The Zeeman effect describes the energy change of an atomic quantum state in magnetic field. The magnitude and the direction of this change depend on the dimensionless Lande g-factor. In quantum solids, the response of the Bloch electron states to the magnetic field also exhibits the Zeeman effect with an effective g-factor that was theoretically predicted to be dependent on the momentum. While typically negligible in many ordinary solids, the momentum-dependent variation of the g-factor is theorized to be substantially enhanced in many topological and magnetic systems. However, the momentum-dependence of the g-factor is notoriously difficult to extract and it is yet to be directly experimentally measured. In this work, we report the experimental discovery of a strongly momentum-dependent g-factor in a kagome magnet YMn6Sn6. Using spectroscopic-imaging scanning tunneling microscopy, we map the evolution of a massive Dirac band in the vicinity of the Fermi level as a function of magnetic field. We find that electronic states at different lattice momenta exhibit markedly different Zeeman energy shifts, giving rise to an anomalous g-factor that peaks around the Dirac point. Our work provides the first momentum-resolved visualization of Dirac band curvature manipulation by magnetic field, which should in principle be highly relevant to other topological kagome magnets.
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 nontrivial 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 Z${_2}$ bulk topology and identify multiple VHSs near the Fermi level ($\textit{E}$${_F}$) in magnetic kagome material GdV${_6}$Sn${_6}$. Using in-sit…
Recently, kagome materials have become an engrossing platform to study the interplay among symmetry, magnetism, topology, and electron correlation. The latest works on RMn6Sn6 (R = rare earth metal) compounds have illustrated that this family could be intriguing to investigate various physical phenomena due to large spin-orbit coupling and strong magnetic ordering. However, combined transport and spectroscopic studies in RMn6Sn6 materials are still limited. Here, we report magnetic, magneto-transport, and angle-resolved photoemission spectroscopy measurements of a kagome magnet ErMn6Sn6 that u…
Kagome lattices host flat bands due to their frustrated lattice geometry, which leads to destructive quantum interference of electron wave functions. Here, we report imaging of the kagome flat band localization in real-space using scanning tunneling microscopy. We identify both the Fe3Sn kagome lattice layer and the Sn2 honeycomb layer with atomic resolution in kagome antiferromagnet FeSn. On the Fe3Sn lattice, at the flat band energy determined by the angle resolved photoemission spectroscopy, tunneling spectroscopy detects an unusual state localized uniquely at the Fe kagome lattice network.…
Electronic properties of the single crystal of GdV6Sn6, where non-magnetic V-kagome layers are separated by magnetic Gd-triangular lattice, are investigated. GdV6Sn6 exhibits unique magnetotransport properties at low-temperature such as non-linear Hall resistivity and increase of resistance R in magnetic field H as R ~ H^0.75 up to 56 T with Shubnikov-De Haas oscillations. Investigation of the non-magnetic analogue YV6Sn6 and the first principles calculations reveal these properties are relevant to the bands arising from the V-kagome layer. A magnetic transition at 5 K in GdV6Sn6 modifies the …
The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co$_3$Sn$_2$S$_2$, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl…
Exploration of rare-earth (RE)-based Kagome lattice magnets with spin-orbital entangled jeff=1/2 moments will provide new platform for investigating the exotic magnetic phases. Here, we report a new family of RE3BWO9 (RE=Pr,Nd,Gd-Ho) boratotungstates with magnetic RE3+ ions arranged on Kagome lattice, and perform its structure and magnetic characterizations. This serial compounds crystallize in hexagonal coordinated structure with space group P63 (No.173), where magnetic RE3+ ions have distorted Kagomé lattice connections within the ab plane and stacked in a AB-type fashion along c axis. The i…
We investigate the electronic and magnetic properties of the kagome mineral averievite (CsCl)Cu$_5$V$_2$O$_{10}$ and its phosphate analog (CsCl)Cu$_5$P$_2$O$_{10}$ using first-principles calculations. The crystal structure of these compounds features Cu$^{2+}$ kagome layers sandwiched between Cu$^{2+}$-P$^{5+}$/Cu$^{2+}$-V$^{5+}$ honeycomb planes, with pyrochlore slabs made of corner-sharing Cu-tetrahedra being formed. The induced chemical pressure effect upon substitution of V by P causes significant changes in the structure and magnetic properties. Even though the in-plane antiferromagnetic …
Strongly correlated Kagome magnets are promising candidates for achieving controllable topological devices owing to the rich interplay between inherent Dirac fermions and correlation-driven magnetism. Here we report tunable local magnetism and its intriguing control of topological electronic response near room temperature in the Kagome magnet Fe3Sn2 using small angle neutron scattering, muon spin rotation, and magnetoresistivity measurement techniques. The average bulk spin direction and magnetic domain texture can be tuned effectively by small magnetic fields. Magnetoresistivity, in response,…
