Using mean-field theory and high resolution Monte Carlo simulation technique based on multi-histogram method, we have investigated the critical properties of an antiferromagnetic XY model on the 2D Kagomé lattice, with single ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first order transition for small values of anisotropy which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behaviour of the system deviates from 2D-$ϕ^6$ model near the tricritical point. This suggests the possibility for existence of a new tricritical universality in two-dimensions.
The ground state phase transitions in the distorted S=1 kagome Heisenberg antiferromagnet (KHAF) with single-site anisotropy D are studied by the numerical exact diagonalization method. For strong easy plane anisotropy, the hexgonal singlet solid (HSS) ground state of the uniform KHAF is destroyed and large-D state is realized. The quantum phase transition between these two states is analogous to the Haldane-large-D transition in the S=1 antiferromagnetic Heisenberg chain. The combined effect of the sqrt(3) times sqrt(3) lattice distortion and single site anisotropy is also investigated. The g…
We report the determination of the Dzyaloshinsky-Moriya interaction, the dominant magnetic anisotropy term in the \kagome spin-1/2 compound {\herbert}. Based on the analysis of the high-temperature electron spin resonance (ESR) spectra, we find its main component $|D_z|=15(1)$ K to be perpendicular to the \kagome planes. Through the temperature dependent ESR line-width we observe a building up of nearest-neighbor spin-spin correlations below $\sim$150 K.
We study the zero-temperature phase diagram of the spin-$\frac{1}{2}$ Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks do…
Tunable bifurcation of magnetic anisotropy and bi-oriented antiferromagnetic order in kagome metal GdTi3Bi4
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics and State Key Laboratory of Surface Physics, Fudan University（复旦大学）
A ferromagnet with spin anisotropies on the 2D Kagome lattice is theoretically studied. This is a typical example of the flat-band ferromagnet. The Berry phase induced by the tilting of the spins opens the band gap and quantized Hall conductance σ_{xy}=\pm e^2/h is realized without external magnetic field. This is the most realistic chiral spin state based on the ferromagnetism. We also discuss the implication of our results to anomalous Hall effect observed in the metallic pyrochlore ferromagnets R_2Mo_2O_7(R=Nd, Sm, Gd).
Properties of thin films of geometrically frustrated ABC stacked antiferromagnetic kagome layers are examined using Metropolis Monte Carlo simulations. The impact of having an easy-axis anisotropy on the surface layers and cubic anisotropy in the interior layers is explored. The spin structure at the surface is shown to be different from that of the bulk 3D fcc system, where surface axial anisotropy tends to align spins along the surface [111] normal axis. This alignment tendency then propagates only weakly to the interior layers through exchange coupling. Results are shown for the specific he…
We investigate the magnetic symmetry of the topological antiferromagnetic material Mn$_3$Ge by using torque measurements. Below the Neel temperature, detailed angle-dependent torque measurements were performed on Mn$_3$Ge single crystals in directions parallel and perpendicular to the Kagome basal plane. The out-of plane torque data exhibit $\pm\sinθ$ and $\sin2θ$ behaviors, of which the former results from the spontaneous ferromagnetism within the basal plane and the latter from the in- and out-of-plane susceptibility anisotropy. The reversible component of the in-plane torque exhibits $\sin6…
We report x-ray absorption and x-ray linear dichroism measurements at the Fe L2,3 edges of the geometrically frustrated systems of potassium and hydronium iron jarosite. Comparison with simulated spectra, involving ligand-field multiplet calculations modelling the 3d-2p hybridization between the iron ion and the oxygen ligands, has yielded accurate estimates for the ligand metal-ion hybridization and the resulting single-ion crystal field anisotropy energy. Using this method we provide an experimentally verified scenario for the appearance of a single-ion anisotropy in this nominally high-spin…
We report thermodynamic measurements of the S=1/2 kagome lattice antiferromagnet ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where $χ_{z}/ χ_{p} > 1$ at high temperatures and $χ_{z}/ χ_{p} < 1$ at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal an anisotropy. By comparing with theoretical calculations, the presence of a s…
We report the crystal field levels of several newly-discovered rare-earth kagome compounds: $\rm{Nd_3Sb_3Mg_2O_{14}}$, $\rm{Nd_3Sb_3Zn_2O_{14}}$, and $\rm{Pr_3Sb_3Mg_2O_{14}}$. We determine the CEF Hamiltonian by fitting to neutron scattering data using a point-charge Hamiltonian as an intermediate fitting step. The fitted Hamiltonians accurately reproduce bulk susceptibility measurements, and the results indicate easy-axis ground state doublets for $\rm{Nd_3Sb_3Mg_2O_{14}}$ and $\rm{Nd_3Sb_3Zn_2O_{14}}$, and a singlet ground state for $\rm{Pr_3Sb_3Mg_2O_{14}}$. These results provide the groun…
