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This thesis reports on the construction and operation of an ultracold atom- based quantum simulator for studying the kagome lattice and the associated flat band. Despite a copious amount of theoretical effort to elucidate the physics of the kagome lattice, experimental kagome physics is still in its infancy. In the case of ultracold atoms, this is mainly due to considerable technical challenges involved in creating an optical kagome lattice, such as the need for active phase stabilization for bichromatic superlattices. We show that we have overcome these challenges and give a thorough account of our machine's technical details. Furthermore, we present calculations and measurements that fully characterise the kagome quantum simulator. Much of the theoretical work on the kagome lattice has focussed on its flat band. Populating flat bands with ultracold atoms has proven to be difficult and it has so far not been possible to prepare flat bands in thermodynamic equilibrium. We show a route towards studying quantum manybody physics in the flat band of the kagome lattice using negative temperatures. In addition we report, for the first time, on the creation of a negative temperature state in a triangular lattice. This thesis additionally serves to collect and consolidate theoretical research that we can directly study with our machine. In particular, we will discuss the properties of bosons in flat bands and their experimental signatures, with the aim of guiding and accelerating the near-term developments and experiments. Finally, we detail our progress towards realizing a quantum gas microscope for the kagome lattice. In this context, we present a new method for super-resolution microscopy of ultracold atoms in optical lattices.

Covalent organic frameworks (COFs) are molecule-based 2D and 3D materials that possess a wide range of mechanical and electronic properties. We have performed a joint experimental and theoretical study of the electronic structure of boroxine-linked COFs grown under ultrahigh vacuum conditions and characterized using scanning tunneling spectroscopy on Au(111) and hBN/Cu(111) substrates. Our results show that a single hBN layer electronically decouples the COF from the metallic substrate, thus suppressing substrate-induced broadening and revealing new features in the COF electronic local density of states (LDOS). The resulting sharpening of LDOS features allows us to experimentally determine the COF band gap, bandwidths, and the electronic hopping amplitude between adjacent COF bridge sites. These experimental parameters are consistent with the results of first-principles theoretical predictions.

The recently reported AV3Sb5 (A = K, Rb, Cs) family of kagome metals are candidates for unconventional superconductivity and chiral charge density wave (CDW) order; both potentially arise from nested saddle points in their band structures close to the Fermi energy. Here, we use chemical substitution to introduce holes into CsV3Sb5 and unveil an unconventional coupling of the CDW and superconducting states. Specifically, we generate a phase diagram for CsV3Sb5−xSnx that illustrates the impact of hole doping the system and lifting the nearest van Hove singularity toward and above EF. Superconductivity exhibits a nonmonotonic evolution with the introduction of holes, resulting in two “domes” peaked at 3.6 and 4.1 K and the rapid suppression of three-dimensional CDW order. The evolution of CDW and superconducting order is compared with the evolution of the electronic band structure of CsV3Sb5−xSnx, where the complete suppression of superconductivity seemingly coincides with an electronlike band comprised of Sb pz orbitals pushed above EF.

In spin systems, geometrical frustration describes the impossibility of minimizing simultaneously all the interactions in a Hamiltonian, often giving rise to macroscopic ground-state degeneracies and emergent low-temperature physics. In this thesis, combining tensor network (TN) methods to Monte Carlo (MC) methods and ground-state energy lower bound approaches, we study two-dimensional frustrated classical Ising models. In particular, we focus on the determination of the residual entropy in the presence of farther-neighbor interactions in kagome lattice Ising antiferromagnets (KIAFM). In general, using MC to determine the residual entropy is a significant challenge requiring ad-hoc updates, a precise evaluation of the energy at all temperatures to allow for thermodynamic integration, and a good control of the finite-size scaling behavior. As an alternative, we turn to TNs; however, we argue that, in the presence of frustration and macroscopic ground-state degeneracy, standard algorithms fail to converge at low temperatures on the usual TN formulation of partition functions. Inspired by methods for constructing ground-state energy lower bounds, we propose a systematic way to find the ground-state local rule using linear programming. Characterizing the rules as tiles that can be tessellated to form ground states of the model gives rise to a natural contractible TN formulation of the partition function. This method provides a direct access to the ground-state properties of frustrated models and, in particular, allows an extremely precise determination of their residual entropy. We then study two models inspired by artificial spin systems on the kagome lattice with out-of-plane (OOP) anisotropy. The first model is motivated by experiments on an array of chirally coupled nanomagnets. We argue that the farther-neighbor to nearest-neighbor couplings ratios in this system are much smaller than in the dipolar case, J2/J1 being of the order of 2%. A comparison of the experimental correlations with the results of extensive TN and MC simulations shows that (1) the experimental second- and third-neighbor correlations are inverted as compared to those of a pure nearest-neighbor model at equilibrium (even with a magnetic field), and (2) second-neighbor couplings as small as 1% of the nearest-neighbor couplings will affect the spin-spin correlations even at fairly high temperatures. Motivated by dipolar coupled artificial spin systems, we turn to the progressive lifting of the ground-state degeneracy of the KIAFM. We provide a detailed study of the ground-state phases of this model with up to third neighbor interactions, for arbitrary J2, J3 such that J1 >> J2, J3, obtaining exact results for the ground-state energies. When all couplings are antiferromagnetic, we exhibit three macroscopically degenerate ground-state phases and establish their residual entropy using our TN approach. Furthermore, in the phase corresponding to the dipolar KIAFM truncated to third neighbors, we use the ground-state tiles to establish the existence of a mapping to the ground-state manifold of the triangular Ising antiferromagnet.

Based on the density functional theory, we examine the origin of ferromagnetism in the Weyl semimetal Co3Sn2S2 using different types of response theories. We argue that the magnetism of Co3Sn2S2 has a dual nature and bears certain aspects of both itineracy and localization. On the one hand, the magnetism is soft, where the local magnetic moments strongly depend on temperature and the angles formed by these moments at different Co sites of the kagome lattice, as expected for itinerant magnets. On the other hand, the picture of localized spins still remains adequate for the description of the local stability of the ferromagnetic (FM) order with respect to the transversal spin fluctuations. For the latter purposes, we employ two approaches, which provide quite different pictures for interatomic exchange interactions: the regular magnetic force theorem and a formally exact theory based on the calculation of the inverse response function. The exact theory predicts Co3Sn2S2 to be a three-dimensional ferromagnet with the strongest interaction operating between next-nearest neighbors in the adjacent kagome planes. The ligand states are found to play a very important role by additionally stabilizing the FM order. When the local moments decrease, the interplane interactions sharply decrease, first causing the FM order to become quasi-two-dimensional, and then making it unstable with respect to the spin-spiral order propagating perpendicular to the kagome plane. The latter instability is partly contributed by the states at the Fermi surface and may be relevant to the magnetic behavior of Co3Sn2S2 near the Curie temperature. Peculiarities of the half-metallic ferromagnetism in Co3Sn2S2 are also discussed. © 2022 American Physical Society. I.V.S. acknowledges useful communication with V. P. Antropov, drawing our attention to Refs. on validity of the Heisenberg model for transition metals, S. Okamoto on details of Ref., S. Streib on the relation between exchange parameters in MFT and the exact approach, and Y. Anahory, drawing our attention to the phenomenon of exchange bias in . The work was supported by the project RSF 20-62-46047 of the Russian Science Foundation in the part of conventional DFT calculations and the program AAAA-A18-118020190095-4 (Quantum) of the Russian Ministry of Science and Higher Education in the part of construction and analysis of microscopic models of interatomic exchange interactions.

