Competing magnetic phases and fluctuation-driven scalar spin chirality in the kagome metal YMn6Sn6

Nanoscale Visualization of Symmetry-Breaking Electronic Orders and Magnetic Anisotropy in a Kagome Magnet YMn6Sn6

A kagome lattice hosts a plethora of quantum states arising from the interplay between nontrivial topology and electron correlations. The recently discovered kagome magnet RMn6Sn6 (R represents a rare-earth element) is believed to showcase a kagome band closely resembling textbook characteristics. Here, we report the characterization of local electronic states and their magnetization response in YMn6Sn6 via scanning tunneling microscopy measurements under vector magnetic fields. Our spectroscopic maps reveal a spontaneously trimerized kagome electronic order in YMn6Sn6, where the 6-fold rotational symmetry is disrupted while translational symmetry is maintained. Further application of an external magnetic field demonstrates a strong coupling of the YMn6Sn6 kagome band to the field, which exhibits an energy shift discrepancy under different field directions, implying the existence of magnetization-response anisotropy and anomalous g factors. Our findings establish YMn6Sn6 as an ideal platform for investigating kagome-derived orbital magnetic moment and correlated magnetic topological states.

Enhancement of the anomalous Hall effect by distorting the Kagome lattice in an antiferromagnetic material

In topological magnetic materials, the topology of the electronic wave function is strongly coupled to the structure of the magnetic order. In general, ferromagnetic Weyl semimetals generate a strong anomalous Hall conductivity (AHC) due to a large Berry curvature that scales with their magnetization. In contrast, a comparatively small AHC is observed in noncollinear antiferromagnets. We investigated HoAgGe, an antiferromagnetic (AFM) Kagome spin-ice compound, which crystallizes in a hexagonal ZrNiAl-type structure in which Ho atoms are arranged in a distorted Kagome lattice, forming an intermetallic Kagome spin-ice state in the ab-plane. It exhibits a large topological Hall resistivity of ~1.6 µΩ-cm at 2.0 K in a field of ~3 T owing to the noncoplanar structure. Interestingly, a total AHC of 2,800 Ω-1 cm-1 is observed at ~45 K, i.e., 4 TN, which is quite unusual and goes beyond the normal expectation considering HoAgGe as an AFM Kagome spin-ice compound with a TN of ~11 K. We demonstrate further that the AHC below TN results from the nonvanishing Berry curvature generated by the formation of Weyl points under the influence of the external magnetic field, while the skew scattering led by Kagome spins dominates above the TN. These results offer a unique opportunity to study frustration in AFM Kagome lattice compounds.

Competing itinerant and local spin interactions in kagome metal FeGe

The combination of a geometrically frustrated lattice, and similar energy scales between degrees of freedom endows two-dimensional Kagome metals with a rich array of quantum phases and renders them ideal for studying strong electron correlations and band topology. The Kagome metal, FeGe is a noted example of this, exhibiting A-type collinear antiferromagnetic (AFM) order at TN ≈ 400 K, then establishes a charge density wave (CDW) phase coupled with AFM ordered moment below TCDW ≈ 110 K, and finally forms a c-axis double cone AFM structure around TCanting ≈ 60 K. Here we use neutron scattering to demonstrate the presence of gapless incommensurate spin excitations associated with the double cone AFM structure of FeGe at temperatures well above TCanting and TCDW that merge into gapped commensurate spin waves from the A-type AFM order. Commensurate spin waves follow the Bose factor and fit the Heisenberg Hamiltonian, while the incommensurate spin excitations, emerging below TN where AFM order is commensurate, start to deviate from the Bose factor around TCDW, and peaks at TCanting. This is consistent with a critical scattering of a second order magnetic phase transition with decreasing temperature. By comparing these results with density functional theory calculations, we conclude that the incommensurate magnetic structure arises from the nested Fermi surfaces of itinerant electrons and the formation of a spin density wave order.

Chiral and flat-band magnetic quasiparticles in ferromagnetic and metallic kagome layers

Magnetic kagome metals are a promising platform to develop unique quantum transport and optical phenomena caused by the interplay between topological electronic bands, strong correlations, and magnetic order. This interplay may result in exotic quasiparticles that describe the coupled electronic and spin excitations on the frustrated kagome lattice. Here, we observe novel elementary magnetic excitations within the ferromagnetic Mn kagome layers in TbMn6Sn6 using inelastic neutron scattering. We observe sharp, collective acoustic magnons and identify flat-band magnons that are localized to a hexagonal plaquette due to the special geometry of the kagome layer. Surprisingly, we observe another type of elementary magnetic excitation; a chiral magnetic quasiparticle that is also localized on a hexagonal plaquette. The short lifetime of localized flat-band and chiral quasiparticles suggest that they are hybrid excitations that decay into electronic states.