Motivated by a recent finding of a spin-flop phenomenon in a system without anisotropy in spin space reported in the S=1/2 Heisenberg antiferromagnet on the square-kagome lattice, we study the S=1/2 Heisenberg antiferromagnets on two other lattices composed of vertex-sharing triangles by the numerical diagonalization method. One is a novel lattice including a shuriken shape with four teeth; the other is the kagome lattice with $\sqrt{3}\times\sqrt{3}$-structure distortion, which includes a shuriken shape with six teeth. We find in the magnetization processes of these systems that a magnetizati…
We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the sim…
We systematically investigate the ground-state and the spectral properties of antiferromagnets on a kagomé lattice with several common types of the planar anisotropy: $XXZ$, single-ion, and out-of-plane Dzyaloshinskii-Moriya. Our main focus is on the role of nonlinear, anharmonic terms, which are responsible for the quantum order-by-disorder effect and for the corresponding selection of the ground-state spin structure in many of these models. The $XXZ$ and the single-ion anisotropy models exhibit a quantum phase transition between the ${\bf q}\!=\!0$ and the $\sqrt{3}\times\!\sqrt{3}$ states a…
Motivated by recent experiments on Nd-langasite, we consider the effect of strong easy axis single-ion anisotropy $D$ on $S > 3/2$ spins interacting with antiferromagnetic exchange $J$ on the Kagome lattice. When $T \ll DS^2$, the collinear low energy states selected by the anisotropy map on to configurations of the classical Kagome lattice Ising antiferromagnet. However, the low temperature limit is quite different from the cooperative Ising paramagnet that obtains classically for $T \ll JS^2$. We find that sub-leading ${\mathcal O}(J^3S/D^2)$ multi-spin interactions arising from the transver…
We investigate the Mott transition in the anisotropic kagomé lattice Hubbard model using the cellular dynamical mean field theory combined with continuous-time quantum Monte Carlo simulations. By calculating the double occupancy and the density of states, we determine the interaction strength of the first-order Mott transition and show that it becomes small as the anisotropy increases. We also calculate the spin correlation functions and the single-particle spectrum, and reveal that the quasiparticle and magnetic properties change dramatically around the Mott transition; the spin correlations …
We performed a comprehensive electron spin resonance, magnetization and heat capacity study on the field-induced magnetic phase transitions in the kagome antiferromagnet $α-Cu_3Mg(OH)_6Br_2$. With the successful preparation of single crystals, we mapped out the magnetic phase diagrams under the $c$-axis and $ab$-plane directional magnetic fields $B$. For $B\|c$, the three-dimensional (3D) magnon Bose-Einstein condensation (BEC) is evidenced by the power law scaling of the transition temperature, $T_c\propto (B_c-B)^{2/3}$. For $B\|ab$, the transition from the canted antiferromagetic (CAFM) sta…
The zero temperature phase diagram of the mono-axial chiral helimagnet in the magnetic field plane formed by the components parallel and perpendicular to the helical axis is thoroughly analyzed. The nature of the transition to the commensurate state depends on the angle between the field and the helical axis. For field directions close to the directions parallel or perpendicular to the helical axis the transition is continuous, while for intermediate angles the transition is discontinuous and the incommensurate and commensurate states coexist on the transition line. The continuous and disconti…
The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the $J_z$ coupling is antiferromagnetic. In the zero magnetic field case, the six previously introduced phases, found using various methods, are: the nondegenerate gapped photon phase which breaks no space symmetry or spin symmetry; the six-fold degenerate phase with plaquette order, which breaks both time reversal symmetry and translational symmetry; the "superfluid" (ferromagnetic) phase with an in-plane global U(1) symmetry broken, when $J_{xy} < 0$; the $\sqrt{3}\times\sqrt{3}$ order whe…
Observation of Magnetic-Anisotropy Crossover and High-Temperature Skyrmions in the Dirac Magnet Fe3Ge with a Distorted Kagome Lattice
Zhejiang University of Technology（浙江工业大学）；Fudan University（复旦大学）；Nanjing University of Posts and Telecommunications（南京邮电大学）；Ningbo University（宁波大学）；Academia Sinica（中央研究院）；Shanghai University（上海大学）；Suzhou University of Technology（苏州科技大学）；Qufu Normal University（曲阜师范大学）；National Taiwan Normal University（台湾师范大学）；Zhejiang University（浙江大学）；Shanghai Jiao Tong University（上海交通大学）
Single crystals of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl were investigated using high-resolution capacitance dilatometry in magnetic fields up to 15 T. Pronounced magnetoelastic coupling is found upon evolution of long-range antiferromagnetic order at T$_{\mathrm{N}} = 26.4(3)$ K. Grüneisen analysis reveals moderate effects of uniaxial pressure on T$_{\mathrm{N}}$, of $1.8(4)$ K/GPa, $-0.62(15)$ K/GPa and $0.33(10)$ K/GPa for $p \parallel a$, $b$, and $c$, respectively. Below 22 K, Grüneisen scaling fails which implies the presence of competing interactions. The structural phase transition at T$_{\math…
We study the ground state properties of a quantum antiferromagnet in the kagome lattice in the presence of a magnetic field, paying particular attention to the stability of the plateau at magnetization 1/3 of saturation. While the plateau is reinforced by certain deformations of the lattice, like the introduction of structural defect lines and against an Ising anisotropy, ground state correlations are seen to be quite different and the undistorted SU(2) case appears to be rather special.
