Classical Spin Spirals in Frustrated Magnets from Free-Fermion Band Topology
arXiv:1705.04073 · doi:10.1103/PhysRevB.96.085145
Abstract
The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose propagation vectors can be described, depending on the lattice geometry, by points (triangular), lines (fcc), surfaces (frustrated diamond) or completely flat bands (pyrochlore). Here we demonstrate an exact mathematical correspondence of these spiral manifolds of classical antiferromagnets with the Fermi surfaces of free-fermion band structures. We provide an explicit lattice construction relating the frustrated spin model to a corresponding free-fermion tight-binding model. Examples of this correspondence relate the 120 order of the triangular lattice antiferromagnet to the Dirac nodal structure of the honeycomb tight-binding model or the spiral line manifold of the fcc antiferromagnet to the Dirac nodal line of the diamond tight-binding model. We discuss implications of topological band structures in the fermionic system to the corresponding classical spin system.
16 pages, 20 figures
References in corpus (10)
- Classification of topological insulators and superconductors in three spatial dimensions
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Fractional quantum Hall effect in the absence of Landau levels
- Order by disorder and spiral spin liquid in frustrated diamond lattice antiferromagnets
- Weyl spin liquids
- A Spin-Orbital Singlet and Quantum Critical Point on the Diamond Lattice: FeSc2S4
- Quantum order by disorder in frustrated diamond lattice antiferromagnets
- Emergent quantum phases in a frustrated J1-J2 Heisenberg model on hyperhoneycomb lattice
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