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV$_3$Sb$_5$. The spectra around $\bar{K}$ is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below $E_{\rm F}$. The peak-dip-hump lineshape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to $E_{\rm F}$ in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of $\sim$0.4 meV is observed on both the electron band around $\bar{\Gamma}$ and the flat band around $\bar{K}$, implying the multiband superconductivity. The finite density of states (DOS) at $E_{\rm F}$ in the CDW phase are most likely in favor of the emergence of multiband superconductivity, particularly the enhanced DOS associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity., Comment: 6 pages, 4 figures, PRL in press

Averievite-type compounds with the general formula (MX)[Cu5O2(TO4)], where M = alkali metal, X = halogen and T = P, V, have been synthesized by crystallization from gases and structurally characterized for six different compositions: 1 (M = Cs, X = Cl, T = P), 2 (M = Cs, T = V), 3 (M = Rb, T = P), 4 (M = K, X = Br, T = P), 5 (M = K, T = P) and 6 (M = Cu, T = V). The crystal structures of the compounds are based upon the same structural unit, the layer consisting of a kagome lattice of Cu2+ ions and are composed from corner-sharing (OCu4) anion-centered tetrahedra. Each tetrahedron shares common corners with three neighboring tetrahedra, forming hexagonal rings, linked into the two-dimensional [O2Cu5]6+ sheets parallel to (001). The layers are interlinked by (T5+O4) tetrahedra (T5+ = V, P) attached to the bases of the oxocentered tetrahedra in a “face-to-face” manner. The resulting electroneutral 3D framework {[O2Cu5](T5+O4)2}0 possesses channels occupied by monovalent metal cations M+ and halide ions X−. The halide ions are located at the centers of the hexagonal rings of the kagome nets, whereas the metal cations are in the interlayer space. There are at least four different structure types of the averievite-type compounds: the P-3m1 archetype, the 2 × 2 × 1 superstructure with the P-3 space group, the monoclinically distorted 1 × 1 × 2 superstructure with the C2/c symmetry and the low-temperature P21/c superstructure with a doubled unit cell relative to the high-temperature archetype. The formation of a particular structure type is controlled by the interplay of the chemical composition and temperature. Changing the chemical composition may lead to modification of the structure type, which opens up the possibility to tune the geometrical parameters of the kagome net of Cu2+ ions.

The family of layered vanadates, arsenates, and phosphates is discussed in terms of a modular concept. The group includes minerals vésignéite and bayldonite, and a number of synthetic analogous and modifications which are not isotypic, but their crystal structures comprise similar blocks (modules) consisting of a central octahedral layer filled by atoms of d elements (Mn, Ni, Cu, or Co) and adjacent [VO4], [AsO4], or [PO4] tetrahedra. The octahedral layers are based on the close-packing of oxygen atoms. Within these layers having the same anionic substructure, the number and distribution of octahedral voids are different. In the crystal structures of compounds participating in the polysomatic series, these blocks alternate with various other structural fragments. These circumstances define the row of structurally-related vanadates, arsenates, and phosphates as a mero-plesiotype series. Most of the series members exhibit magnetic properties, representing two-dimensional antiferromagnets or frustrated magnets.

This thesis presents results of studies of novel compounds modeling complex fundamental physics phenomena. Cu2OSO4 is a copper based magnetic Mott Insulator system, where spin half magnetic moments form a new type of lattice. These intrinsically quantum pins are exhibiting atypical magnetic order and spin dynamics. The recent success in the growth of large single crystals of Cu2OSO4 enabled to perform measurements probing its static and fluctuating properties. The peculiarity of this sample is that its atoms are forming layers, with a geometry close to the intensively studied Kagomé lattice, but with a third of its spins replaced by dimers. This quantum magnetism system has been probed in its bulk, by the means of heat capacity and DC-susceptibility measurements, revealing a transition to a magnetically long range ordered state upon cooling, the details of which are revealed by neutron scattering. Single crystal inelastic neutron scattering shed light on the spin-dynamics in the system, with clear spin waves appearing as fluctuations around the peculiar ground state of the system: a 120 degrees spin configuration where the magnetic moment of the spin-dimer causes the sample to be globally ferrimagnetic. The presented results indicate that Cu2OSO4 represents a new type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored. The magnetic excitations of the compound can be modeled by a yet-to-be-understood internal effective mean-field that no simple magnetic coupling seems to reproduce. K2Ni2(SO4)3 is another compound that allows for the existence of non-trivial topological phases. This thesis presents results of the study of the unusual magnetic behavior of K2Ni2(SO4)3. No clear sign of well-established magnetic long range order has been observed down to dilution temperatures. Neutron scattering reveals the details of the competition between frustration and fluctuations that prevent order from settling in. Low temperature spin excitations take the form of a continuum at 500 mK, but also of broad, energy independent continua at higher temperatures. Bulk and neutron scattering measurements are put in perspective and linked together with a view to building up a better understanding of how quantum spin liquids can be stabilized in general, and in particular in this model compound. Finally, the last contribution of this thesis to the field of condensed matter physics regards the establishment of a state-of-the-art technique to fit heat capacity and unit cell volume of samples to try and make the extraction of magnetic information from specific heat measurements more robust. This newly-developed technique consists in modeling lattice contributions with better accuracy by using data from multiple experimentally accessible quantities to consolidate the fitting scheme. This method has been cautiously applied to several compounds at the forefront of research in experimental physics.

Fractons are topological quasiparticles with limited mobility. While there exists a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the more common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fracton-like excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a 2D cut of a 3D cubic lattice model. Our extensive classical Monte-Carlo simulations further indicate a crossover into a low temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte-Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures., Comment: 21 pages, 23 figures

We investigate the nature of the ground state of the spin-12 Heisenberg antiferromagnet on the shuriken lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo (mVMC), and pseudofermion/pseudo-Majorana functional renormalization group (PFFRG/PMFRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

Graphical abstract, Highlights • Structure parameters and electronic properties of graphene with kagome lattice structure is calculated. • Various XC and dispersion correction methods are used and similar results are obtained. • Pristine graphene with kagome lattice structure shows very small magnetic properties. • A kagome flat-band structure is observed near the EF. • High DOS at flat-band is mostly consisting of pz orbital and also dxz and dyz orbital contributions., In this paper, the electronic properties of a carbon allotrope, graphene with a kagome lattice structure, are investigated. Spin-polarized density functional theory (DFT) calculations with Grimme dispersion corrections were done. Bond lengths, electronic band structure, and projected density of states were calculated. Electronic band structure calculations show kagome flat-band formation with higher d-orbital contributed bonding behavior than the pristine graphene structure. The structural parameters and electronic band results of this 2D carbon allotrope show wider possible usage in many applications from desalination membranes to possible high-temperature superconductors.

