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Ba$_{3}$NbFe$_{3}$Si$_{2}$O$_{14}$ (langasite) is structurally andmagnetically single domain chiral with the magnetic helicity induced throughcompeting symmetric exchange interactions. Using neutron scattering, we showthat the spin-waves in antiferromagnetic langasite display directionalanisotropy. On applying a time reversal symmetry breaking magnetic field alongthe $c$-axis, the spin wave energies differ when the sign is reversed foreither the momentum transfer $\pm$ $\vec{Q}$ or applied magnetic field $\pm$$\mu_{0}$H. When the field is applied within the crystallographic $ab$-plane,the spin wave dispersion is directionally \textit{isotropic} and symmetric in$\pm$ $\mu_{0}$H. However, a directional anisotropy is observed in the spinwave intensity. We discuss this directional anisotropy in the dispersion inlangasite in terms of a field induced precession of the dynamic unit cellstaggered magnetization. Directional anisotropy, or often referred to as nonreciprocal responses, can occur in antiferromagnetic phases in the absence ofthe Dzyaloshinskii-Moriya interaction or other effects resulting fromspin-orbit coupling.

Spin-wave directional anisotropies in antiferromagnetic Ba$_{3}$NbFe$_{3}$Si$_{2}$O$_{14}$