  We theoretically investigate possible effects of electric current on the spin
wave dynamics for the N\'{e}el-type antiferromagnetic order in a honeycomb
lattice. Based on a general vector decomposition of the spin polarization of
conduction electrons, we find that there can exist reciprocal and nonreciprocal
terms in the current-induced torque acting on the local spins in the system.
Furthermore, we show that the reciprocal terms will cause the spin wave Doppler
effect, while the nonreciprocal terms can induce rich non-Hermitian topological
phenomena in the spin wave dynamics, including exceptional points, bulk Fermi
arc, non-Hermitian skin effect, etc. Our results indicate the capability to
manipulate non-Hermitian magnons in magnetic materials by electric current,
which could be important for both fundamental physics and technology
applications.
