Experimental observation of current-driven antiskyrmion sliding in stripe domains.

Magnetic skyrmions are promising as next-generation information units. Their antiparticle-the antiskyrmion-has also been discovered in chiral magnets. Here we experimentally demonstrate antiskyrmion sliding in response to a pulsed electric current at room temperature without the requirement of an external magnetic field. This is realized by embedding antiskyrmions in helical stripe domains, which naturally provide one-dimensional straight tracks along which antiskyrmion sliding can be easily launched with low current density and without transverse deflection from the antiskyrmion Hall effect. The higher mobility of the antiskyrmions in the background of helical stripes in contrast to the typical ferromagnetic state is a result of intrinsic material parameters and elastic energy of the stripe domain, thereby smearing out the random pinning potential, as supported by micromagnetic simulations. The demonstration and comprehensive understanding of antiskyrmion movement along naturally straight tracks offers a new perspective for (anti)skyrmion application in spintronics.

Light-driven nanoscale vectorial currents.

Controlled charge flows are fundamental to many areas of science and technology, serving as carriers of energy and information, as probes of material properties and dynamics1 and as a means of revealing2,3 or even inducing4,5 broken symmetries. Emerging methods for light-based current control5-16 offer particularly promising routes beyond the speed and adaptability limitations of conventional voltage-driven systems. However, optical generation and manipulation of currents at nanometre spatial scales remains a basic challenge and a crucial step towards scalable optoelectronic systems for microelectronics and information science. Here we introduce vectorial optoelectronic metasurfaces in which ultrafast light pulses induce local directional charge flows around symmetry-broken plasmonic nanostructures, with tunable responses and arbitrary patterning down to subdiffractive nanometre scales. Local symmetries and vectorial currents are revealed by polarization-dependent and wavelength-sensitive electrical readout and terahertz (THz) emission, whereas spatially tailored global currents are demonstrated in the direct generation of elusive broadband THz vector beams17. We show that, in graphene, a detailed interplay between electrodynamic, thermodynamic and hydrodynamic degrees of freedom gives rise to rapidly evolving nanoscale driving forces and charge flows under the extremely spatially and temporally localized excitation. These results set the stage for versatile patterning and optical control over nanoscale currents in materials diagnostics, THz spectroscopies, nanomagnetism and ultrafast information processing.

Electron-Assisted Generation and Straight Movement of Skyrmion Bubble in Kagome TbMn6 Sn6.

Topological magnetic textures are promising candidates as binary data units for the next-generation memory device. The precise generation and convenient control of nontrivial spin topology at zero field near room temperature endows the critical advantages in skyrmionic devices but is not simultaneously integrated into one material. Here, in the Kagome plane of quantum TbMn6 Sn6 , the expedient generation of the skyrmion bubbles in versatile forms of lattice, chain, and isolated one by converging the electron beam, where the electron intensity gradient contributes to the dynamic generation from local anisotropy variation near spin reorientation transition (SRT) is reported. Encouragingly, by utilizing the dynamic shift of the SRT domain interface, the straight movement is actualized with the skyrmion bubble slave to the SRT domain interface forming an elastic composite object, avoiding the usual deflection from the skyrmion Hall effect. The critical contribution of the SRT domain interface via conveniently electron-assisted heating is further theoretically validated in micromagnetic simulation, highlighting the compatible application possibility in advanced devices.

Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain.

We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.

Discovery of Topological Magnetic Textures near Room Temperature in Quantum Magnet TbMn6 Sn6.

The study of topology in quantum materials has fundamentally advanced the understanding in condensed matter physics and potential applications in next-generation quantum information technology. Recently, the discovery of a topological Chern phase in the spin-orbit-coupled Kagome lattice TbMn6 Sn6 has attracted considerable interest. Whereas these phenomena highlight the contribution of momentum space Berry curvature and Chern gap on the electronic transport properties, less is known about the intrinsic real space magnetic texture, which is crucial for understanding the electronic properties and further exploring the unique quantum behavior. Here, the stabilization of topological magnetic skyrmions in TbMn6 Sn6 using Lorentz transmission electron microscopy near room temperature, where the spins experience full spin reorientation transition between the a- and c-axes, is directly observed. An effective spin Hamiltonian based on the Ginzburg-Landau theory is constructed and micromagnetic simulation is performed to clarify the critical role of Ruderman-Kittel-Kasuya-Yosida interaction on the stabilization of skyrmion lattice. These results not only uncover nontrivial spin topological texture in TbMn6 Sn6 , but also provide a solid basis to study its interplay with electronic topology.