Abundant Lattice Instability in Kagome Metal ScV_{6}Sn_{6}

Kagome materials are emerging platforms for studying charge and spin orders. In this Letter, we have revealed a rich lattice instability in a Z_{2} kagome metal ScV_{6}Sn_{6} by first-principles calculations. Beyond verifying the sqrt[3]×sqrt[3]×3 charge density wave (CDW) order observed by the recent experiment, we further identified three more possible CDW structures, i.e., sqrt[3]×sqrt[3]×2 CDW with P6/mmm symmetry, 2×2×2 CDW with Immm symmetry, and 2×2×2 CDW with P6/mmm symmetry. The former two are more energetically favored than the sqrt[3]×sqrt[3]×3 phase, while the third one is comparable in energy. These CDW distortions involve mainly out-of-plane motions of Sc and Sn atoms, while V atoms constituting the kagome net are almost unchanged. We attribute the lattice instability to the smallness of Sc atomic radius. In contrast, such instability disappears in its sister compounds RV_{6}Sn_{6} (R is Y, or a rare-earth element), which exhibit quite similar electronic band structures to the Sc compound, because R has a larger atomic radius. Our work indicates that ScV_{6}Sn_{6} might exhibit varied CDW phases in different experimental conditions and provides insights to explore rich charge orders in kagome materials.

Orbital character of the spin-reorientation transition in TbMn6Sn6

Ferromagnetic (FM) order in a two-dimensional kagome layer is predicted to generate a topological Chern insulator without an applied magnetic field. The Chern gap is largest when spin moments point perpendicular to the kagome layer, enabling the capability to switch topological transport properties, such as the quantum anomalous Hall effect, by controlling the spin orientation. In TbMn6Sn6, the uniaxial magnetic anisotropy of the Tb3+ ion is effective at generating the Chern state within the FM Mn kagome layers while a spin-reorientation (SR) transition to easy-plane order above TSR = 310 K provides a mechanism for switching. Here, we use inelastic neutron scattering to provide key insights into the fundamental nature of the SR transition. The observation of two Tb excitations, which are split by the magnetic anisotropy energy, indicates an effective two-state orbital character for the Tb ion, with a uniaxial ground state and an isotropic excited state. The simultaneous observation of both modes below TSR confirms that orbital fluctuations are slow on magnetic and electronic time scales < ps and act as a spatially-random orbital alloy. A thermally-driven critical concentration of isotropic Tb ions triggers the SR transition.

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.

Topological kagome magnets and superconductors

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter.

Charge Density Wave in Kagome Lattice Intermetallic ScV_{6}Sn_{6}

Materials hosting kagome lattices have drawn interest for the diverse magnetic and electronic states generated by geometric frustration. In the AV_{3}Sb_{5} compounds (A=K, Rb, Cs), stacked vanadium kagome layers give rise to unusual charge density waves (CDW) and superconductivity. Here we report single-crystal growth and characterization of ScV_{6}Sn_{6}, a hexagonal HfFe_{6}Ge_{6}-type compound that shares this structural motif. We identify a first-order phase transition at 92 K. Single crystal x-ray and neutron diffraction reveal a charge density wave modulation of the atomic lattice below this temperature. This is a distinctly different structural mode than that observed in the AV_{3}Sb_{5} compounds, but both modes have been anticipated in kagome metals. The diverse HfFe_{6}Ge_{6} family offers more opportunities to tune ScV_{6}Sn_{6} and explore density wave order in kagome lattice materials.

The theory of transport in helical spin-structure crystals

We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For low exchange integrals, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. The latter can be interpreted as a planar Hall effect. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potentialµ. We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. We find the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in aMnPsingle crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.