We consider interaction energies $E_f[L]$ between a point $O\in \mathbb{R}^d$, $d\geq 2$, and a lattice $L$ containing $O$, where the interaction potential $f$ is assumed to be radially symmetric and decaying sufficiently fast at infinity. We investigate the conservation of optimality results for $E_f$ when integer sublattices $k L$ are removed (periodic arrays of vacancies) or substituted (periodic arrays of substitutional defects). We consider separately the non-shifted ($O\in k L$) and shifted ($O\not\in k L$) cases and we derive several general conditions ensuring the (non-)optimality of a universal optimizer among lattices for the new energy including defects. Furthermore, in the case of inverse power laws and Lennard-Jones type potentials, we give necessary and sufficient conditions on non-shifted periodic vacancies or substitutional defects for the conservation of minimality results at fixed density. Different examples of applications are presented, including optimality results for the Kagome lattice and energy comparisons of certain ionic-like structures., 21 pages. 6 figures

By using first-principles calculations we put forward the Cu-dicyanoanthracene lattice as a platform to investigate strong electronic correlations in the family of Kagome metal-organic frameworks. We show that the low-energy model is composed by molecular orbitals which arrange themselves in a typical Kagome lattice at n = 2/3 filling, where the Fermi level lies at the Dirac point. The Coulomb interaction matrix expressed in this molecular orbitals basis, as obtained by large-scale constrained random-phase approximation calculations, is characterized by local U and non-local U ′ parameters exceeding more than ten times the Kagome bandwidth. For such Kagome systems, our findings suggest the possible emergence of peculiar electron–electron collective phenomena, such as an exotic valence bond solid order characterized by modulated bond strengths.

We report an ultra-high vacuum low-temperature scanning tunneling microscopy (STM) study of the C60 monolayer grown on Cd(0001). Individual C60 molecules adsorbed on Cd(0001) may exhibit a bright or dim contrast in STM images. When deposited at low temperatures close to 100 K, C60 thin films present a curved structure to release strain due to dominant molecule–substrate interactions. Moreover, edge dislocation appears when two different wavy structures encounter each other, which has seldomly been observed in molecular self-assembly. When growth temperature rose, we found two forms of symmetric kagome lattice superstructures, 2 × 2 and 4 × 4, at room temperature (RT) and 310 K, respectively. The results provide new insight into the growth behavior of C60 films.

[EN] We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in kagome and modified kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices with different valley Chern numbers. By means of a plane wave expansion method and the multiple scattering theory for periodic and finite systems, respectively, we computed the Berry curvature, the band inversion, mode shapes, and edge modes in plate systems. We also find that appropriate multipoint excitations in finite system gives rise to propagating waves along a one-sided path only., N.L and J.V.A. acknowledges financial support from MINECO grant FIS2015-64886-C5-5-P. N.L. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through The María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), and also hospitality from the Universitat Jaume I in Castellon where part of this work was done. D.T. acknowledges financial support through the “Ramón y Cajal” fellowship under grant number RYC-2016-21188. P.S.-J. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through Grant No. FIS2015-65706-P (MINECO/FEDER). J.C. acknowledges the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA and from the MINECO through a Ramón y Cajal grant (Grant No. RYC-2015-17156).

In the field of quantum magnetism, the advent of numerous spin-orbit assisted Mott insulating compounds, such as the family of Kitaev materials, has led to a growing interest in studying general spin models with non-diagonal interactions that do not retain the SU(2) invariance of the underlying spin degrees of freedom. However, the exchange frustration arising from these non-diagonal and often bond-directional interactions for two- and three-dimensional lattice geometries poses a serious challenge for numerical many-body simulation techniques. In this paper, we present an extended formulation of the pseudo-fermion functional renormalization group that is capable of capturing the physics of frustrated quantum magnets with generic (diagonal and off-diagonal) two-spin interaction terms. Based on a careful symmetry analysis of the underlying flow equations, we reveal that the computational complexity grows only moderately, as compared to models with only diagonal interaction terms. We apply the formalism to a kagome antiferromagnet which is augmented by general in-plane and out-of-plane Dzyaloshinskii-Moriya (DM) interactions, as argued to be present in the spin liquid candidate material herbertsmithite. We calculate the complete ground state phase diagram in the strength of in-plane and out-of-plane DM couplings, and discuss the extended stability of the spin liquid of the unperturbed kagome antiferromagnet in the presence of these couplings., Comment: 19 pages, 6 figures

Averievite-type compounds with the general formula (MX)[Cu5O2(TO4)], where M = alkali metal, X = halogen and T = P, V, have been synthesized by crystallization from gases and structurally characterized for six different compositions: 1 (M = Cs; X = Cl; T = P), 2 (M = Cs; X = Cl; T = V), 3 (M = Rb; X = Cl; T = P), 4 (M = K; X = Br; T = P), 5 (M = K; X = Cl; T = P) and 6 (M = Cu; X = Cl; T = V). The crystal structures of the compounds are based upon the same structural unit, the layer consisting of a kagome lattice of Cu2+ ions and are composed from corner-sharing (OCu4) anion-centered tetrahedra. Each tetrahedron shares common corners with three neighboring tetrahedra, forming hexagonal rings, linked into the two-dimensional [O2Cu5]6+ sheets parallel to (001). The layers are interlinked by (T5+O4) tetrahedra (T5+ = V, P) attached to the bases of the oxocentered tetrahedra in a “face-to-face” manner. The resulting electroneutral 3D framework {[O2Cu5](T5+O4)2}0 possesses channels occupied by monovalent metal cations M+ and halide ions X−. The halide ions are located at the centers of the hexagonal rings of the kagome nets, whereas the metal cations are in the interlayer space. There are at least four different structure types of the averievite-type compounds: the P-3m1 archetype, the 2 × 2 × 1 superstructure with the P-3 space group, the monoclinically distorted 1 × 1 × 2 superstructure with the C2/c symmetry and the low-temperature P21/c superstructure with a doubled unit cell relative to the high-temperature archetype. The formation of a particular structure type is controlled by the interplay of the chemical composition and temperature. Changing the chemical composition may lead to modification of the structure type, which opens up the possibility to tune the geometrical parameters of the kagome net of Cu2+ ions.

