Low-energy spin dynamics of orthoferrites AFeO₃ (A  =  Y, La, Bi)

YFeO₃ and LaFeO₃ are members of the rare-earth orthoferrites family with Pbnm space group. Using inelastic neutron scattering, the low-energy spin excitations have been measured around the magnetic Brillouin zone center. Splitting of magnon branches and finite magnon gaps (∼2 meV) are observed for both compounds, where the Dzyaloshinsky-Moriya interactions account for most of this gap with some additional contribution from single-ion anisotropy. We also make comparisons with multiferroic BiFeO₃ (R3c space group), in which similar behavior was observed. By taking into account all relevant local Dzyaloshinsky-Moriya interactions, our analysis allows for the precise determination of all experimentally observed parameters in the spin-Hamiltonian. We find that different properties of the Pbnm and R3c space group lead to the stabilization of a spin cycloid structure in the latter case but not in the former, which explains the difference in the levels of complexity of magnon band structures for the respective compounds.