Large Room Temperature Anomalous Transverse Thermoelectric Effect in Kagome Antiferromagnet YMn6 Sn6

Kagome magnets possess several novel nontrivial topological features owing to the strong correlation between topology and magnetism that extends to their applications in the field of thermoelectricity. Conventional thermoelectric (TE) devices use the Seebeck effect to convert heat into electrical energy. In contrast, transverse thermoelectric devices based on the Nernst effect are attracting recent attention due to their unique transverse geometry, which uses a single material to eliminate the need for a multitude of electrical connections compared to conventional TE devices. Here, a large anomalous transverse thermoelectric effect of ≈2 µV K^-1 at room temperature in a kagome antiferromagnet YMn₆ Sn₆ single crystal is obtained. The obtained value is larger than that of state-of-the-art canted antiferromagnetic (AFM) materials and comparable with ferromagnetic systems. The large anomalous Nernst effect (ANE) can be attributed to the net Berry curvature near the Fermi level. Furthermore, the ANE of the AFM YMn₆ Sn₆ exceeds the magnetization scaling relationship of conventional ferromagnets. The results clearly illustrate that AFM material YMn₆ Sn₆ is an ideal topological material for room-temperature transverse thermoelectric applications.

Tunable topological Dirac surface states and van Hove singularities in kagome metal GdV6Sn6

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a ℤ₂ bulk topology and identify multiple VHSs near the Fermi level (E_F) in magnetic kagome material GdV₆Sn₆. Using in situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below E_F, which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV₆Sn₆ as a fascinating platform for studying the nontrivial topology, magnetism, and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

Discovery of charge density wave in a kagome lattice antiferromagnet

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies^1,2. A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity^1,2. Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons^3,4, non-trivial topology^5-7, chiral magnetic order^8,9, superconductivity and CDW order^10-15. Although CDW has been found in weakly electron-correlated non-magnetic AV₃Sb₅ (A = K, Rb, Cs)^10-15, it has not yet been observed in correlated magnetic-ordered kagome lattice metals^4,16-21. Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs. ^16-19). The CDW in FeGe occurs at wavevectors identical to that of AV₃Sb₅ (refs. ^10-15), enhances the AFM ordered moment and induces an emergent anomalous Hall effect^22,23. Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase^24-28, in stark contrast to strongly correlated copper oxides^1,2 and nickelates^29-31, in which the CDW precedes or accompanies the magnetic order.

Simple Chemical Rules for Predicting Band Structures of Kagome Materials

Compounds featuring a kagome lattice are studied for a wide range of properties, from localized magnetism to massless and massive Dirac Fermions. These properties come from the symmetry of the kagome lattice, which gives rise to Dirac cones and flat bands. However, not all compounds with a kagome sublattice show properties related to it. We derive chemical rules predicting if the low-energy physics of a material is determined by the kagome sublattice and bands arising from it. After sorting out all known crystals with the kagome lattice into four groups, we use chemical heuristics and local symmetry to explain additional conditions that need to be met to have kagome bands near the Fermi level.

Evolution of the Chern Gap in Kagome Magnet HoMn6Sn6−xGex

The Chern gap is a unique topological feature that can host non-abelian particles. The Kagome lattice hosts Chern fermions. Upon the inclusion of magnetism, the Kagome system hosts a Chern gap at the K points in the lattice. In this work, the effect of Ge doping on HoMn6Sn6 is investigated. It is seen that with increased doping, a multi-stack Chern gap in formed in HoMn6Sn6−xGex. In addition, the Chern gaps are much more pronounced and disperse more in energy in HoMn6Ge6 then in HoMn6Sn6.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Realizing Kagome Band Structure in Two-Dimensional Kagome Surface States of RV_{6}Sn_{6} (R=Gd, Ho)

We report angle resolved photoemission experiments on a newly discovered family of kagome metals RV_{6}Sn_{6} (R=Gd, Ho). Intrinsic bulk states and surface states of the vanadium kagome layer are differentiated from those of other atomic sublattices by the real-space resolution of the measurements with a small beam spot. Characteristic Dirac cone, saddle point, and flat bands of the kagome lattice are observed. Our results establish the two-dimensional (2D) kagome surface states as a new platform to investigate the intrinsic kagome physics.

