Persistence of the flat band in a kagome magnet with dipolar interactions

Abstract

The weathervane modes of the classical Heisenberg antiferromagnet on the kagome lattice constitute possibly the earliest and certainly the most celebrated example of a flat band of zero-energy excitations. Such modes arise from the underconstraint that has since become a defining criterion of strong geometrical frustration. We investigate the fate of this flat band when dipolar interactions are added. These change the nearest-neighbour model fundamentally as they remove the Heisenberg spin-rotational symmetry while also introducing a long- range component to the interaction. We explain how the modes continue to remain approximately dispersionless, while being lifted to finite energy as well as being squeezed: they change their ellipticity described by the ratio of the amplitudes of the canonically conjugate variables comprising them. This phenomenon provides interesting connections between concepts such as constraint counting and self-screening underpinning the field of frustrated magnetism. We discuss variants of these phenomena for different interactions, lattices and dimension.

arXiv comment12 pages, 7 figures

References in corpus (39)

• Magnetic Monopoles in Spin Ice
• Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
• Topological Flat Band Models and Fractional Chern Insulators
• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Fractional Quantum Hall Physics in Topological Flat Bands
• Aharonov-Bohm cages in two-dimensional structures
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Band touching from real space topology in frustrated hopping models
• Local spin resonance and spin-Peierls-like phase transition in a geometrically frustrated antiferromagnet
• Spin Ice, Fractionalization and Topological Order
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Destructive quantum interference in spin tunneling problems
• Symmetry breaking due to Dzyaloshinsky-Moriya interactions in the kagome lattice
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Artificial square ice and related dipolar nanoarrays
• Why spin ice obeys the ice rules
• Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Lattice generalization of the Dirac equation to general spin and the role of the flat band
• Topological Flat Bands from Dipolar Spin Systems
• Cooperative Ordering in Lattices of Interacting Two-Level Dipoles
• Removing the spin ice cap: magnetic ground states of rare earth tripod kagome lattice Mg${}_2$RE${}_3$Sb${}_3$O${}_{14}$ (RE = Gd, Dy, Er)
• Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet
• High field properties of geometrically frustrated magnets
• The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System
• Magnetic Structure and Spin Waves in the Kagomé Jarosite compound $\mathbf{KF}{\mathbf{e}}_3(\mathbf{S}{\mathbf{O}}_4{)}_2(\mathbf{OH}{)}_6$
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Quantum spin fluctuations in the dipolar Heisenberg-like rare earth pyrochlores
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Order and excitations in large-$S$ kagomé-lattice antiferromagnets
• Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements
• Linear independence of localized magnon states
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Classical dipoles on the kagome lattice
• A Kagome Map of Spin Liquids: from XXZ to Dzyaloshinskii-Moriya Ferromagnet
• Dispersionless spin waves in Gadolinium Gallium Garnet

Cited by in corpus (10)

• Disordered flat bands on the kagome lattice
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• Isolated flat bands in an interlocking-circles lattice
• Quantum Phases of Kagome Electron System with Half-Filled Flat Bands
• Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems
• Zero-energy excitation in the classical kagome antiferromagnet NaBa${}_2$Mn${}_3$F${}_{11}$
• Continuous degeneracy of the fcc kagome lattice with magnetic dipolar interactions
• Inelastic Neutron Scattering in Weakly Coupled Triangular Spin Tubes CsCrF${}_4$
• Effects of exchange distortions in the magnetic Kagome lattice
• Non-ergodic one-magnon magnetization dynamics of the kagome lattice antiferromagnet