A new mineral, dioskouriite, CaCu4Cl6(OH)4∙4H2O, represented by two polytypes, monoclinic (2M) and orthorhombic (2O), which occur together, was found in moderately hot zones of two active fumaroles, Glavnaya Tenoritovaya and Arsenatnaya, at the Second scoria cone of the Northern Breakthrough of the Great Tolbachik Fissure Eruption, Tolbachik volcano, Kamchatka, Russia. Dioskouriite seems to be a product of the interactions involving high-temperature sublimate minerals, fumarolic gas and atmospheric water vapor at temperatures not higher than 150 &deg, C. It is associated with avdoninite, belloite, chlorothionite, eriochalcite, sylvite, halite, carnallite, mitscherlichite, chrysothallite, sanguite, romanorlovite, feodosiyite, mellizinkalite, flinteite, kainite, gypsum, sellaite and earlier hematite, tenorite and chalcocyanite in Glavnaya Tenoritovaya and with avdoninite and earlier hematite, tenorite, fluorophlogopite, diopside, clinoenstatite, sanidine, halite, aphthitalite-group sulfates, anhydrite, pseudobrookite, powellite and baryte in Arsenatnaya. Dioskouriite forms tabular, lamellar or flattened prismatic, typically sword-like crystals up to 0.01 mm &times, 0.04 mm &times, 0.1 mm combined in groups or crusts up to 1 &times, 2 mm2 in area. The mineral is transparent, bright green with vitreous luster. It is brittle, cleavage is distinct. The Mohs hardness is ca. 3. Dmeas is 2.75(1) and Dcalc is 2.765 for dioskouriite-2O and 2.820 g cm&minus, 3 for dioskouriite-2M. Dioskouriite-2O is optically biaxial (+), &alpha, = 1.695(4), &beta, = 1.715(8), &gamma, = 1.750(6) and 2Vmeas. = 70(10)&deg, The Raman spectrum is reported. The chemical composition (wt%, electron microprobe data, H2O calculated by total difference, dioskouriite-2O/dioskouriite-2M) is: K2O 0.03/0.21, MgO 0.08/0.47, CaO 8.99/8.60, CuO 49.24/49.06, Cl 32.53/32.66, H2O(calc.) 16.48/16.38, O=Cl &minus, 7.35/&minus, 7.38, total 100/100. The empirical formulae based on 14 O + Cl apfu are: dioskouriite-2O: Ca1.04(Cu4.02Mg0.01)&Sigma, 4.03[Cl5.96(OH)3.90O0.14]&Sigma, 10∙4H2O, dioskouriite-2M: (Ca1.00K0.03)&Sigma, 4.03(Cu4.01Mg0.08)&Sigma, 4.09[Cl5.99(OH)3.83O0.18]&Sigma, 10∙4H2O. Dioskouriite-2M has the space group P21/c, a = 7.2792(8), b = 10.3000(7), c = 20.758(2) &Aring, &beta, = 100.238(11)&deg, V = 1531.6(2) &Aring, 3 and Z = 4, dioskouriite-2O: P212121, a = 7.3193(7), b = 10.3710(10), c = 20.560(3) &Aring, V = 1560.6(3) &Aring, 3 and Z = 4. The crystal structure (solved from single-crystal XRD data, R = 0.104 and 0.081 for dioskouriite-2M and -2O, respectively) is unique. The structures of both polytypes are based upon identical BAB layers parallel to (001) and composed from Cu2+-centered polyhedra. The core of each layer is formed by a sheet A of edge-sharing mixed-ligand octahedra centered by Cu(1), Cu(2), Cu(3), Cu(5) and Cu(6) atoms, whereas distorted Cu(4)(OH)2Cl3 tetragonal pyramids are attached to the A sheet on both sides, along with the Ca(OH)2(H2O)4Cl2 eight-cornered polyhedra, which provide the linkage of the two adjacent layers via long Ca&minus, Cl bonds. The Cu(4) and Ca polyhedra form the B sheet. The difference between the 2M and 2O polytypes arises as a result of different stacking of layers along the c axis. The cation array of the layer corresponds to the capped kagom&eacute, lattice that is also observed in several other natural Cu hydroxychlorides: atacamite, clinoatacamite, bobkingite and avdoninite. The mineral is named after Dioskouri, the famous inseparable twin brothers of ancient Greek mythology, Castor and Polydeuces, the same in face but different in exercises and achievements, the name is given in allusion to the existence of two polytypes that are indistinguishable in appearance but different in symmetry, unit cell configuration and XRD pattern.

The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band. The corresponding excitations can be localized on loops in real space and have been coined "localized magnons". Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them. Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice. We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations. The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field. We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM). For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures., Comment: published version; 17 pages of text including 10 figures and Ukrainian abstract

This paper details the design, manufacture and testing of an adaptive structure based on the kagome lattice geometry – a pattern with well documented interesting structural characteristics. The structure is used to produce in-plane travelling waves of variable length and speed in a flat surface. The geometry and dimensions, as well as the location and compliance of boundary conditions, were optimized numerically, and a pneumatically-actuated working demonstrator was manufactured. Static and dynamic photogrammetric and force measurements were taken. The structure was found to be capable of producing dynamic planar waveforms of variable wavelength with large strains. The lattice structure was then surfaced with a pre-tensioned membrane skin allowing these waveforms to be produced over a continuous plane.

Frustrated magnets gain a lot of interest due to promise of states with exotic properties, such as spinons in quantum spin liquids, emergent electrodynamics in quantum spin ices, and strong quantum effects in long-range ordered systems. Magnetic frustration is a situation where classical energy cannot be minimized for all interactions simultaneously, and different phases may be very competitive, or even degenerate. Such competition can either result in ordered states with significant quantum effects or it can completely destroy long-range order. Frustration in these systems can be induced either through geometry of the lattice or through anisotropic interactions.Very often three-magnon interactions become allowed in frustrated magnets. Since magnons are bosons, as long as kinematic conditions are satisfied (energy and momentum conservation), magnons acquire finite lifetime from decaying into two magnons. There are two main ways to achieve three-magnon interaction: noncollinear ground state of isotropic model or anisotropic interactions.We performed spin-wave theory calculations for easy-plane models, where frustration and magnon decays are induced with out-of-plane magnetic field. Thus, in easy-plane honeycomb and triangular antiferromagnets out-of-plane magnetic field makes the spins cant out of the plane, forming highly non-collinear structure, and affects magnon spectrum providing kinematic conditions for magnon decays. We also studied a ferromagnet on kagome lattice with Dzyaloshinkii-Moriya interactions. As we found out, the anisotropic interactions do not affect the ground state, but they affect magnon spectrum and magnon interactions depending on the direction of the magnetic moment, which can be controlled externally. This system is of interest because magnons on kagome lattice are known to exhibit topological properties. Strong magnon interactions, however, put validity of quasiparticle picture in those systems to question.As it turns out even finding ground states and excitations of anisotropic models is not a trivial task. In honeycomb system with bond-dependent interactions, so-called Kitaev-Heisenberg model, we were able to estimate magnon decay rate which matched numerics of my coauthors. We explored the same model on triangular lattice and found regions of quantum spin liquid and peculiarities of magnon spectrum, such as hidden accidental degeneracies and unexpectedly small quantum corrections to average magnetization.

