Order and excitations in large-$S$ kagomé-lattice antiferromagnets

Abstract

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 $\mathbf{q}=0$ and the $\sqrt{3}\times \sqrt{3}$ states as a function of the anisotropy parameter, offering a rare example of the quantum order-by-disorder fluctuations favoring a ground state which is different from the one selected by thermal fluctuations. The nonlinear terms are also shown to be crucial for a very strong near-resonant decay phenomenon leading to the quasiparticle breakdown in the kagomé-lattice antiferromagnets whose spectra are featuring flat or weakly dispersive modes. The effect is shown to persist even in the limit of large spin values and should be common to other frustrated magnets with flat branches of excitations. Model calculations of the spectrum of the $S=5/2$ Fe-jarosite with Dzyaloshinskii-Moriya anisotropy provide a convincing and detailed characterization of the proposed scenario.

17 pages, 13 figures, published version. Recipient of the PRB beauty award (Editors' Suggestion)

References in corpus (13)

• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Spontaneous Magnon Decays
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Magnetic Structure and Spin Waves in the Kagomé Jarosite compound $\mathbf{KF}{\mathbf{e}}_3(\mathbf{S}{\mathbf{O}}_4{)}_2(\mathbf{OH}{)}_6$
• Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions
• Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisites Cu${}_3$Bi(SeO${}_3{)}_2$O${}_2$X
• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Dispersionless spin waves in Gadolinium Gallium Garnet
• Strong quantum effects in an almost classical antiferromagnet on a kagome lattice

Cited by in corpus (48)

• Damped Topological Magnons in the Kagomé-Lattice Ferromagnets
• Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions
• Frustrated two dimensional quantum magnets
• Interaction-stabilized topological magnon insulator in ferromagnets
• Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice
• Intrinsic spin Nernst effect of magnons in a noncollinear antiferromagnet
• Topological Phases in Magnonics
• Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice
• Spin order and dynamics in the diamond-lattice Heisenberg antiferromagnets CuRh2O4 and CoRh2O4
• Spin Seebeck and Spin Nernst Effects of Magnons in Noncollinear Antiferromagnetic Insulators
• Antichiral spin order its Goldstone modes and their hybridization with phonons in the topological semimetal Mn3Ge
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets
• Field-induced dynamical properties of the $XXZ$ model on a honeycomb lattice
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics
• How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?
• Quantum Damping of Skyrmion Crystal Eigenmodes due to Spontaneous Quasiparticle Decay
• Magnonic Analogue of Edelstein Effect in Antiferromagnetic Insulators
• Anisotropic magnetic interactions in hexagonal AB-stacked kagome lattice structures: Applications to ${\mathrm{Mn}}_3\mathrm{X}$ ($\mathrm{X}$ = $\mathrm{Ge}$, $\mathrm{Sn}$, $\mathrm{Ga}$) compounds
• Spin ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Topological Hybrids of Magnons and Magnon Bound Pairs
• Degenerate and chiral states in the extended Heisenberg model in the kagome lattice
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Structures of magnetic excitations in the spin-1/2 kagome-lattice antiferromagnets Cs${}_2$Cu${}_3$SnF${}_{12}$ and Rb${}_2$Cu${}_3$SnF${}_{12}$
• Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study
• Anisotropic magnetic excitations from single-chirality antiferromagnetic state in Ca-kapellasite
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Fragility of ${\mathcal{Z}}_2$ topological invariant characterizing triplet excitations in a bilayer kagome magnet
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Resonant inelastic x-ray scattering study of vector chiral ordered kagome antiferromagnet
• Pressure induced collapse of magnetic order in jarosite
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Designs of magnetic atom-trap lattices for quantum simulation experiments
• Breakdown of Linear Spin-wave Theory and Existence of Spinon Bound States in the Frustrated Kagome Lattice Antiferromagnet
• Impact of Dzyaloshinskii-Moriya and anisotropic exchange interactions on the cubic kagome antiferromagnets Mn${}_3$X and Mn${}_3$AB
• Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: A message from spin waves
• Magnon Confinement on the Two-Dimensional Penrose Lattice: Perpendicular-Space Analysis of the Dynamic Structure Factor
• Pinch points and half moons encode Berry curvature
• Magnetic Order in Laser-Irradiated Kagome Antiferromagnets
• The free energy of anisotropic quantum spin systems: Functional integral representation
• Is Herbertsmithite far from an ideal antiferromagnet? Ab-initio answer including in-plane Dzyaloshinskii-Moriya interactions and coupling with extra-plane impurities
• Quantifying the Phase Diagram and Hamiltonian of $S=1/2$ Kagome Antiferromagnets: Bridging Theory and Experiment
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Decision making by Berry's flux