Giant magnetoresistance and topological Hall effect in the EuGa4antiferromagnet

We report on systematic temperature- and magnetic field-dependent studies of the EuGa₄binary compound, which crystallizes in a centrosymmetric tetragonal BaAl₄-type structure with space groupI4/mmm. The electronic properties of EuGa₄single crystals, with an antiferromagnetic (AFM) transition atT_N∼ 16.4 K, were characterized via electrical resistivity and magnetization measurements. A giant nonsaturating magnetoresistance was observed at low temperatures, reaching∼7×104% at 2 K in a magnetic field of 9 T. In the AFM state, EuGa₄undergoes a series of metamagnetic transitions in an applied magnetic field, clearly manifested in its field-dependent electrical resistivity. BelowT_N, in the ∼4-7 T field range, we observe also a clear hump-like anomaly in the Hall resistivity which is part of the anomalous Hall resistivity. We attribute such a hump-like feature to the topological Hall effect, usually occurring in noncentrosymmetric materials known to host topological spin textures (as e.g., magnetic skyrmions). Therefore, the family of materials with a tetragonal BaAl₄-type structure, to which EuGa₄and EuAl₄belong, seems to comprise suitable candidates on which one can study the interplay among correlated-electron phenomena (such as charge-density wave or exotic magnetism) with topological spin textures and topologically nontrivial bands.

Metal Organic Spin Transistor

Organic molecules and specifically bio-organic systems are attractive for applications due to their low cost, variability, environmental friendliness, and facile manufacturing in a bottom-up fashion. However, due to their relatively low conductivity, their actual application is very limited. Chiral metallo-bio-organic crystals, on the other hand, have improved conduction and in addition interesting magnetic properties. We developed a spin transistor using these crystals and based on the chiral-induced spin selectivity effect. This device features a memristor type behavior, which depend on trapping both charges and spins. The spin properties are monitored by Hall signal and by an external magnetic field. The spin transistor exhibits nonlinear drain-source currents, with multilevel controlled states generated by the magnetization of the source. Varying the source magnetization enables a six-level readout for the two-terminal device. The simplicity of the device paves the way for its technological application in organic electronics and bioelectronics.

Emergent electromagnetic induction beyond room temperature

Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet the research is still in its infancy and many issues must be resolved toward its application. One such problem is how to increase working temperature to room temperature, and possible thermal agitation effects on the quantum process of the emergent induction are unknown. We report here large emergent electromagnetic induction achieved around and above room temperature, making use of a few tens of micrometer-sized devices based on the high-temperature (up to 330 K) and short-period (≤ 3 nm) spin-spiral states of a metallic helimagnet. The observed inductance value L and its sign are observed to vary to a large extent, depending not only on the spin-helix structure controlled by temperature and applied magnetic field but also on the applied current density. The present finding on room-temperature operation and possible sign control of L may provide a step toward realizing microscale quantum inductors on the basis of emergent electromagnetism in spin-helix states.

Rare Earth Engineering in RMn_{6}Sn_{6} (R=Gd-Tm, Lu) Topological Kagome Magnets

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.

Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6

Kagome-lattices of 3d-transition metals hosting Weyl/Dirac fermions and topological flat bands exhibit non-trivial topological characters and novel quantum phases, such as the anomalous Hall effect and fractional quantum Hall effect. With consideration of spin-orbit coupling and electron correlation, several instabilities could be induced. The typical characters of the electronic structure of a kagome lattice, i.e., the saddle point, Dirac-cone, and flat band, around the Fermi energy (EF) remain elusive in magnetic kagome materials. We present the experimental observation of the complete features in ferromagnetic kagome layers of YMn6Sn6 helically coupled along the c-axis, by using angle-resolved photoemission spectroscopy and band structure calculations. We demonstrate a Dirac dispersion near EF, which is predicted by spin-polarized theoretical calculations, carries an intrinsic Berry curvature and contributes to the anomalous Hall effect in transport measurements. In addition, a flat band and a saddle point with a high density of states near EF are observed. These multi-sets of kagome features are of orbital-selective origin and could cause multi-orbital magnetism. The Dirac fermion, flat band and saddle point in the vicinity of EF open an opportunity in manipulating the topological properties in magnetic materials.

Field-induced topological Hall effect and double-fan spin structure with a c-axis component in the metallic kagome antiferromagnetic compound YMn6Sn6

Geometric frustration in the kagome lattice makes it a great host for the flat electronic band, nontrivial topological properties, and novel magnetism. Here, we use magnetotransport measurements to map out the field-temperature phase diagram of the centrosymmetric YMn6Sn6 with a Mn kagome lattice and show that the system exhibits the topological Hall effect (THE) with an in-plane applied magnetic field around 240 K. In addition, our neutron diffraction results demonstrate that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double-fan spin structure with c -axis components. This paper provides a platform to understand the influence of a field-induced novel magnetic structure on magnetoelectric response in topological kagome metals.