Figure 1

Asymmetric spin-filter effect achieved by sending nonpolarized electrons through a medium with spatially non-uniform magnetization and biased by spin-torque. The combination time-dependent effective magnetic field and spin-torque experienced by individual spins creates a protocol of parametrically encircling an EP of the corresponding effective non-Hermitian Hamiltonian’s complex eigenspectrum, resulting in non-reciprocal spin transport properties. Spins sent left-to-right (a) and right-to-left (b) come out polarized in different directions, controlled by the magnitudes of spin-torque and effective magnetic field experienced by the spins. Blue and red flat arrows (anti-)parallel to the y-axis represent spin accumulations generated, e.g., by spin Hall effect. As a result, spin-torque is exerted on incident spins propagating through a medium (gray) with spatially varying magnetic field (orange arrows).