It is noted that the pair correlation matrix $\hat{\chi}$ of the nearest neighbor Ising model on periodic three-dimensional ($d=3$) kagome-like lattices of corner-sharing triangles can be calculated partially exactly. Specifically, a macroscopic number $1/3 \, N+1$ out of $N$ eigenvalues of $\hat{\chi}$ are degenerate at all temperatures $T$, and correspond to an eigenspace $\mathbb{L}_{-}$ of $\hat{\chi}$, independent of $T$. Degeneracy of the eigenvalues, and $\mathbb{L}_{-}$ are an exact result for a complex $d=3$ statistical physical model. It is further noted that the eigenvalue degeneracy describing the same $\mathbb{L}_{-}$ is exact at all $T$ in an infinite spin dimensionality $m$ limit of the isotropic $m$-vector approximation to the Ising models. A peculiar match of the opposite $m=1$ and $m\rightarrow \infty$ limits can be interpreted that the $m\rightarrow\infty$ considerations are exact for $m=1$. It is not clear whether the match is coincidental. It is then speculated that the exact eigenvalues degeneracy in $\mathbb{L}_{-}$ in the opposite limits of $m$ can imply their quasi-degeneracy for intermediate $1 \leqslant m < \infty$. For an anti-ferromagnetic nearest neighbor coupling, that renders kagome-like models highly geometrically frustrated, these are spin states largely from $\mathbb{L}_{-}$ that for $m\geqslant 2$ contribute to $\hat{\chi}$ at low $T$. The $m\rightarrow\infty$ formulae can be thus quantitatively correct in description of $\hat{\chi}$ and clarifying the role of perturbations in kagome-like systems deep in the collective paramagnetic regime. An exception may be an interval of $T$, where the order-by-disorder mechanisms select sub-manifolds of $\mathbb{L}_{-}$., Comment: 7 pages, 2 figures

The solid solution Cs2-xRbxSnCu3F12 (x = 0, 0.5, 1.0, 1.5) has been investigated crystallographically between 100 and 300 K using synchrotron X-ray powder diffraction and, in the case of x = 0, neutron powder diffraction., Comment: 14 pages, 9 figures

Linear algebra methods for determining modes of kinematic and static indeterminacy in jointed frames are extended to reveal modes of compliance in otherwise rigid assemblies. These modes are extracted from a structural model, based on finite elements, via a singular value decomposition and yield the ways in which a structure can be most easily deformed. This modal approach also allows for the formulation of a reduced-order structural model, whereby relevant modes are selected and used as the basis for the optimisation of a complaint structure. The method detailed is shown to be a useful design tool, demonstrated by its application to a structure based on the Kagome lattice geometry. For certain frameworks, first order effects produce tightening under actuation. As a result, a scheme to adjust the modes to take nonlinear effects into account is also given.

© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. In the present work, we directly visualize the multi-quanta cages (MQCs) consisting of the giant vortices pinned by the elongated antidots using low-temperature scanning Hall probe microscopy. The periodic but sufficiently isolated MQCs, observed at various magnetic fields, are in a good agreement with the simulated vortex states based on the time-dependent Ginzburg-Landau (tdGL) equations. Due to the competition between the interstitial vortices and the pinned giant vortices, the formation and collapse of the MQCs can be tuned by varying magnetic field. The experimental statistics of the interstitial vortices confined in the MQCs show that the interstitial vortex patterns become more disordered at higher magnetic fields. The stability of the degenerate vortex states and the multi-quanta confinement effects under an external current are also investigated by using the tdGL simulations. The splitting of the free energy of the degenerate vortex states indicates that applying external current can eliminate parts of the degenerate vortex states. ispartof: NEW JOURNAL OF PHYSICS vol:20 issue:9 status: published

application/pdf, 論文(Article), The magnetic structure of geometrically frustrated system Co₂Cl(OH)₃ is determined by comparison with the observed proton NMR spectrum and the numerical calculated ones of various magnetic models. The best fit model structure is that the magnetic moments in the triangular plane are parallel to the principal axis of local crystal field, and the magnetic moments in the kagome lattice plane are random disorder in a-b plane, of which angle is almost intermediate between the principal axis of local field and the direction to body center in the tetrahedra lattice. The coexistence of ferromagnetic order moments in the triangular plane and the random disorder moments in the kagome plane is consistent with the results of other measurements by Zheng et al. However, the directions of magnetic moments in both triangular and kagome plane are not the directions to the body center of tetrahedron as characteristic in "spin ice" magnetic structure. Our result suggests that the transition metal compound Co₂Cl(OH)₃ is different from the "spin ice" in magnetic structure, although it is similar to rare earth pyrochlores in crystal structure.

application/pdf, 論文(Article), NMR studies are carried out at low temperature on ⁵⁹Co and ¹H nuclei of geometrically frustrated system Co₂Cl(OH)₃. Long range ordered ferromagnetic moments on triangular lattice plane coexist microscopically with disordered moments on kagome lattice plane whose moment direction is not ordered. Although the disordered moments freeze within the NMR observation time, 10⁻⁴s,at low temperature, the frozen moments begin to fluctuate with increasing temperature. Up to 4.2K (0.4Tc),the magnitude of the ferromagnetically ordered moments is independent of temperature.

In this work we investigated the critical properties of the anti-ferromagnetic XY model on a two dimensional Kagome lattice under single-ion easy-axes anisotropy. Employing the mean field theory, we found that this model shows a second order phase transition from disordered to all-in all-out state for any value of anisotropy.

The collaboration between the University of St Andrews and Moscow State University was funded by a Royal Society International Exchanges grant, in collaboration with the Russian Foundation for Basic Research (12-03-92604). Lewis Downie thanks the EPSRC for a Ph.D. studentship via a Doctoral Training grant (EP/P505097/1). This work was carried out with the support of the Diamond Light Source, beamtime application EE7980. Alexandre Vasiliev acknowledges support of RFBR through grants Numbers 13-02-00174, 14-02-92002 and 14-02-92693. Two new members of the A2B′Cu3F12 family of kagome-related materials have been prepared, in order to further understand the crystal-chemical relationships, phase transitions and magnetic behaviour within this family of potentially frustrated S = ½ two-dimensional quantum magnets. Cs2TiCu3F12 adopts a crystal structure with the ideal kagome lattice topology (space group R m) at ambient temperature. Diffraction studies reveal different symmetry-lowering structural phase transitions in single crystal and polycrystalline forms at sub-ambient temperatures, with the single crystal form retaining rhombohedral symmetry and the powder form being monoclinic. In both cases, long-range antiferromagnetic order occurs in the region 16–20 K. Rb2TiCu3F12 adopts a distorted triclinic structure even at ambient temperatures. Publisher PDF

