Zn-Paratacamite is a rare spin 1/2 antiferromagnetic insulator with an ideal kagome lattice structure in part of its phase diagram. As a function of Zn doping, this material undergoes a structural distortion which relieves the frustration and introduces magnetic order in the ground state, though the precise nature of the order is not clear at this point. In this paper, we present strong evidence for Neel ordering in the strongly distorted phase of Zn-Paratacamite through the application of quantum Monte-Carlo techniques. These numerical results support a recent Schwinger-boson mean field theory of Zn-Paratacamite. For weak distortion, close to the ideal kagome limit, our results indicate a regime with no Neel order but with a broken glide-plane symmetry. For this model the glide-plane symmetry is broken by any valence bond crystal. Hence, our results lend support to recent proposals of a valence bond crystal ground state for the undistorted lattice. The phase transition between the two phases could be in the deconfined universality class if it is not a first order transition.
Recently, neutron scattering data on powder samples of Zn-paratacamite, Zn$_x$Cu$_{4-x}$(OH)$_6$Cl$_{2}$, with small Zn concentration has been interpreted as evidence for valence bond solid and Néel ordering [1]. We study the classical and quantum Heisenberg models on the distorted kagome lattice appropriate for Zn-paratacamite at low Zn doping. Our theory naturally leads to the emergence of the valence bond solid and collinear magnetic order at zero temperature. Implications of our results to the existing experiments are discussed. We also suggest future inelastic neutron and X-ray scattering…
We report MuSR measurements on the S=1/2 (Cu2+) paratacamite Zn_xCu_{4-x}(OH)_6Cl_2 family. Despite a Weiss temperature of -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagome Heisenberg antiferromagnet. We find that the limit between a dynamical and a frozen inhomogeneous ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.
The Zn-paratacamite family, Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$Cl$_{2}$ for $x \, \geq$ 0.33, is an ideal system for studying spin-1/2 frustrated magnetism in the form of antiferromagnetic Cu$^{2+}$ kagome planes. Here we report a new synthesis method by which high quality millimeter-sized single crystals of Zn-paratacamite have been produced. These crystals have been characterized by metal analysis, x-ray diffraction, neutron diffraction, and thermodynamic measurements. The $x$ = 1 member of the series displays a magnetic susceptibility that is slightly anisotropic at high temperatures with $χ_{c} \…
The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in …
We have obtained the zero-temperature phase diagram of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson mean-field theory. We find quantum phase transitions (first or second order) between different topological spin liquids and Neel ordered phases (either the $\sqrt{3} \times \sqrt{3}$ state or the so-called Q=0 state). In the regime of small Schwinger-boson density, the results bear some resemblances with exact diagonalization results and we briefly discuss some issues of the mean-field treatment. We calculate the equal-time structure factor (and its angul…
We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2 moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv κJ_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for $κ< 1/2$ has collinear ferrimagnetic (Néel$'$) order where the $J_2$-coupled chain spins are ferromagnetically ordered in one…
The kagomé lattice exhibits peculiar magnetic properties due to its strongly frustated cristallographic structure, based on corner sharing triangles. For nearest neighbour antiferromagnetic Heisenberg interactions there is no Neel ordering at zero temperature both for quantum and classical s pins. We show that, due to the peculiar structure, antisymmetric Dzyaloshinsky-Moriya interactions (${\bf D} . ({\bf S}_i \times {\bf S}_j)$) are present in this latt ice. In order to derive microscopically this interaction we consider a set of localized d-electronic states. For classical spins systems, we…
We report polarized neutron scattering studies of spin-wave excitations and spin fluctuations in the S=5/2 kagome lattice antiferromagnet KFe3(OH)6(SO4)2 (jarosite). Inelastic polarized neutron scattering measurements at 10 K on a single crystal sample reveal two spin gaps, associated with in-plane and out-of-plane excitations. The polarization analysis of quasi-elastic scattering at 67 K shows in-plane spin fluctuations with XY symmetry, consistent with the disappearance of the in-plane gap above the Neel temperature T_N = 65 K. Our results suggest that jarosite is a promising candidate for s…