Current-Induced Magnetic Skyrmions with Controllable Polarities in the Helical Phase.

We report the current-induced creation of magnetic skyrmions in a chiral magnet FeGe nanostructure by using in situ Lorentz transmission electron microscopy. We show that magnetic skyrmions with controllable polarity can be transferred from the helical ground state simply by controlling the direction of the current flow at zero magnetic fields. The force analysis and symmetry consideration, backed up by micromagnetic simulations, well explain the experimental results, where magnetic skyrmions are created because of the edge instability of the helical state in the presence of spin-transfer torque. The on-demand generation of skyrmions and control of their polarity by electric current without the need for a magnetic field will enable novel purely electric-controlled skyrmion devices.

Field-free topological behavior in the magnetic domain wall of ferrimagnetic GdFeCo.

Exploring and controlling topological textures such as merons and skyrmions has attracted enormous interests from the perspective of fundamental research and spintronic applications. It has been predicted theoretically and proved experimentally that the lattice form of topological meron-skyrmion transformation can be realized with the requirement of external magnetic fields in chiral ferromagnets. However, such topological transition behavior has yet to be verified in other materials. Here, we report real-space observation of magnetic topology transformation between meron pairs and skyrmions in the localized domain wall of ferrimagnetic GdFeCo films without the need of magnetic fields. The topological transformation in the domain wall of ferrimagnet is introduced by temperature-induced spin reorientation transition (SRT) and the underlying mechanism is revealed by micromagnetic simulations. The convenient electric-controlling topology transformation and driving motion along the confined domain wall is further anticipated, which will enable advanced application in magnetic devices.

Current-Induced Reversal of Anomalous Hall Conductance in Twisted Bilayer Graphene.

It is observed experimentally that the sign of the Hall resistance can be flipped by a dc electric current in the twisted bilayer graphene (TBG) at 3/4 filling of the fourfold degenerate conduction flat bands. The experiment implies a switching of the valley polarization (VP) and topology in TBG. Here we present a theory on the current-induced switching of VP and topology. The presence of current in the bulk causes the redistribution of electron occupation in bands near the Fermi energy, which then deforms and shifts the band dispersion due to the Coulomb interaction. Above a critical current, the original occupied and empty bands can be swapped, resulting in the switching of VP and topology.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field.

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Skyrmion Crystal from RKKY Interaction Mediated by 2D Electron Gas.

We consider a C_{6} invariant lattice of magnetic moments coupled via a Kondo exchange J with a 2D electron gas (2DEG). The effective Ruderman-Kittel-Kasuya-Yosida interaction between the moments stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. An attractive aspect of this mechanism is that the magnitude of the magnetic ordering wave vectors, Q_{ν} (ν=1, 2, 3), is dictated by the Fermi wave number k_{F}: |Q_{ν}|=2k_{F}. Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes of the order of the quantized value, e^{2}/h, when J is comparable to the Fermi energy ε_{F}.

Face Centered Cubic and Hexagonal Close Packed Skyrmion Crystals in Centrosymmetric Magnets.

Skyrmions are disklike objects that typically form triangular crystals in two-dimensional systems. This situation is analogous to the so-called pancake vortices of quasi-two-dimensional superconductors. The way in which Skyrmion disks or "pancake Skyrmions" pile up in layered centrosymmetric materials is dictated by the interlayer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed Skyrmion crystals for different choices of the interlayer exchange, in addition to the conventional triangular crystal of Skyrmion lines. Moreover, an inhomogeneous current induces a sliding motion of pancake Skyrmions, indicating that they behave as effective mesoscale particles.

Resonances in the Field-Angle-Resolved Thermal Conductivity of CeCoIn_{5}.

The thermal conductivity measurement in a rotating magnetic field is a powerful probe of the structure of the superconducting energy gap. We present high-precision measurements of the low-temperature thermal conductivity in the unconventional heavy-fermion superconductor CeCoIn_{5}, with the heat current J along the nodal [110] direction of its d_{x^{2}-y^{2}} order parameter and the magnetic field up to 7 T rotating in the ab plane. In contrast to the smooth oscillations found previously for J∥[100], we observe a sharp resonancelike peak in the thermal conductivity when the magnetic field is also in the [110] direction, parallel to the heat current. We explain this peak qualitatively via a model of the heat transport in a d-wave superconductor. In addition, we observe two smaller but also very sharp peaks in the thermal conductivity for the field directions at angles Θ≈±33° with respect to J. The origin of the observed resonances at Θ≈±33° at present defies theoretical explanation. The challenge of uncovering their source will dictate exploring theoretically more complex models, which might include, e.g., fine details of the Fermi surface, Andreev bound vortex core states, a secondary superconducting order parameter, and the existence of gaps in spin and charge excitations.

