Effects of frustration on the spin dynamics of the zigzag honeycomb lattice

This investigation covers the effects of variable exchange interactions on the spin dynamics of the zigzag honeycomb lattice. Using a Holstein-Primakoff expansion of the Heisenberg Hamiltonian with easy-axis anisotropy, we characterize the effects of multiple nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions with asymmetry within the context of a frustrated and nonfrustrated zigzag magnetic configuration. By building the model term by term, we directly observe the behavioral contributions from each interaction, how the system changes with anisotropy, and how asymmetric terms transform the system from a nonfrustrated to a frustrated state. By analyzing geometric frustration, we are able to demonstrate the role that NN and NNN interactions play within an asymmetric honeycomb lattice, show the emergence of direction-dependent Dirac nodes, and postulate that the standard Heisenberg interaction has a notable contribution to the behavior observed in the spin excitation behavior within the high-symmetry pathway $\mathrm{\ensuremath{\Gamma}}$-M. Furthermore, to examine the efficacy of our model, we compare it to known inelastic neutron scattering data for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, which has been established to host a zigzag honeycomb ground state dominated by anisotropic interactions.