We report on the observation of a large topological Hall effect (THE) over a wide temperature region in a geometrically frustrated Fe3Sn2 magnet with a kagome-bilayer structure. We found that the magnitude of the THE resistivity increases with temperature and reaches -0.875 μΩ.cm at 380 K. Moreover, the critical magnetic fields with the change of THE are consistent with the magnetic structure transformation, which indicates that the real-space fictitious magnetic field is proportional to the formation of magnetic skyrmions in Fe3Sn2. The results strongly suggest that the large THE originates f…
The magnetization process of single crystals of the metallic kagomé ferromagnet Co3Sn2S2 was carefully measured via magnetization and AC susceptibility. Field-dependent anomalous transitions in the magnetization indicate a low-field unconventionally ordered phase stabilized just below TC. The magnetic phase diagrams in applied fields along different crystallographic directions were determined. The magnetic relaxation process studied in frequencies covering five orders of magnitude from 0.01 to 1000 Hz indicates characteristic relaxation times of several seconds at the boarders of the anomalous…
This study examines the effect of distorted triangular magnetic interactions in the Kagome lattice. Using a Holstein-Primakoff expansion, we determine the analytical solutions for classical energies and the spin-wave modes for various magnetic configurations. By understanding the magnetic phase diagram, we characterize the changes in the spin waves and examine the spin distortions of the ferromagnetic (FM), Antiferrimagnetic (AfM), and 120$^{\circ}$ phases that are produced by variable exchange interactions and lead to various non-collinear phases, which provides a deeper understanding of the …
We report magnetic and electrical properties for single crystals of NdMn$_6$Sn$_6$ and SmMn$_6$Sn$_6$. They crystallize into a structure which has distorted, Mn-based kagome lattices, compared to the pristine kagome lattices in heavy-rare-earth-bearing RMn$_6$Sn$_6$ compounds. They are hightemperature ferromagnets of which the R moment is parallel with the Mn moment. We observed a large intrinsic anomalous Hall effect (AHE) that is comparable to the ferrimagnetic, heavy-R siblings in a wide range of temperature. We conclude that their intrinsic AHE is stemming from the Mn-based kagome lattice,…
The search for two dimensional quantum spin liquids, exotic magnetic states with an entangled ground state remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism during the last decades. Recently, fractionalized excitations, called spinons, emerging from these states, have been evidenced in kagome and triangular antiferromagnets. In contrast, quantum ferromagnetic spin liquids in two dimensions, namely quantum kagome ices, have been less investigated, yet their classical counterparts exhibit amazing properties, magnetic monopole crystals as well as ma…
The structural-magnetic models of 25 AFM kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2) - a perspective spin liquid - have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is…
The competition between interactions in frustrated magnets allows a wide variety of new ground states, often exhibiting emergent physics and unique excitations. Expanding the suite of lattices available for study enhances our chances of finding exotic physics. Mn$_2$Sb$_2$O$_7$ forms in a chiral, kagome-based structure in which a fourth member is added to the kagome-plane triangles to form an armchair unit and link adjacent kagome planes. This structural motif may be viewed as intermediate between the triangles of the kagome network and the tetrahedra in the pyrochlore lattice. Mn$_2$Sb$_2$O$_…
Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn$_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 massive Dirac fermions. Our observation dem…
We present the crystal structures and magnetic properties of RE3Sb3Mg2O14 (La3Sb3Mg2O14, Pr3Sb3Mg2O14, Sm3Sb3Mg2O14, Eu3Sb3Mg2O14, Tb3Sb3Mg2O14, and Ho3Sb3Mg2O14), a family of novel materials based on a perfect geometry 2D rare earth Kagome lattice. Structure refinements were performed by the Rietveld method using X-ray diffraction data, indicating that the layered compounds are fully structurally ordered. The compounds crystallize in a rhombohedral supercell of the cubic pyrochlore structure, in the space group R-3m. As indicated by magnetic susceptibility measurements, they exhibit predomina…
Electronic flat band systems are a fertile platform to host correlation-induced quantum phenomena such as unconventional superconductivity, magnetism and topological orders. While flat band has been established in geometrically frustrated structures, such as the kagome lattice, flat band-induced correlation effects especially in those multi-orbital bulk systems are rarely seen. Here we report negative magnetoresistance and signature of ferromagnetic fluctuations in a prototypical kagome metal CoSn, which features a flat band in proximity to the Fermi level. We find that the magnetoresistance i…
Kagome Chern Magnets are lattices which host a Chern state when they are non-magnetic and a Chern Gap when they become magnetic. These Chern gaps can host fractional Chern Fermions. There has been extensive research in the RMn$_6$Sn$_6$ system which hosts a small Chern gap with many trivial bands surrounding them. RMn$_6$Ge$_6$ is studied theoretically in order to find a more insulating Kagome magnetic with fewer bands near the Chern gap.
