Low-energy spin dynamics of orthoferrites AFeO${}_3$ (A = Y, La, Bi)

YFeO${}_3$ and LaFeO${}_3$ are members of the rare-earth orthoferrites family with $\mathit{\text{Pbnm}}$ space group. Using inelastic neutron scattering, the low-energy spin excitations have been measured around magnetic Brillouin zone center. Splitting of magnon branches and non-zero magnon gap is observed for both compounds, which is similar to the behavior observed in multiferroic BiFeO${}_3$. Spin wave calculations which include both Dzyaloshinsky-Moriya interactions and single-ion anisotropy in the spin-Hamiltonian comprehensively accounts for all the experimentally observed features. Our results offer insight into the unifying physics underlying the Fe${}^{3+}$-based perovskites as well as their distinguishing characteristics.