Topological insulators have attracted abundant attention for a variety of reasons-notably, the possibility for lossless energy transport through edge states "protected" against disorder. Topological effects such as the quantum Hall state can be induced through a gauge field, which is, however, hard to create in practice, especially for charge-neutral particles. One way to induce an effective gauge potential is through a dynamic, time-periodic modulation of the lattice confining such particles. In this way, the Haldane quantum Hall effect was recently observed in a cold-atom system. Here, we show how this same effect can be induced for light confined to a lattice of identical optical resonators, using an on-site modulation of the resonant frequencies. In this system, coupled-mode analysis shows the presence of one-direction edge states immune to backscattering losses. We also discuss possible realizations of the model, which could enable slow-light devices of unprecedented quality. (C) 2016 Optical Society of America

This thesis deals with the physics of magnetic systems in an external field and when frustration, arising either from the geometry or from competing interations, is present. We have studied several models in low dimensions, where the effects of the quantum fluctuations are more important and can lead to the apparition of new intersting quantum phases. This manuscript is divided in three parts, each one being dedicated to a given model. In the first two parts, we consider two one-dimensional spin tube models, respectively made of three and four coupled spin chains, that we study by using various analytical and numerical methods. We show that, beyond the appearance of magnetization plateaux, a rich physics can emerge, with the role of the non magnetic modes for the first model, or, in the second case, the consequences of a continuous degeneracy at the classical level on the quantum phase diagram. In the third part, we use numerical Quantum Monte-Carlo simulations to study an anisotropic spin model on the two-dimensional Kagomé lattice, designed for the search of topological phases. We obtain the phase diagram on one of the magnetization plateaux of this model, and use this example to discuss the relevance of the computation of the entanglement entropies in order to identify phases in numerical simulations.; Les travaux présentés dans cette thèse concernent l'étude des systèmes magnétiques sous champ pour lesquels une frustration, géométrique ou due à des interactions en compétition, est présente. Nous avons pour cela considéré différents types de modèles en basses dimensions, où les effets des fluctuations quantiques sont renforcés et permettent ainsi l'apparition de nouvelles phases quantiques intéressantes. Ce travail est organisé en trois parties, chacune d'entre elles correspondant à l'étude d'un modèle particulier. Dans les deux premières, nous nous intéressons à deux modèles unidimensionnels de tubes de spin, respectivement composés de trois et quatres chaînes de spin, que nous abordons à l'aide de plusieurs techniques analytiques et numériques. Nous montrons comment, au-delà de la présence de plateaux d'aimantation, une physique riche peut émerger, avec notamment le rôle des modes non magnétiques pour le premier modèle ou, pour le second, les conséquences d'une dégénérescence continue au niveau classique sur le diagramme de phases quantiques. Dans la troisième partie, nous étudions par des simulations de Monte-Carlo Quantique un modèle possédant une anisotropie de spin sur le réseau bidimensionnel Kagomé, proposé pour la recherche de phases topologiques. Nous obtenons le diagramme de phases sur un des plateaux d'aimantation de ce modèle, et utilisons cet exemple pour discuter la pertinence de l'utilisation des entropies d'intrication comme outil d'identification de différentes phases dans des simulations numériques.

We provide strong numerical evidence, using improved variational wave functions, for a ground state with vanishing spin gap in the spin-$1/2$ quantum Heisenberg model on the kagome lattice. Starting from the algebraic $U(1)$ Dirac spin liquid state proposed by Y. Ran $et al.$ [Phys. Rev. Lett. $98$, $117205$ ($2007$)] and iteratively applying a few Lanczos steps, we compute the lowest $S=2$ excitation constructed by exciting spinons close to the Dirac nodes. Our results are compatible with a vanishing spin gap in the thermodynamic limit and in consonance with a power-law decay of long distance spin-spin correlations in real space. The competition with a gapped (topological) spin liquid is discussed., Comment: 5 pages, 3 figures, 2 tables. Published version

The hole-doped kagome lattice of Cu${}^{2+}$ ions in LaCuO${}_{2.66}$ was investigated by nuclear quadrupole resonance, electron spin resonance, electrical resistivity, bulk magnetization, and specific-heat measurements. For temperatures above $\ensuremath{\sim}180$ K, the spin and charge properties show an activated behavior suggestive of a narrow-gap semiconductor. At lower temperatures, the results indicate an insulating ground state which may or may not be charge ordered. While the frustrated spins in remaining patches of the original kagome lattice might not be directly detected here, the observation of coexisting nonmagnetic sites, free spins, and frozen moments reveals an intrinsically inhomogeneous magnetism. Numerical simulations of a $\frac{1}{3}$-diluted kagome lattice rationalize this magnetic state in terms of a heterogeneous distribution of cluster sizes and morphologies near the site-percolation threshold.

We study the energy and the static spin structure factor of the ground state of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2 spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site E/J=-0.4365(2), which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations., Comment: Final published version. Main Paper (6 pages, 4 figures, 1 table) + Supplementary Material (4 pages, 8 figures)

