Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure.

Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi2Te4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets.

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6 Sn6 . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6 Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6.

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

Evidence of magnetism-induced topological protection in the axion insulator candidate EuSn2P2.

We unravel the interplay of topological properties and the layered (anti)ferromagnetic ordering in EuSn2P2, using spin and chemical selective electron and X-ray spectroscopies supported by first-principle calculations. We reveal the presence of in-plane long-range ferromagnetic order triggering topological invariants and resulting in the multiple protection of topological Dirac states. We provide clear evidence that layer-dependent spin-momentum locking coexists with ferromagnetism in this material, a cohabitation that promotes EuSn2P2 as a prime candidate axion insulator for topological antiferromagnetic spintronics applications.

Layer Hall effect in a 2D topological axion antiferromagnet.

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s1. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi2Te4-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi2Te4 shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e2/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

Fermion-boson many-body interplay in a frustrated kagome paramagnet.

Kagome-nets, appearing in electronic, photonic and cold-atom systems, host frustrated fermionic and bosonic excitations. However, it is rare to find a system to study their fermion-boson many-body interplay. Here we use state-of-the-art scanning tunneling microscopy/spectroscopy to discover unusual electronic coupling to flat-band phonons in a layered kagome paramagnet, CoSn. We image the kagome structure with unprecedented atomic resolution and observe the striking bosonic mode interacting with dispersive kagome electrons near the Fermi surface. At this mode energy, the fermionic quasi-particle dispersion exhibits a pronounced renormalization, signaling a giant coupling to bosons. Through the self-energy analysis, first-principles calculation, and a lattice vibration model, we present evidence that this mode arises from the geometrically frustrated phonon flat-band, which is the lattice bosonic analog of the kagome electron flat-band. Our findings provide the first example of kagome bosonic mode (flat-band phonon) in electronic excitations and its strong interaction with fermionic degrees of freedom in kagome-net materials.

Realization of an intrinsic ferromagnetic topological state in MnBi8Te13.

Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

Many-Body Resonance in a Correlated Topological Kagome Antiferromagnet.

We use scanning tunneling microscopy to elucidate the atomically resolved electronic structure in the strongly correlated kagome Weyl antiferromagnet Mn_{3}Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with increasing temperature, signaling strongly interacting physics. We show that this resonance can be understood as the result of geometrical frustration and strong correlation based on the kagome lattice Hubbard model. Our results point to the emergent many-body resonance behavior in a topological kagome magnet.

Quantum-limit Chern topological magnetism in TbMn6Sn6.

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, and may enable the observation of topological quantum phenomena in the RMn6Sn6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.

A New Magnetic Topological Quantum Material Candidate by Design.

Magnetism, when combined with an unconventional electronic band structure, can give rise to forefront electronic properties such as the quantum anomalous Hall effect, axion electrodynamics, and Majorana fermions. Here we report the characterization of high-quality crystals of EuSn2P2, a new quantum material specifically designed to engender unconventional electronic states plus magnetism. EuSn2P2 has a layered, Bi2Te3-type structure. Ferromagnetic interactions dominate the Curie-Weiss susceptibility, but a transition to antiferromagnetic ordering occurs near 30 K. Neutron diffraction reveals that this is due to two-dimensional ferromagnetic spin alignment within individual Eu layers and antiferromagnetic alignment between layers-this magnetic state surrounds the Sn-P layers at low temperatures. The bulk electrical resistivity is sensitive to the magnetism. Electronic structure calculations reveal that EuSn2P2 might be a strong topological insulator, which can be a new magnetic topological quantum material (MTQM) candidate. The calculations show that surface states should be present, and they are indeed observed by angle-resolved photoelectron spectroscopy (ARPES) measurements.