Classical spin spirals in frustrated magnets from free-fermion band topology

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 tightbinding 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.

Quantum paramagnet and frustrated quantum criticality in a spin-one diamond lattice antiferromagnet

“…where we have set the lattice constant to unity. This relation coincides with the degenerate spiral surface that was obtained in the classical treatment of the J 1 -J 2 model 34,43 . In Fig.…”

Kagome van-der-Waals Pd3P2S8 with flat band

“…Materials having the kagome lattice have attracted significant interest in the field of condensed matter physics, in particular from the magnetism community, as it is believed to host an exotic spin liquid phase due to geometrical frustration. The electronic version of this magnetic frustration is the flat band in the electronic structure 54 . In this report, we have demonstrated the first ideal kagome vdW material, Pd3P2S8, in which core ions are transition metal ions with strong spin-orbit coupling.…”

Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings

“…In MnSc 2 S 4 , the antiferromagnetic skyrmion lattice inherits the three-sublattice character of the triangular lattice in the (111) layers. However, the mechanism that we discovered, which utilizes anisotropic couplings to stabilize a triple-q phase, can be generalized to antiferromagnetic systems with different geometries 41,42 . Especially on the bipartite honeycomb lattice 43 , anisotropic couplings might stabilize a two-sublattice antiferromagnetic skyrmion lattice with opposite winding spin textures, thus lending an ideal platform to explore antiferromagnetic skyrmion transport 6,7 .…”