Spin waves in an antiferromanget with a local triangular symmetry*

We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar 120⁰ magnetic order [1]. The three Goldstone modes can be separated by point-group symmetry into a singlet α₀ and a doublet β. The α₀ singlet is described by the standard theory of a free relativistic scalar field. The field theory of the β doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse “speeds of sound.” The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn₃X family with stacked kagome layers and extract the exchange coefficients for a model spin Hamiltonian by fitting to neutron scattering data [2].

[1] S. Dasgupta and O. Tchernyshyov, Phys. Rev. B 102, 144417 (2020)
[2] Y. Chen et al Phys. Rev. B 102, 054403 (2020)