crucial ingredients in emerging quantum materials, yet their intersection in experimental systems has been relatively limited to date. Strongly correlated Weyl semimetals, particularly when magnetism is incorporated, offer a unique and fertile platform to explore emergent phenomena in novel topological matter and topological spintronics. The antiferromagnetic Weyl semimetal Mn3Sn exhibits many exotic physical properties such as a large spontaneous Hall effect and has recently attracted intense interest. In this work, we report synthesis of epitaxial Mn3+x Sn1-x films with greatly extended compositional range in comparison with that of bulk samples. As Sn atoms are replaced by magnetic Mn atoms, the Kondo effect, which is a celebrated example of strong correlations, emerges, develops coherence, and induces a hybridization energy gap. The magnetic doping and gap opening lead to rich extraordinary properties, as exemplified by the prominent DC Hall effects and resonance-enhanced terahertz Faraday rotation.