We present magnetization measurements on oriented powder of ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ along and perpendicular to the orienting field. We find a dramatic difference in the magnetization between the two directions. It is biggest at low measurement fields $H$ or high temperatures. We show that the difference at high temperatures must emerge from Ising-like exchange anisotropy. This allows us to explain muon spin rotation data at $T\to 0$ in terms of an exotic ferromagnetic ground state.
The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determ…
Thermodynamic properties such as magnetic susceptibility and specific heat have been computed for the Heisenberg Antiferromagnet with spatially anisotropic exchange on the kagome lattice on clusters up to N=24 spins from the full spectra obtained by exact diagonalization. This approach is shown to provide a good represention of these thermodynamic properties above temperatures of about $J_{\rm av}/5$ where $J_{\rm av}$ is an average of the coupling constants. Comparison with experimental Volborthite data obtained by Hiroi {\it {et al}} [J. Phys. Soc. Jpn. {\bf 70},3377 (2001)] shows that Volbo…
Selection of the ground state of the kagomé-lattice $XXZ$ antiferromagnet by quantum fluctuations is investigated by combining non-linear spin-wave and real-space perturbation theories. The two methods unanimously favor ${\bf q}=0$ over $\sqrt{3}\times\sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\leq Δ\leq 0.72$. Both approaches are also in an accord on the magnitude of the quantum order-by-disorder effect generated by topologically non-trivial, loop-like spin-flip processes. A tentative $S-Δ$ phase diagram of the model is proposed.
In this work, the magnetism of the single crystal Cr$_{1/3}$NbS$_{2}$, which exhibits chiral magnetic soliton lattice (CSL) state, is investigated. The magnetization displays strong magnetic anisotropy when the field is applied perpendicularly and parallel to the $c$-axis in low field region ($H<H_{S}$, $H_{S}$ is the saturation field). The critical exponents of Cr$_{1/3}$NbS$_{2}$ are obtained as $β=$ 0.370(4), $γ=$ 1.380(2), and $δ=$ 4.853(6), which are close to the theoretical prediction of three-dimensional Heisenberg model. Based on the scaling equation and the critical exponents, the $H-…
We use the coupled cluster method to high orders of approximation in order to calculate the ground-state phase diagram of the XXZ spin-$s$ kagome antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter $Δ$ varies between $Δ=1$ (isotropic Heisenberg model) and $Δ=0$ ($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground state is magnetically disordered in the entire region $0 \le Δ\le 1$. For $s=1$ the ground state is disordered for $0.818 < Δ\le 1$, it exhibits $\sqrt{3}\times\sqrt{3}$ magnetic long-range order for $0.281 < Δ<0.818$, and $q=0$ magnetic lon…
Mott transition and ferrimagnetism are studied in the Hubbard model on the anisotropic kagomé lattice using the variational cluster approximation and the phase diagram at zero temperature and half-filling is analyzed. The ferrimagnetic phase rapidly grows as the geometric frustration is relaxed, and the Mott insulator phase disappears in moderately frustrated region, showing that the ferrimagnetic fluctuations stemming from the relaxation of the geometric frustration is enhanced by the electron correlations. In metallic phase, heavy fermion behavior is observed and mass enhancement factor is c…
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 consider spin-orbit coupling effects in Na$_4$Ir$_3$O$_8$, a material in which Ir$^{4+}$ spins form an hyper-kagomé lattice, a three-dimensional network of corner-sharing triangles. We argue that both low temperature thermodynamic measurements and the impurity susceptibility induced by dilute substitution of Ti for Ir are suggestive of significant spin-orbit effects. Because of uncertainties in the crystal-field parameters, we consider two limits in which the spin-orbit coupling is either weak or strong compared to the non-cubic atomic splittings. A semi-microscopic calculation of the excha…
