Nonreciprocal spin waves in a chiral antiferromagnet without the Dzyaloshinskii-Moriya interaction

Non-reciprocal spin wave can facilitate the realization of spin wave logic devices. It has been demonstrated that the non-reciprocity can emerge when an external magnetic field is applied to chiral magnets, of which spin structures depend crucially on an asymmetric exchange interaction, that is, the Dzyaloshinskii-Moriya interaction (DMI). Here we demonstrate that the non-reciprocity can arise even without the DMI. We demonstrate this idea for the chiral antiferromagnet Ba$_2$NbFe$_3$Si$_2$O$_{14}$, of which DMI is very small and chiral spin structure arises mainly from the competition between symmetric exchange interactions. We show that when an external magnetic field is applied, asymmetric energy gap shift occurs and the spin wave becomes non-reciprocal from the competition between symmetric exchange interactions and the external magnetic field.