Magnetic frustration helps destabilizing conventional Néel order at T = 0 in dimensions 2, and therefore allows the emergence of new original quantum phases. The S=1/2 Heisenberg Hamiltonian on the highly frustrated kagome lattice, which is made of corner-sharing triangles, is expected to stabilize such quantum states, including the spin liquid ones which do not break any symmetry even at T = 0. This thesis work focuses on the experimental study of two kinds of S=1/2 (Cu2+) kagome compounds using NMR and μSR local probes as well as thermodynamic measurements (magnetic susceptibility, specific heat).In Mg-herbertsmithite magnetic frustration occurs thanks to a first nearest-neighbor antiferromagnetic interaction J and is responsible for the spin liquid behavior observed down to T = J/10000. In comparison with the formerly known isostructural counterpart Zn-herbertsmithite, we showed that it shares similar physical magnetic properties while allowing sensitive structural refinements and therefore a control of the level of Cu/Mg substitutions defects. Our experiments performed on such well controlled materials allow us to investigate the origin of the dynamical relaxation in these compounds in relation with the existence of interplane spins defects. Kapellasite and haydeite possess both ferromagnetic (J1) and antiferromagnetic (Jd) interactions. They offer the possibility to explore the phase diagram generated by such competing interactions on the kagome lattice. For kapellasite, our μSR experiments evidenced a spin liquid character down to T ≈ J1/1000. We tracked the temperature dependence of the magnetic susceptibility probed by 35Cl-NMR as well as of the specific heat, from which the ratio Jd/J1 = 0.85 can be evaluated. This ratio locates the ground-state of kapellasite to be within an original non-coplanar spin phase described by 12 magnetic sublattices and called cuboc2. Magnetic exchanges in haydeite locate its ground-state within the ferromagnetic phase. Both our local and thermodynamic measurements point to a partial ferromagnetic transition at T = 4 K. This study confirms the relevance of the frustrated quantum kagome lattice to stabilize original quantum phases and suggests the existence of a new spin liquid phase, distinct from the one expected for antiferromagnetically coupled spins.; La déstabilisation de l’ordre antiferromagnétique de Néel au profit de nouvelles phases quantiques à température nulle à deux dimensions est envisageable grâce au phénomène de frustration magnétique. Le modèle théorique de spins Heisenberg S=1/2 répartis sur le réseau bidimensionnel frustré kagome, constitué de triangles joints uniquement par leurs sommets, est susceptible de stabiliser des phases quantiques originales de liquides de spin, qui ne présentent aucune brisure de symétrie à T = 0. Cette thèse a été consacrée à l’étude expérimentale de deux types de composés de spins S=1/2 (Cu2+) à géométrie kagome à l’aide de techniques spectroscopiques locales, la RMN et la μSR, ainsi que de mesures thermodynamiques (susceptibilité magnétique, chaleur spécifique). Dans Mg-herbertsmithite, la frustration est générée par une interaction d’échange premiers voisins antiferromagnétique J et est responsable d’un comportement liquide de spin jusqu’à des températures de l’ordre de J/10000. Par rapport au composé isostructural antérieur, Zn-herbertsmithite, nous avons montré qu’il possédait des propriétés physiques similaires tout en permettant une caractérisation fine du taux de défauts de substitutions Cu/Mg. Nos expériences réalisées à partir d’échantillons contrôlés permettent d’étudier finement l’origine des plateaux de relaxation observés en μSR à basse température en lien avec l’existence des défauts de spins interplans. La kapellasite et l’haydéite possèdent des interactions ferromagnétiques (J1) et antiferromagnétiques (Jd), offrant la possibilité d’explorer le diagramme de phases générées par la compétition de ces interactions sur le réseau kagome. Pour la kapellasite, nos mesures de μSR démontrent le caractère liquide de spin jusqu’à T ≈ J1/1000. La dépendance en température de la susceptibilité magnétique sondée par RMN du 35Cl ainsi que de la chaleur spécifique permettent d’évaluer le rapport Jd/J1 = 0.85, qui localise classiquement son fondamental au sein d’une phase originale de spins non coplanaires à 12 sous-réseaux appelée cuboc2. Les interactions présentes dans l’haydéite localisent son fondamental au sein de la phase ferromagnétique, en bon accord avec nos mesures qui indiquent une transition partielle à caractère ferromagnétique à T = 4 K. Cette étude confirme la pertinence du réseau kagome frustré pour la stabilisation de phases quantiques originales et démontre l’existence d’une nouvelle phase liquide de spin sur ce réseau, distincte de celle attendue pour des spins couplés antiferromagnétiquement.

Magnetic frustration helps destabilizing conventional Néel order at T = 0 in dimensions 2, and therefore allows the emergence of new original quantum phases. The S=1/2 Heisenberg Hamiltonian on the highly frustrated kagome lattice, which is made of corner-sharing triangles, is expected to stabilize such quantum states, including the spin liquid ones which do not break any symmetry even at T = 0. This thesis work focuses on the experimental study of two kinds of S=1/2 (Cu2+) kagome compounds using NMR and μSR local probes as well as thermodynamic measurements (magnetic susceptibility, specific heat).In Mg-herbertsmithite magnetic frustration occurs thanks to a first nearest-neighbor antiferromagnetic interaction J and is responsible for the spin liquid behavior observed down to T = J/10000. In comparison with the formerly known isostructural counterpart Zn-herbertsmithite, we showed that it shares similar physical magnetic properties while allowing sensitive structural refinements and therefore a control of the level of Cu/Mg substitutions defects. Our experiments performed on such well controlled materials allow us to investigate the origin of the dynamical relaxation in these compounds in relation with the existence of interplane spins defects. Kapellasite and haydeite possess both ferromagnetic (J1) and antiferromagnetic (Jd) interactions. They offer the possibility to explore the phase diagram generated by such competing interactions on the kagome lattice. For kapellasite, our μSR experiments evidenced a spin liquid character down to T ≈ J1/1000. We tracked the temperature dependence of the magnetic susceptibility probed by 35Cl-NMR as well as of the specific heat, from which the ratio Jd/J1 = 0.85 can be evaluated. This ratio locates the ground-state of kapellasite to be within an original non-coplanar spin phase described by 12 magnetic sublattices and called cuboc2. Magnetic exchanges in haydeite locate its ground-state within the ferromagnetic phase. Both our local and thermodynamic measurements point to a partial ferromagnetic transition at T = 4 K. This study confirms the relevance of the frustrated quantum kagome lattice to stabilize original quantum phases and suggests the existence of a new spin liquid phase, distinct from the one expected for antiferromagnetically coupled spins., La déstabilisation de l’ordre antiferromagnétique de Néel au profit de nouvelles phases quantiques à température nulle à deux dimensions est envisageable grâce au phénomène de frustration magnétique. Le modèle théorique de spins Heisenberg S=1/2 répartis sur le réseau bidimensionnel frustré kagome, constitué de triangles joints uniquement par leurs sommets, est susceptible de stabiliser des phases quantiques originales de liquides de spin, qui ne présentent aucune brisure de symétrie à T = 0. Cette thèse a été consacrée à l’étude expérimentale de deux types de composés de spins S=1/2 (Cu2+) à géométrie kagome à l’aide de techniques spectroscopiques locales, la RMN et la μSR, ainsi que de mesures thermodynamiques (susceptibilité magnétique, chaleur spécifique). Dans Mg-herbertsmithite, la frustration est générée par une interaction d’échange premiers voisins antiferromagnétique J et est responsable d’un comportement liquide de spin jusqu’à des températures de l’ordre de J/10000. Par rapport au composé isostructural antérieur, Zn-herbertsmithite, nous avons montré qu’il possédait des propriétés physiques similaires tout en permettant une caractérisation fine du taux de défauts de substitutions Cu/Mg. Nos expériences réalisées à partir d’échantillons contrôlés permettent d’étudier finement l’origine des plateaux de relaxation observés en μSR à basse température en lien avec l’existence des défauts de spins interplans. La kapellasite et l’haydéite possèdent des interactions ferromagnétiques (J1) et antiferromagnétiques (Jd), offrant la possibilité d’explorer le diagramme de phases générées par la compétition de ces interactions sur le réseau kagome. Pour la kapellasite, nos mesures de μSR démontrent le caractère liquide de spin jusqu’à T ≈ J1/1000. La dépendance en température de la susceptibilité magnétique sondée par RMN du 35Cl ainsi que de la chaleur spécifique permettent d’évaluer le rapport Jd/J1 = 0.85, qui localise classiquement son fondamental au sein d’une phase originale de spins non coplanaires à 12 sous-réseaux appelée cuboc2. Les interactions présentes dans l’haydéite localisent son fondamental au sein de la phase ferromagnétique, en bon accord avec nos mesures qui indiquent une transition partielle à caractère ferromagnétique à T = 4 K. Cette étude confirme la pertinence du réseau kagome frustré pour la stabilisation de phases quantiques originales et démontre l’existence d’une nouvelle phase liquide de spin sur ce réseau, distincte de celle attendue pour des spins couplés antiferromagnétiquement.

