  Understanding the joint dynamics of electron and nuclear spins is central to
core concepts in solid-state magnetic resonance - such as spin-lattice
relaxation and dynamic nuclear polarization - but a generalization that
capitalizes on competing polarization loss and gain channels is still lacking.
Here, we theoretically study the non-Hermitian dynamics of hybrid
electron/nuclear spin systems in the simultaneous presence of electron spin
pumping and spin-lattice relaxation. Focusing on periodic, one-dimensional
chains, we find that by adjusting the electron spin pumping to a critical
level, it is possible to steer the flow of nuclear polarization to create
site-dependent distributions where either end of the array polarizes in
opposite ways, irrespective of the initial state. By contrast, we show that
ring-like patterns - where the limit nuclear polarization is uniform - exhibit
a non-decaying, externally-driven nuclear spin current. Interestingly, cyclic
magnetic field modulation can render these processes largely robust to defects
in the chain, a response featuring some interesting similarities - and
differences - with recent findings in other non-Hermitian physical platforms.