The kagome lattice -- a two-dimensional (2D) arrangement of corner-sharing triangles -- is at the forefront of the search for exotic states generated by magnetic frustration. Such states have been observed experimentally for Heisenberg and planar spins. In contrast, frustration of Ising spins on the kagome lattice has previously been restricted to nano-fabricated systems and spin-ice materials under applied magnetic field. Here, we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scatte…
Magnetization plateaus in quantum spin systems emerges in two-dimensional frustrated systems such as kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on square-kagome lattice is also appropriate for the study of magnetization plateau. Motivated by recent experimental finding of such a square-kagome lattice with nonequivalent three bonds, we investigate the phase diagrams and magnetization plateaus of the lattice by the exact diagonalization method. In addition to previously reported the 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose …
RV6Sn6 (R=rare earth) compounds are appealing materials platforms for exploring the interplay between R-site magnetism and nontrivial band topology associated with the nonmagnetic vanadium-based kagome network. Here we present the synthesis and characterization of the kagome metal TbV6Sn6 via single-crystal x-ray diffraction, magnetization, transport, and heat capacity measurements. Magnetization measurements reveal strong, uniaxial magnetic anisotropy rooted in the alignment of Tb3Å moments in the interplane direction below 4.3(2) K. TbV6Sn6 exhibits multiband transport behavior with high mob…
Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using th…
Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge order, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to non-kagome surface layers. Here we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifes a 2x2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin-mapping across steps of unit-cell-height demonstrates that this charge order emerges from spin-polarized electrons with an antiferr…
We obtain a classical spin liquid (CSL) phase by applying a magnetic field in $J_1$-$J_2$-$J_3$ Ising model on a kagome lattice. As we proved in the previous study [Phys. Rev. Lett. {\bf 119}, 077207 (2017)], this model realizes one species of CSL, the hexamer CSL, at zero magnetic field, which consists of macroscopically degenerate spin configurations with mixed total magnetization, $M$. The magnetic field selects its subset, which can be mapped to a trimer covering of the dual lattice, and forms a magnetization plateau of $M=1/9$. In addition to this CSL, we find two other magnetization plat…
In this Letter, we identify a noncoplanar chiral spin texture on the distorted kagomé-lattice antiferromagnets induced by the presence of a magnetic field applied perpendicular to the distorted kagomé plane. The noncoplanar chiral spin texture has a nonzero scalar spin chirality similar to a chiral quantum spin liquid with broken time-reversal symmetry. In the noncoplanar regime we observe nontrivial topological magnetic excitations and thermal Hall response through the emergent field-induced scalar spin chirality in contrast to collinear ferromagnets in which the Dzyaloshinskii-Moriya (DM) sp…
Kagome magnet usually hosts nontrivial electronic or magnetic states drawing great interests in condensed matter physics. In this paper, we report a systematic study on transport properties of kagome magnet TmMn$_6$Sn$_6$. The prominent topological Hall effect (THE) has been observed in a wide temperature region spanning over several magnetic phases and exhibits strong temperature and field dependence. This novel phenomenon due to non-zero spin chirality indicates possible appearance of nontrival magnetic states accompanying with strong fluctuations. The planar applied field drives planar Hall…
The spin-1/2 kagome antiferromagnets are key prototype materials for studying frustrated magnetism. Three isostructural kagome antiferromagnets LnCu$_3$(OH)$_6$Cl$_3$ (Ln = Gd, Tb, Dy) have been successfully synthesized by the hydrothermal method. LnCu$_3$(OH)$_6$Cl$_3$ adopts space group $P\overline{3}m1$ and features the layered Cu-kagome lattice with lanthanide Ln$^{3+}$ cations sitting at the center of the hexagons. Although heavy lanthanides (Ln = Gd, Tb, Dy) in LnCu$_3$(OH)$_6$Cl$_3$ provide a large effective magnetic moment and ferromagnetic-like spin correlations compared to light-lant…
An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.
