Magnon Spin-Momentum Locking: Various Spin Vortices and Dirac Magnons in Noncollinear Antiferromagnets

Abstract

We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120${}^{\circ }$ structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can be explained in the context of a singular band point or a $U(1)$ symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number $Q=-2$, while the typical one observed in topological insulator surface states is characterized by $Q=+1$. A magnonic analogue of the surface states, the Dirac magnon with $Q=+1$, is found in another kagome lattice antiferromagnet. We also derive the sum rule for $Q$ by using the Poincaré-Hopf index theorem.

7 pages, 4 figures, Supplemental material is added

References in corpus (8)

• Observation of the Magnon Hall Effect
• Topological Magnon Insulator in Insulating Ferromagnet
• Spin chirality on a two-dimensional frustrated lattice
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Spin Seebeck effect in antiferromagnets and compensated ferrimagnets
• Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
• Magnon Hall Effect without Dzyaloshinskii-Moriya Interaction
• Pumping of magnons in a Dzyaloshinskii-Moriya ferromagnet

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