Theory of spin waves in a hexagonal antiferromagnet

Abstract

We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar $120^{\circ }$ magnetic order. The three Goldstone modes can be separated by point-group symmetry into a singlet ${\alpha }_0$ and a doublet $({\beta }_x,{\beta }_y)$. The ${\alpha }_0$ singlet is described by the standard theory of a free relativistic scalar field. The field theory of the $({\beta }_x,{\beta }_y)$ doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse "speeds of sound". The well-known Heisenberg models on the triangular and kagome lattices with nearest-neighbour exchange turn out to be special cases with accidental degeneracy of the spin-wave velocities. The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn${}_3$X family with stacked kagome layers.

10 pages, 6 figures, Referee comments incorporated, Includes appendices with details on Mn3Ge model

References in corpus (4)

• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Propulsion of a domain wall in an antiferromagnet by magnons
• Spin excitations in the frustrated triangular lattice antiferromagnet NaYbO${}_2$
• Antichiral spin order its Goldstone modes and their hybridization with phonons in the topological semimetal Mn3Ge

Cited by in corpus (19)

• Piezomagnetic switching of anomalous Hall effect in an antiferromagnet at room temperature
• Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a $2\times 2$ matrix operator and physical origin of flat-bands at magic angles
• Non-Collinear Spin Current for Switching of Chiral Magnetic Textures
• Hybrid topological magnon-phonon modes in honeycomb and kagome lattices
• 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
• Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition
• Spin superfluidity in noncollinear antiferromagnets
• Strong Magneto-Elastic Coupling in Mn${}_3$X (X = Ge, Sn)
• Zeeman term for the Néel vector in a two sublattice antiferromagnet using Dzyaloshinsky-Moriya interaction and magnetic field
• Fracton excitations in classical frustrated kagome spin models
• Intertwined Charge and Spin Density Waves in a Topological Kagome Material
• Spin-frame field theory of a three-sublattice antiferromagnet
• Strain tuning the magnetic and transport properties of Mn${}_3$Ge
• Majorana zero modes in a magnetic and superconducting hybrid vortex
• Tuning the Hall response of a noncollinear antiferromagnet via spin-transfer torques and oscillating magnetic fields
• Electrically Tunable Picosecond-scale Octupole Fluctuations in Chiral Antiferromagnets
• Ground states and magnonics in orthogonally-coupled symmetric all-antiferromagnetic junctions
• Slonczewski-spin-current driven dynamics of 180${}^{\circ }$ domain walls in spin valves with interfacial Dzyaloshinskii-Moriya interaction
• Uniaxial stress tuning of the anomalous Hall effect in Mn3Ge