Phenomenological theory of coherent and incoherent spin currents in antiferromagnetic spin pumping

Magnetic resonance driven by coherent microwaves can pump spin currents into a neighboring nonmagnetic system. Owing to non-linear effects, however, coherentlly driven spin dynamics inevitably generates incoherent magnons through thermalization, which makes it complicated to distinguish between coherent and incoherent contributions in real experiments. Recent measurements have demonstrated spin pumping effects in antiferromagnets at the sub-THz frequency, where coherent and incoherent magnons contribute oppositely to the spin current and are thus distinguishable. We formulate a phenomenological theory to capture the coupled dynamics of coherent and incoherent magnons in collinear antiferromagnets driven by sub-THz sources, which can fit very well with the experimental observation and explain why the competition between coherent and incoherent magnons leads to a sign change in the spin current at a turning temperature. Our phenomenological theory predicts that using magnetic thin films can substantially suppress the undesirable incoherent contribution and magnify coherent spin pumping.