Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore

Abstract

The kagome lattice is a paragon of geometrical frustration, long-studied for its association with novel ground-states including spin liquids (SLs). Many recently synthesized kagome materials feature rare-earth ions, which may be expected to exhibit highly anisotropic exchange interactions. The consequences of this combination of strong exchange anisotropy and extreme geometrical frustration are yet to be fully understood. Here, we establish a general picture of the interactions and resulting ground-states (GSs) arising from nearest neighbour exchange anisotropy on the kagome lattice. We determine a generic anisotropic exchange Hamiltonian from symmetry arguments. In the high-symmetry case where reflection in the kagome plane is a symmetry of the system, the generic nearest-neighbour Hamiltonian can be locally defined as a XYZ model with out-of-plane Dzyaloshinskii-Moriya interactions. We proceed to study its phase diagram in the classical limit, making use of an exact reformulation of the Hamiltonian in terms of irreducible representations (irreps) of the lattice symmetry group. This reformulation in terms of irreps naturally explains the three-fold mapping between SLs recently studied on kagome by the present authors [Nat Commun 7, 10297 (2016)]. In addition, a number of unusual states are stabilised in the regions where different forms of GS order compete, including a stripy phase with a local Z8 symmetry and a classical analogue of a chiral SL. This generic Hamiltonian also turns out to be a fruitful hunting ground for coexistence of different forms of magnetic order, or of order and disorder, which we find is a particular property of the kagome lattice arising from the odd number of spins per frustrated unit. These results are compared and contrasted with those obtained on the pyrochlore lattice, and connection is made with recent progress in understanding quantum models with S = 1/2

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• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions
• Coexistence of magnetic order and persistent spin dynamics in a quantum kagome antiferromagnet with no intersite mixing
• Topological magnons in a kagome lattice spin system with $XXZ$ and Dzyaloshinskii-Moriya interactions
• Negative-vector-chirality 120${}^{\circ }$ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu${}_3$(OH)${}_6$Cl${}_3$
• Ground state phase diagram of dipolar-octupolar pyrochlores
• Half moons are pinch points with dispersion
• 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
• 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
• Degenerate and chiral states in the extended Heisenberg model in the kagome lattice
• Ordering phenomena of spin trimers accompanied by large geometrical Hall effect
• Symmetry analysis of light-induced magnetic interactions via Floquet engineering
• Determination of spin chirality using x-ray magnetic circular dichroism
• 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
• Scalar spin chirality induced by a circularly polarized electric field in a classical kagome magnet
• Effects of exchange distortions in the magnetic Kagome lattice
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Impact of Dzyaloshinskii-Moriya and anisotropic exchange interactions on the cubic kagome antiferromagnets Mn${}_3$X and Mn${}_3$AB
• Pinch points and half moons encode Berry curvature
• Pinch-line spin liquids as layered Coulomb phases and applications to cubic models
• Nonreciprocal magnon excitations by the Dzyaloshinskii-Moriya interaction on the basis of bond magnetic toroidal multipoles
• Constructing Emergent U(1) Symmetries in the Gamma-prime $\left({\mathbf{\Gamma }}^{\prime }\right)$ model
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Magnetic anisotropy effect on stabilizing magnetization plateaus of kagome strip chain Heisenberg antiferromagnets
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands