There is a growing family of rare-earth kagome materials with dominant nearest-neighbor interactions and strong spin orbit coupling. The low symmetry of these materials makes theoretical description complicated, with six distinct nearest-neighbor coupling parameters allowed. In this Article, we ask what kinds of classical, ordered, ground states can be expected to occur in these materials, assuming generic (i.e. non-fine-tuned) sets of exchange parameters. We use symmetry analysis to show that there are only five distinct classical ground state phases occurring for generic parameters. The five phases are: (i) a coplanar, 2-fold degenerate, state with vanishing magnetization (${\sf A_1}$), (ii) a noncoplanar, 2-fold degenerate, state with magnetization perpendicular to the kagome plane (${\sf A_2}$), (iii) a coplanar, 6-fold degenerate, state with magnetization lying within the kagome plane (${\sf E}$-coplanar), (iv) a noncoplanar, 6-fold degenerate, state with magnetization lying within a mirror plane of the lattice (${\sf E}$-noncoplanar$_{6}$), (v) a noncoplanar, 12-fold degenerate, state with magnetization in an arbitrary direction (${\sf E}$-noncoplanar$_{12}$). All five are translation invariant (${\bf q}=0$) states. Having found the set of possible ground states, the ground state phase diagram is obtained by comparing numerically optimized energies for each possibility as a function of the coupling parameters. The state ${\sf E}$ noncoplanar$_{12}$ is extremely rare, occupying $<1\%$ of the full phase diagram, so for practical purposes there are four main ordered states likely to occur in anisotropic kagome magnets with dominant nearest neighbor interactions. These results can aid in interpreting recent experiments on ``tripod kagome'' systems R$_3$A$_2$Sb$_3$O$_{14}$, as well as materials closer to the isotropic limit such as Cr- and Fe- jarosites.
Neutron scattering measurements have been performed on deuterated powder samples of claringbullite and Zn-doped claringbullite (Zn$_x$Cu$_{4-x}$(OD)$_{6}$FCl). At low temperatures, claringbullite Cu$_4$(OD)$_{6}$FCl forms a distorted pyrochlore lattice with long-range magnetic order and spin-wave-like magnetic excitations. Partial Zn doping leads to the nominal ZnCu$_3$(OD)$_{6}$FCl compound, a geometrically frustrated spin-1/2 kagome antiferromagnet that shows no transition to magnetic order down to 1.5 K. The magnetic excitations form a gapless continuum, a signature of fractional excitation…
We have systematically investigated the variation of the exchange parameters and the ground state in the $S = 1/2$ kagome-lattice antiferromagnet (Rb$_{1-x}$Cs$_{x}$)$_2$Cu$_3$SnF$_{12}$, via magnetic measurements using single crystals. One of the parent compounds, Rb$_2$Cu$_3$SnF$_{12}$, which has a distorted kagome lattice accompanied by four sorts of nearest-neighbor exchange interaction, has a disordered ground state described by a pinwheel valence-bond-solid state. The other parent compound, Cs$_2$Cu$_3$SnF$_{12}$, which has a uniform kagome lattice at room temperature, has an ordered gro…
Three different tensor network optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the $\sqrt{3} \times \sqrt{3}$ state, rather than the $q = 0$ state, is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. A 1/3-magnetization plateau in the magnetic curve is observed, being consistent with the experimental observation. The absence of a zero-magnetization plateau indicates …
The spin-$\frac{1}{2}$ kagome antiferromagnet is considered an ideal host for a quantum spin liquid ground state. We find that when the bonds of the kagome lattice are modulated with a periodic pattern, new quantum ground states emerge. Newly synthesized crystalline barlowite (Cu$_4$(OH)$_6$FBr) and Zn-substituted barlowite demonstrate the delicate interplay between singlet states and spin order on the spin-$\frac{1}{2}$ kagome lattice. Comprehensive structural measurements demonstrate that our new variant of barlowite maintains hexagonal symmetry at low temperatures with an arrangement of dis…
A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground state energies. A well-known example is the copper oxides, where 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. Recently, such rich phase diagrams have also been revealed in correlated topological materials. In two-dimensional kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can pr…
We study the impact of trimerization (breathing) of the nearest-neighbor (NN) exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including additional four-site ring exchange. For uniform NN exchange, this model has previously been shown to transit from a long-range ordered ferromagnet into a Z2 quantum spin liquid by virtue of the ring exchange. Using quantum Monte-Carlo calculations, based on the stochastic series expansion, we present results for the spin stiffness, the quantum phase diagram, the longitudinal static, as well as the transverse dynamic structure factor. Our …
We present a $^{35}$Cl NMR study for spin $S=1/2$ perfect kagome antiferromagnet Ca-kapellasite (CaCu$_{3}$(OH)$_{6}$Cl$_{2}\cdot$0.6H$_{2}$O) with a magnetic transition at $T^{\ast}=7.2$ K. The static magnetic structure in the ground state has been determined to be a chirality-ordered $Q=0$ state, which is selected by a finite Dzyaloshinskii-Moriya interaction. The low-energy magnetic excitations in the ordered state are investigated by the nuclear spin-lattice relaxation rate measurement. We detect a weakly temperature dependent contribution in the magnetic fluctuations perpendicular to the …
The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".