We study the spin-1/2 Heisenberg model in a lattice that interpolates between the triangular and the kagome lattices. The exchange interaction along the bonds of the kagome lattice is J, and the one along the bonds connecting kagome and non-kagome sites is J', so that J'=J corresponds to the triangular limit and J'=0 to the kagome one. We use variational and exact diagonalization techniques. We analyze the behavior of the order parameter for the antiferromagnetic phase of the triangular lattice, the spin gap, and the structure of the spin excitations as functions of J'/J. Our results indicate …
A simple ``brute-force'' parallelisation procedure for the computational implementation of high-order coupled cluster method (CCM) calculations is presented here. This approach is investigated and illustrated by an application of high-order CCM to the Heisenberg antiferromagnet on the Kagomé lattice with nearest- and next-nearest-neighbour bonds. Ferromagnetic next-nearest-neighbour bonds are used to stabilise a model state which contains three sublattices in which the spins make angles of 120$^{\circ}$ to each other. Ground-state results for up to approximately 10000 fundamental clusters are …
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…
A spin-1/2 Heisenberg model on honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired by Cu$_2$(pymca)$_3$(ClO$_4$), has three different antiferromagnetic exchange interactions ($J_A$, $J_B$, $J_C$) on three different sets of nearest-neighbour bonds which form a kagome superlattice. While the model is bipartite and unfrustrated, its quantum phase diagram is found to be dominated by a quantum paramagnetic phase that is best described as a spin-gapped hexagonal-singlet state. The Néel antiferromagnetic order survives only in a small…
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 study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagomé lattice with first-, second-, and third-neighbor interactions $J_1$, $J_2$, and $J_3$ by means of density matrix renormalization group. For small $J_2$ and $J_3$, this model sustains a time-reversal invariant quantum spin liquid phase. With increasing $J_2$ and $J_3$, we find in addition a $q=(0,0)$ Néel phase, a chiral spin liquid phase, a valence-bond crystal phase, and a complex non-coplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral…
Motivated by recent experiments on an S=1/2 antiferromagnet on the kagome lattice, we investigate the Heisenberg J1-J2 model with ferromagnetic J1 and antiferromagnetic J2. Classically the ground state displays Neel long range order with 12 non-coplanar sublattices. The order parameter has the symmetry of a cuboctahedron so that it fully breaks SO(3) as well as the spin-flip symmetry, and we expect from the latter a Z2 symmetry breaking pattern. As might be expected from the Mermin-Wagner theorem in two dimensions, the SO(3) symmetry is restored by thermal fluctuations while the Z2 symmetry br…
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.
The layered compound with distorted Kagome nets, Dy3Ru4Al12, was previously reported to undergo antiferromagnetic ordering below (TN=) 7 K, based on investigations on single crystals. Here, we report the results of our investigation of ac and dc magnetic susceptibility (\c{hi}), isothermal remnant magnetization (MIRM), heat-capacity, magnetocaloric effect and magnetoresistance measurements on polycrystals. The present results reveal that there is an additional magnetic anomaly around 20 K, as though the Néel order is preceded by the formation of ferromagnetic clusters. We attribute this featur…
Experimental studies of high-purity kagome-lattice antiferromagnets (KAFM) are of great importance in attempting to better understand the predicted enigmatic quantum spin-liquid ground state of the KAFM model. However, realizations of this model can rarely evade magnetic ordering at low temperatures due to various perturbations to its dominant isotropic exchange interactions. Such a situation is for example encountered due to sizable Dzyaloshinskii-Moriya magnetic anisotropy in YCu$_3$(OH)$_6$Cl$_3$, which stands out from other KAFM materials by its perfect crystal structure. We find evidence …
We discuss exact plaquette-ordered ground states of the generalized Hubbard model based on the projection operator method for several corner sharing lattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exact ground states are interpreted as Néel ordered states on the plaquette-located electrons. We demonstrate that these models also have exact edge states. We also calculate the entanglement entropy exactly in these systems.