Electrical Conductivity through a Single Atomic Step Measured with the Proximity-Induced Superconducting Pair Correlation.

Local disordered nanostructures in an atomically thick metallic layer on a semiconducting substrate play significant and decisive roles in transport properties of two-dimensional (2D) conductive systems. We measured the electrical conductivity through a step of monoatomic height in a truly microscopic manner by using as a signal the superconducting pair correlation induced by the proximity effect. The transport property across a step of a one-monolayer Pb surface metallic phase, formed on a Si(111) substrate, was evaluated by inducing the pair correlation around the local defect and measuring its response, i.e., the reduced density of states at the Fermi energy using scanning tunneling microscopy. We found that the step resistance has a significant contribution to the total resistance on a nominally flat surface. Our study also revealed that steps in the 2D metallic layer terminate the propagation of the pair correlation. Superconductivity is enhanced between the first surface step and the superconductor-normal-metal interface by reflectionless tunneling when the step is located within a coherence length.

Frustration and chiral orderings in correlated electron systems.

The term frustration refers to lattice systems whose ground state cannot simultaneously satisfy all the interactions. Frustration is an important property of correlated electron systems, which stems from the sign of loop products (similar to Wilson products) of interactions on a lattice. It was early recognized that geometric frustration can produce rather exotic physical behaviors, such as macroscopic ground state degeneracy and helimagnetism. The interest in frustrated systems was renewed two decades later in the context of spin glasses and the emergence of magnetic superstructures. In particular, Phil Anderson's proposal of a quantum spin liquid ground state for a two-dimensional lattice S = 1/2 Heisenberg magnet generated a very active line of research that still continues. As a result of these early discoveries and conjectures, the study of frustrated models and materials exploded over the last two decades. Besides the large efforts triggered by the search of quantum spin liquids, it was also recognized that frustration plays a crucial role in a vast spectrum of physical phenomena arising from correlated electron materials. Here we review some of these phenomena with particular emphasis on the stabilization of chiral liquids and non-coplanar magnetic orderings. In particular, we focus on the ubiquitous interplay between magnetic and charge degrees of freedom in frustrated correlated electron systems and on the role of anisotropy. We demonstrate that these basic ingredients lead to exotic phenomena, such as, charge effects in Mott insulators, the stabilization of single magnetic vortices, as well as vortex and skyrmion crystals, and the emergence of different types of chiral liquids. In particular, these orderings appear more naturally in itinerant magnets with the potential of inducing a very large anomalous Hall effect.

Magnetic Vortex Induced by Nonmagnetic Impurity in Frustrated Magnets.

We study the effect of a nonmagnetic impurity inserted in a two-dimensional frustrated ferromagnet above its saturation magnetic field H_{sat} for arbitrary spin S. We demonstrate that the ground state includes a magnetic vortex that is nucleated around the impurity over a finite range of magnetic field H_{sat}≤H≤H_{sat}^{I}. Upon approaching the quantum critical point at H=H_{sat}, the radius of the magnetic vortex diverges as the magnetic correlation length: ξ∝1/sqrt[H-H_{sat}]. These results are derived both for the lattice and in the continuum limit.

Ground state, collective mode, phase soliton and vortex in multiband superconductors.

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

ac current generation in chiral magnetic insulators and Skyrmion motion induced by the spin Seebeck effect.

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications.

Stiffness from disorder in triangular-lattice Ising thin films.

We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime down to T=0. Numerical results are complemented with the derivation of an effective low-temperature dimer theory. Contrary to order by disorder, we present a new scenario for fluctuation-induced ordering in frustrated spin systems. While short-range spin-spin correlations are enhanced by fluctuations, quasi-long-range ordering is precluded at low enough temperatures by proliferation of topological defects.

I-V characteristics of short superconducting nanowires with different bias and shunt: a dynamic approach.

We derived the I-V characteristics of short nanowire in a circuit with and without resistive and inductive shunt. For this we used numerical calculations in the framework of time-dependent Ginzburg-Landau equations with different relaxation times for the amplitude and phase dynamics. We also derived the dependence of the I-V characteristics on flux in a superconducting quantum interference device made of two such weak links.

Orbital magnetism induced by heat currents in Mott insulators.

We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality χ(jkl)=S(l)·(S(j)×S(k)). This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. The relative orientation of the orbital moments depends on the particular lattice of magnetic ions. This subtle effect arises from the symmetries that the heat and electric currents have in common.