Neste trabalho estudamos o modelo da rede de Kondo em uma rede kagome, buscando uma maior compreensão dos efeitos da frustração geométrica em sistemas de férmions pesados. Para tanto, fizemos uma aproximação de campo médio no hamiltoniano do sistema que serve para todas as fases do sistema. Analisamos inicialmente o caso não magnético. Obtemos neste limite as energias eletrônicas e as funções de Green necessárias ao cálculo numérico autoconsistente das ocupações e do parâmetro de Kondo. Os resultados encontrados estão em concordância qualitativa com trabalhos publicados em outras geometrias. A seguir analisamos o caso magnético, onde introduzimos uma aproximação suplementar, a qual é compatível com a de campo médio já considerada e, em princípio, existente apenas em sistemas com frustração geométrica. Realizamos cálculos autoconsistentes através de somas sobre as frequências de Matsubara. Os resultados mostram que não há coexistência entre ordem magnética e efeito Kondo, além de haver a supressão do antiferromagnetismo com o aumento de temperatura e variações no preenchimento de bandas. In this work we study the Kondo Lattice model for the kagome lattice, in order to understand better the effects of geometrical frustration in heavy-fermion systems. In this context, we consider a mean field scheme valid for all the system’s phases. Firstly, we analyzed the nonmagnetic case. In this approximation the electron energies and spectral functions are reachable, then we use the density of states to calculate the occupations selfconsistently. Our results are qualitatively compared with previous works in other geometries. In the second part we introduce an approximation for magnestism, which takes into account the mean field scheme considered and the presence of geometrical frustration. Self-consistent calculations are done through the frequencies summation method. Our results show that the magnetism is supressed when the temperature is increased or the band filling deviates from half-filling. Besides, the coexistence of magnetic order and Kondo effect is not observable.

In this dissertation we present the results of a theoretical investigation of spin models on two-dimensional and quasi one-dimensional lattices, all unified under the concept of quantum frustrated antiferromagnetism, and all discussing various aspects of the antiferromagnetic Heisenberg model on the kagomé lattice. In the Introduction (Chapter 1), we discuss at some length such concepts as frustration and superexchange, among others, which are of common relevance in the rest of the chapters. In Chapter 2, we study the effect of Dzyaloshinskii--Moriya (DM) interactions on the zero-temperature magnetic susceptibility of systems whose low energy can be described by short-range valence bond states. Our work shows that this treatment is consistent with the experimentally observed non-vanishing susceptibility -- in the specified temperature limit -- of the spin-1/2 kagomé antiferromagnetic compound ZnCu3(OH)6Cl2, also known as herbertsmithite. Although the objective of this work is explaining the aforementioned characteristic of the experimental system, our methods are more general and we apply them to the checkerboard and Shastry-Sutherland lattices as well. In Chapter 3, we discuss our findings in the study of ghost-mediated domain wall interactions in the diamondback ladder. These domain walls are the the spin excitations -- the kinks and the antikinks -- separating the ground states along one chain of the ladder. While as individual entities an antikink is energy costly and a kink energy free, our study finds that both interact via the ghosts that they produce in the opposite side of the ladder from where they are located. Through the study of these ghosts, we find that domain walls proliferate in the system above a critical value of the system's coupling constants. It is this proliferation that makes their treatment as free, non-interacting particles impossible, so we study here their interactions both quantitatively and qualitatively, in a region where the latter are yet not very strong, namely below the critical point. Based on the calculated two-body interaction potential, domain walls interact attractively (repulsively) when separated at even (odd) distances, with a strength that decays as 1/sp, where s is their separation and p

The highly-frustrated spin-1/2 quantum Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a {\it small} ferromagnetic next-nearest-neighbor exchange coupling $|J_2|>0.09 J_1$ leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL: instead it possesses a non-trivial flux pattern and large dimerization., 5 pages, 4 figures

Volborthite Cu 3 V 2 O 7 ( OH ) 2 · 2 H 2 O is a natural frustrated antiferromagnet with a kagome-like magnetic lattice decorated by S = 1 2 spins. Our μ SR results confirm the existence of a dynamical plateau below 2 K, as initially demonstrated in [Phys. Rev. Lett. 91 (2003) 207603] despite sensible quantitative differences in the relaxation rate values. Thanks to additional low temperature SQUID and NMR data we show that this plateau occurs concurrently with a freezing transition. Moreover, we revisited the effect of diluting the magnetic lattice for small dilution rates between 1% and 15%. Comparison is made with the well studied kagome bilayer compounds. The ground state of volborthite appears to be far less stable with respect to dilution.

The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out.

In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagome lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J2|~0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL., 16 pages, 25 figures. Invited paper for Focus issue on "Quantum Spin Liquids" of the New Journal of Physics

We investigate spin dynamics of microstates in artificial spin ice (ASI) in Ni81Fe19 nanomagnets arranged in an interconnected kagome lattice using microfocus Brillouin light scattering, broadband ferromagnetic resonance, magnetic force microscopy, x-ray photoemission electron microscopy, and simulations. We experimentally reconfigure microstates in ASI using a 2D vector field protocol and apply microwave-assisted switching to intentionally trigger reversal. Our work is key for the creation of avalanches inside the kagome ASI and reprogrammable magnonics based on ASIs.

Phase diagram of the two-dimensional antiferromagnet Ni-5(TeO3)(4)Br-2 with triangular arrangement of Ni2+ (S=1) magnetic moments within the [Ni5O17Br2] subunits has been investigated by temperature and magnetic field dependent heat-capacity, magnetization, and magnetic-torque measurements down to 1.5 K and up to 23 T. A nonzero magnetic contribution to the heat capacity observed up to 2.3T(N) is consistent with short-range magnetic ordering and the two-dimensional nature of the system. Below the Neel temperature T-N=29 K several antiferromagnetic phases were identified. The zero-field phase is characterized by a planar antiferromagnetic arrangement of the two in-layer neighboring [Ni5O17Br2] magnetic clusters within the magnetic unit cell. When the magnetic field is applied along the a(*) crystal axis, a spin-flop-like transition to a phase with a complex out-of-plane arrangement of Ni2+ (S=1) magnetic moments occurs at similar to 10 T. Using a molecular-field approach we predict that this transition will shift to higher fields with increasing temperature and that a magnetic phase with ferromagnetic ordering of [Ni5O17Br2] magnetic clusters will occur above 24 T. We ascribe the richness of the magnetic phases to strongly exchange-coupled clusters, being the basic building blocks of the investigated layered system.