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.
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 …
The magnetization of two spin-1/2 kagome antiferromagnets, volborthite and vesignieite, has been measured in pulsed magnetic fields up to 68 T. A magnetization plateau is observed for each compound near the highest magnetic field. Magnetizations at saturation are approximately equal to 0.40Ms for both compounds, where Ms is the fully saturated magnetization, irrespective of a difference in the distortion of the kagome lattice between the two compounds. It should be noted that these values of magnetizations are significantly larger than Ms/3 predicted theoretically for the one-third magnetizati…
Spin-1/2 Heisenberg model on kagome lattice is a typical frustrated quantum spin system. A basic structure of kagome lattice is also present in kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-1/2 Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions by the density-matrix renormalization group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking either translati…
Unconventional features of the magnetization curve at zero temperature such as plateaus or jumps are a hallmark of frustrated spin systems. Very little is known about their behavior at non-zero temperatures. Here we investigate the temperature dependence of the magnetization curve of the kagome lattice antiferromagnet in particular at 1/3 of the saturation magnetization for large lattice sizes of up to N=48 spins. We discuss the phenomenon of asymmetric melting and trace it back to a combined effect of unbalanced magnetization steps on either side of the investigated plateau as well as on the …
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 discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.
We report magnetization and neutron scattering measurements down to 60 mK on a new family of Fe based kagome antiferromagnets, in which a strong local spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce unfamiliar slow spin dynamics in the ordered phase, evolving from exchange-released spin-flips towards a cooperative behavior on decreasing the temperature, probably due to the onset of long-range dipolar interaction. A domain structure of independent magnetic grains is obtained t…
We report $^{51}$V NMR, $μ$SR and zero applied field $^{63,65}$Cu NMR measurements on powder samples of Sr-vesignieite, SrCu$_3$V$_2$O$_8$(OH)$_2$, a $S = 1/2$ nearly-kagome Heisenberg antiferromagnet. Our results demonstrate that the ground state is a $\mathbf{q} = 0$ magnetic structure with spins canting either in or out of the kagome plane, giving rise to weak ferromagnetism. We determine the size of ordered moments and the angle of canting for different possible $\mathbf{q} = 0$ structures and orbital scenarios, thereby providing insight into the role of the Dzyaloshinskii-Moriya (DM) inte…
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…
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…
The mineral haydeeite, alpha-MgCu3(OD)6Cl2, is a S=1/2 kagome ferromagnet that displays long-range magnetic order below TC=4.2 K with a strongly reduced moment. Our inelastic neutron scattering data show clear spin-wave excitations that are well described by a Heisenberg Hamiltonian with ferromagnetic nearest-neighbor exchange J1=-38 K and antiferromagnetic exchange Jd=+11 K across the hexagons of the kagome lattice. These values place haydeeite very close to the quantum phase transition between ferromagnetic order and non-coplanar twelve-sublattice cuboc2 antiferromagnetic order. Diffuse dyna…
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…
We clarify the existence of several magnetization plateaux for the kagome $S=1/2$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=1/3$, $5/9$, and $7/9$ of the saturation value. These results are confirmed using large-scale Exact Diagonalization on lattices up to 63 sites.