The phase diagram of the uniaxially anisotropic $s=1$ antiferromagnet on the kagomé lattice includes a critical line exactly described by the classical three-color model. This line is distinct from the standard geometric classical criticality that appears in the classical limit ($s \to \infty$) of the 2D XY model; the $s=1$ geometric T=0 critical line separates two unconventional plaquette-ordered phases that survive to nonzero temperature. The experimentally important correlations at finite temperature and the nature of the transitions into these ordered phases are obtained using the mapping …
Exploration of exotic transport behavior for quantum materials is of great interest and importance for revealing exotic orders to bring new physics. In this Letter, we report the observation of exotic prominent planar Hall effect (PHE) and planar anisotropic magnetoresistivity (PAMR) in strange kagome metal KV$_3$Sb$_5$. The PHE and PAMR, which are driven by an in-plane magnetic field and display sharp difference from other Hall effects driven by an out-of-plane magnetic field or magnetization, exhibit exotic higher-order oscillations in sharp contrast to those following empirical rule only al…
We study the nearest neighbor $XXZ$ Heisenberg quantum antiferromagnet on the kagome lattice. Here we consider the effects of several perturbations: a) a chirality term, b) a Dzyaloshinski-Moriya term, and c) a ring-exchange type term on the bowties of the kagome lattice, and inquire if they can suppport chiral spin liquids as ground states. The method used to study these Hamiltonians is a flux attachment transformation that maps the spins on the lattice to fermions coupled to a Chern-Simons gauge field on the kagome lattice. This transformation requires us to consistently define a Chern-Simon…
Structural and magnetic phases of topological kagome metal Fe$_3$Sn$_2$ under pressure
UGC-DAE Consortium for Scientific Research Mumbai Centre（UGC-DAE 科学研究联盟孟买中心）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS, Laboratoire de Physique des Solides（法国国家科学研究中心固体物理实验室）；Uppsala University（乌普萨拉大学）；Bennett University（贝内特大学）；Indian Institute of Technology-Delhi（印度德里理工学院）；Synchrotron SOLEIL（索莱尔同步辐射中心）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Institut universitaire de France (IUF)（法国高等研究院）
Strong metamagnetic switching and anisotropic magnetotransport in the distorted kagome magnet Tb6Ti4Al43
Indian Institute of Technology Delhi（印度理工学院德里分校）；Max-Planck-Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Department of Physics, Institute for Materials Research, Tohoku University（东北大学物质材料研究学院物理学系）
Co$_3$Sn$_2$S$_2$, a Weyl semimetal that consists of layers of Kagome lattices, transitions from a high-temperature paramagnetic phase to a low-temperature ferromagnetic phase below 177 K. The phase transition occurs through an intermediate non-trivial magnetic phase, the so-called "A"-phase just below the Curie temperature. The "A"-phase was earlier linked with a competing anti-ferromagnetic phase, a spin-glass phase and certain indirect measurements indicated the possibility of magnetic Skyrmions in this phase. We have imaged the magnetic domain structure in a single crystal of Co$_3$Sn$_2$S…
We investigate the magnetic ground state of Sm$_3$BWO$_9$ with the distorted kagome lattice. A magnetic phase transition is identified at $T_N=0.75$ K from the temperature dependence of specific heat. From $^{11}$B nuclear magnetic resonance (NMR) measurements, an incommensurate magnetic order is shown by the double-horn type spectra under a $c$-axis magnetic field. While, absence of line splitting is observed for field oriented within the $ab$-plane, indicating the incommensurate modulation of the internal field strictly along $c$-axis. From the spin dynamics, the critical slowing down behavi…
We study numerically the spin-1/2 XXZ model in a field on an infinite Kagome lattice. We use different algorithms based on infinite Projected Entangled Pair States (iPEPS) for this, namely: (i) with simplex tensors and 9-site unit cell, and (ii) coarse-graining three spins in the Kagome lattice and mapping it to a square-lattice model with nearest-neighbor interactions, with usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emerg…
