  Non-conservative physical systems admit a special kind of spectral
degeneracy, known as exceptional point (EP), at which eigenvalues and
eigenvectors of the corresponding non-Hermitian Hamiltonian coalesce. Dynamical
parametric encircling of the EP can lead to non-adiabatic evolution associated
with a state flip, a sharp transition between the resonant modes. Physical
consequences of the dynamical encircling of EPs in open dissipative systems
have been explored in optics and photonics. Building on the recent progress in
understanding the parity-time (PT)-symmetric dynamics in spin systems, we use
topological properties of EPs to implement chiral non-reciprocal transmission
of a spin through the material with non-uniform magnetization, like helical
magnet. We consider an exemplary system, spin-torque-driven single spin
described by the time-dependent non-Hermitian Hamiltonian. We show that
encircling individual EPs in parameter space results in non-reciprocal spin
dynamics and find the range of optimal protocol parameters for high-efficiency
asymmetric spin filter based on this effect. Our findings offer a platform for
non-reciprocal spin devices for spintronics and magnonics.