Theory of unconventional magnetism in a Cu-based kagome metal
Universität Würzburg（维尔茨堡大学）；Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche（意大利国家研究委员会材料研究所）；ETH Zürich（苏黎世联邦理工学院）；University of Geneva（日内瓦大学）；University of Technology Sydney（悉尼科技大学）；Columbia University（哥伦比亚大学）；University of Bologna（博洛尼亚大学）
Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena. Here, utilizing angle-resolved photoemission spectroscopy, we demonstrate Weyl lines with strong out-of-plane dispersion in an A-A stacked kagome magnet TbxGd1-xMn6Sn6. On the Gd rich side, the Weyl line remains nearly spin-orbit-gapless due to a remarkable cooperative interplay between Kane-Mele spin-orbit-coupling, low site symmetry and in-plane magnetic order. Under Tb substitution, the kagome Weyl line gaps due to a magnetic reorientation to out-of-plane order. Our results illustrate the magnetic…
The ground state of the simple Heisenberg nearest-neighbor quantum kagome antiferromagnetic model is a magnetically disordered spin liquid, yet various perturbations may lead to fundamentally different states. Here we disclose the origin of magnetic ordering in the structurally-perfect kagome material YCu$_3$(OH)$_6$Cl$_3$, which is free of the widespread impurity problem. {\it Ab-initio} calculations and modeling of its magnetic susceptibility reveal that, similar to the archetypal case of herbertsmithite, the nearest-neighbor exchange is by far the dominant isotropic interaction. Dzyaloshins…
Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the three-fold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establi…
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 a…
Kagome magnets are expected to feature emergent properties due to the interplays among geometry, magnetism, electronic correlation, and band topology. The magnetism and topological electronic states can be tuned via the rare earth engineering in RV6Sn6 kagome metals, where R is a rare earth element. Herein, we present the synthesis and characterization of SmV6Sn6, a metal with two-dimensional kagome nets of vanadium and frustrated triangular Sm lattice. Partial of the Sm atoms are shifted from the normal R positions by c/2 along the c axis. Magnetic measurements reveal obvious anisotropy, wher…
Singlet Ground State and Spin Gap in S=1/2 Kagome Antiferromagnet Rb$_2$Cu$_3$SnF$_{12}$
本文研究了Rb $_2$ Cu $_3$ SnF $_{12}$的晶体结构和磁性。该化合物由角共享的CuF $_{6}$八面体的可果美层组成，与适当的可果美层相比，具有2a x 2a的放大单元。Rb $_2$ Cu $_3$ SnF $_{12}$在磁性上被描述为具有四种相邻交换作用的$S$ =1/2修正的可果美反铁磁体。从磁化率和高场磁化强度测量，它被发现，基态是一个无序的单重态与自旋间隙，从最近的理论预测。精确对角化的12个站点的可果美集群进行分析的磁化率，和个人的交换相互作用进行了评估。
The magnetization and specific heat measurements have been performed on single-crystalline Gd_3_Ru_4_Al_12_ with a distorted Kagome lattice structure. This spin system is regarded as an antiferromagnetic triangular lattice of XY like Heisenberg model at low temperatures. The magnetic phase diagrams indicate the existence of frustration and Z_2_ degeneracy. The magnetization and specific heat imply the successive phase transitions with partial disorder and a T-shaped spin structure in the ground state.