At zero magnetic field, a series of five phase transitions occur in Co3V2O8. The Neel temperature, TN=11.4 K, is followed by four additional phase changes at T1=8.9 K, T2=7.0 K, T3=6.9 K, and T4=6.2 K. The different phases are distinguished by the commensurability of the b-component of its spin density wave vector. We investigate the stability of these various phases under magnetic fields through dielectric constant and magnetic susceptibility anomalies. The field-temperature phase diagram of Co3V2O8 is completely resolved. The complexity of the phase diagram results from the competition of di…
This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in m…
The frustrated magnet clinoatacamite, $γ$-Cu$_2$(OH)$_3$Cl, is attracting a lot of interest after suggestions that at low temperature it forms an exotic quantum state termed a Valence Bond Solid (VBS) made from dimerised Cu$^{2+}$ ($S=1/2$) spins.\cite{Lee_clinoatacamite} Key to the arguments surrounding this proposal were suggestions that the kagomé planes in the magnetic pyrochlore lattice of clinoatacamite are only weakly coupled, causing the system to behave as a quasi-2-dimensional magnet. This was reasoned from the near 95$^\circ$ angles made at the bridging oxygens that mediate exchange…
We report on a single-crystal neutron diffraction study of the evolution of the antiferromagnetic order in the heavy-fermion compound CePd$_{1-x}$Ni$_x$Al which exhibits partial geometric frustration due to its distorted Kagomé structure. The magnetic structure is found to be unchanged with a propagation vector $Q_\mathrm{AF} \approx (0.5~0~0.35)$ for all Ni concentrations $x$ up to $x_c \approx 0.14$. Upon approaching the quantum critical concentration $x_c$, the ordered moment vanishes linearly with Néel temperature $T_{\rm N}$, in good agreement with CePdAl under hydrostatic pressure. For a…
We have studied the frustrated system YBaCo4O7 generally described as an alternating stacking of Kagome and triangular layers of magnetic ions on a trigonal lattice, by single crystal neutron diffraction experiments above the Neel ordering transition. Experimental data reveals pronounced magnetic diffuse scattering, which is successfully modeled by direct Monte-Carlo simulations. Long-range magnetic correlations are found along the c-axis, due to the presence of corner-sharing bipyramids, creating quasi one-dimensional order at finite temperature. In contrast, in the Kagome layers ab-plane, th…
We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as Néel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagomé lattice, and determine parameter regions of the exact ground states.
We study quantum antiferromagnets on two-dimensional bipartite lattices. We focus on local variations in the properties of the ordered phase which arise due to the presence of inequivalent sites or bonds in the lattice structure, using linear spin wave theory and quantum Monte Carlo methods. Our primary finding is that sites with a high coordination tend to have a low ordered moment, at odds with the simple intuition of high coordination favoring more robust Neel ordering. The lattices considered are the dice lattice, which is dual to the kagome, the CaVO lattice, an Archimedean lattice with t…
The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $π$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent…
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120$^\circ$ structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can…
Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up…
A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Neel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL…
Dimensional reduction by singlet blockade in the distorted kagome magnet YCa$_3$(CrO)$_3$(BO$_3$)$_4$
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Okayama University（冈山大学）；ISIS Neutron and Muon Source, Rutherford Appleton Laboratory（卢瑟福阿普尔顿实验室ISIS中子和缪子源）
Orbital degrees of freedom mediating an interaction between spin and lattice were predicted to raise strong magnetoelectric effect, i.e. realize an efficient coupling between magnetic and ferroelectric orders. However, the effect of orbital fluctuations have been considered only in a few magnetoelectric materials, as orbital degeneracy driven Jahn-Teller effect rarely couples to polarization. Here, we explore the spin-lattice coupling in multiferroic Swedenborgites with mixed valence and Jahn-Teller active transition metal ions on a stacked triangular/Kagome lattice using infrared and dielectr…
We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the Heisenberg model) and/or if the lattice has more than one site per unit cell. To deal with these situations, we introduce a family of variational spin configurations, dubbed "regular states", which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is explicited through a gr…
Interlocked Vortex Order in the Frustrated $A_3$V$_9$Te$_{13}$ Lattice ($A$=Cs,Rb)
New Cornerstone Science Laboratory, Center for Correlated Matter, Zhejiang University（新Cornerstone科学实验室，关联物质中心，浙江大学）；School of Physics, Zhejiang University（物理学院，浙江大学）；Institute for Advanced Study in Physics, Zhejiang University（物理学高等研究院，浙江大学）
Ground states of quantum XY dipoles on the Archimedean lattices
Harvard University（哈佛大学）；Carnegie Mellon University（卡内基梅隆大学）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
