Theory of magnon hydrodynamics in collinear antiferromagnets

We develop a theoretical framework for the transport of spin angular momentum and linear momentum carried by magnons in electrically insulating collinear antiferromagnets (AFs). Focusing on both transverse and longitudinal nonlocal geometries, we model magnons as a viscous fluid and examine the hydrodynamic regime that arises when the momentum-conserving magnon-magnon scattering length is shorter than the momentum-relaxation length associated with momentum-nonconserving processes. The hydrodynamic regime in these two geometries is marked by distinct flow patterns: vortex structures in the transverse setup and Poiseuille flow in the longitudinal setup. We show that scattering between magnon modes carrying opposite spin angular momentum induces draglike effects, significantly altering magnon spin current propagation in AFs. Furthermore, we uncover mode-dependent transport regimes at specific distances by tuning the magnetic field, which enables selective control of viscous and diffusive transport in individual magnon modes. Our results position AFs as a promising platform for realizing magnon-fluid dynamics and studying collective spin transport phenomena.