Magnon kinetic theory of the antiferromagnetic Hanle effect

Motivated by the recently discovered magnonic Hanle effect in an insulating antiferromagnet Wimmer et al., Phys. Rev. Lett. 125, 247204 (2020), we develop a spin transport theory based on low-energy waves of antiferromagnetic N\'eel order. These waves have two polarizations, which we describe in analogy to optics using the Stokes vector on the Poincar\'e sphere. We find that the polarization, which encodes the magnon spin angular momentum, changes periodically with a frequency that is nonlinear in the magnetic field. This explains the observed asymmetry in the Hanle signal as a function of the magnetic field, along with other salient experimental features. By providing an energy-resolved description of the spin injection, our theory combines the kinetic transport of magnons with the coherent dynamics of their polarization in an intuitive way. This opens a general perspective on a coherent control of magnonic spin density in collinear antiferromagnets.