A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet

Abstract

The kagome lattice sits at the crossroad of present research efforts in quantum spin liquids, chiral phases, emergent skyrmion excitations and anomalous Hall effects to name but a few. In light of this diversity, our goal in this paper is to build a unifying picture of the underlying magnetic degrees-of-freedom on kagome. Motivated by a growing mosaic of materials, we especially consider a broad range of nearest-neighbour interactions consisting of Dzyaloshinskii-Moriya as well as anisotropic ferro$-$ and antiferromagnetic coupling. We present a three-fold mapping on the kagome lattice which transforms the celebrated Heisenberg antiferromagnet and XXZ model onto two lines of time-reversal invariant Hamiltonians. The mapping is exact for classical and quantum spins alike, i.e. it preserves the energy spectrum of the original Heisenberg and XXZ models. As a consequence, at the classical level, all phases have an extensive ground-state degeneracy. These ground states support a variety of phenomena such as ferromagnetically induced pinch points in the structure factor and the possibility for spontaneous scalar chirality. For quantum spin$-1/2$, the XXZ model has been recently shown to be a quantum spin liquid. Applying our three-fold mapping to the XXZ model gives rise to a connected network of quantum spin liquids, centered around a paragon of quantum disorder, namely the Ising antiferromagnet. We show that this quantum disorder spreads over an extended region of the phase diagram at linear order in spin wave theory, which overlaps with the parameter region of Herbertsmithite ZnCu${}_3$(OH)${}_6$Cl${}_2$. We conclude this work by discussing the connection of our results to the chiral spin liquids found on kagome with further nearest-neighbour interactions, and to the recently synthesized ternary intermetallic materials.

8 pages, 4 figures

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• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Combined approach to analyze and classify families of classical spin liquids
• Skyrmion fluid and bimeron glass protected by a chiral spin liquid on a kagome lattice
• Machine learning techniques to construct detailed phase diagrams for skyrmion systems
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Flat-band physics in the spin-1/2 sawtooth chain
• Resonating quantum three-coloring wavefunctions for the kagome quantum antiferromagnet
• Motif magnetism and quantum many-body scars
• Reentrance of disorder in the anisotropic shuriken Ising model
• Crystal Field Levels and Magnetic Anisotropy in the Kagome Compounds $\mathrm{N}{\mathrm{d}}_3\mathrm{S}{\mathrm{b}}_3\mathrm{M}{\mathrm{g}}_2{\mathrm{O}}_{14}$, $\mathrm{N}{\mathrm{d}}_3\mathrm{S}{\mathrm{b}}_3\mathrm{Z}{\mathrm{n}}_2{\mathrm{O}}_{14}$, and $\mathrm{P}{\mathrm{r}}_3\mathrm{S}{\mathrm{b}}_3\mathrm{M}{\mathrm{g}}_2{\mathrm{O}}_{14}$
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• Degenerate and chiral states in the extended Heisenberg model in the kagome lattice
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Noncoplanar multi-k states in frustrated spinel and kagome magnets
• Ordered ground states of kagome magnets with generic exchange anisotropy
• Pressure induced collapse of magnetic order in jarosite
• From chiral spin liquids to skyrmion fluids and crystals, and their interplay with itinerant electrons
• Exactly solvable spin-1/2 XYZ models with highly-degenerate, partially ordered, ground states
• Magnetic interactions in AB-stacked kagome lattices: magnetic structure, symmetry, and duality
• Emergence of magnetic long-range order in kagome quantum antiferromagnets
• Waveguide QED toolboxes for universal quantum matter