The magnetic ground state of the ideal quantum kagome antiferromagnet (QKA) has been a long-standing puzzle, mainly because perturbations to the nearest-neighbor isotropic Heisenberg Hamiltonian can lead to various fundamentally different ground states. Here we investigate a recently synthesized QKA representative YCu$_3$(OH)$_6$Cl$_3$, where perturbations commonly present in real materials, like lattice distortion and intersite ion mixing, are absent. Nevertheless, this compound enters a long-range magnetically ordered state below $T_N=15$ K. Our powder neutron diffraction experiment reveals …
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…
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。
In quantum spin liquid states, the fractionalized spinon excitations can carry fractional crystal symmetry quantum numbers, and this symmetry fractionalization distinguishes different topologically ordered spin liquid states. In this work we propose a simple way to detect signatures of such crystal symmetry fractionalizations from the crystal symmetry representations of the ground state wave function. We demonstrate our method on projected $\mathbb Z_2$ spin liquid wave functions on the kagome lattice, and show that it can be used to classify generic wave functions. Particularly our method can…
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.
We study dynamical spin structure factor (DSSF) of S = 1/2 Heisenberg model on the kagome lattice (KAFM) by means of density-matrix renormalization group. By comparison with the well-defined magnetic ordered state and chiral spin liquid sitting nearby in the phase diagram, the KAFM with the nearest-neighbor interaction shows distinct dynamical response behaviors. First of all, the DSSF displays important spectral intensity predominantly at low frequency region around Q = M point in momentum space, and shows a broad spectral distribution at high frequency region for momenta along the boundary o…
Elucidating the symmetry of intertwined orders in exotic superconductors is at the quantum frontier. Recent surface sensitive studies of the topological kagome superconductor CsV$_3$Sb$_5$ discovered a cascade 4a$_0$ superlattice below the charge density wave (CDW) ordering temperature, which can be related to the pair density modulations in the superconducting state. If the 4a$_0$ phase is a bulk and intrinsic property of the kagome lattice, this would form a striking analogy to the stripe order and pair density wave discovered in the cuprate high-temperature superconductors, and the cascade …
3D XY Universality and Nonlinear magnetic susceptibility in a kagome ice compound
Beihang University（北京航空航天大学）；University of Augsburg（奥格斯堡大学）；ShanghaiTech University（上海科技大学）；RWTH Aachen University（亚琛工业大学）；Colorado State University（科罗拉多州立大学）；Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室）；Forshungszentrum Jülich GmbH（于利希研究中心有限公司）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Spectroscopic origin of giant anomalous Hall effect in an interwoven magnetic kagome metal
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；ShanghaiTech University（上海科技大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Rutgers University（罗格斯大学）；Weizmann Institute of Science（魏茨曼科学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Chinese Academy of Sciences（中国科学院）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Stanford University（斯坦福大学）；Wuhan University（武汉大学）；University of Oxford（牛津大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Magnetic competition in topological kagome magnets is studied by incorporating the spin-orbit coupling, the anisotropic Hund coupling and spin exchange into the kagome lattice. Using the Bogoliubov variational principle we find the stable phases at zero and finite temperatures. At zero temperature and in the strong Ising-Hund coupling regime, a magnetic tunability from the out-of-plane ferromagnetism (FM) to the in-plane antiferromagnetism (AFM) is achieved by a universal property of the critical in-plane Hund coupling. At two-thirds filling the phase transition from the out-of-plane FM to the…
We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisenberg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers, S. The values of the critical magnetic fields and the widths of the magnetization plateaus are fully consistent with recent numerical results from exact diagonalization and infinite projected entangled paired states.
Highly frustrated spin systems such as the kagome lattice (KL) are a treasure trove of new quantum states with large entanglements. We thus study the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain (KSC), which is one-dimensional KL, using the density-matrix renormalization group (DMRG) method. Calculating central charge and entanglement spectrum for the KSC, we find a novel gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated by dynamical DMRG meth…
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…
