Theory of magnon hydrodynamics in collinear antiferromagnets

We investigate the transport of spin angular momentum and linear momentum carried by magnons in electrically insulating collinear antiferromagnets (AFs). Focusing on both transverse and longitudinal geometries, we model magnons as a viscous fluid and explore the hydrodynamic transport regime that emerges when the magnon-magnon scattering length is shorter than the momentum-relaxation length, such that momentum-conserving processes dominate over momentum-relaxing ones. We develop a theoretical framework to investigate viscous effects in the magnon hydrodynamic regime, which give rise to measurable transport signatures such as nonlocal resistance and spin and thermal conductance. Accounting for both momentum and spin relaxations, we derive hydrodynamic equations governing magnon momentum and spin transport. Notably, interspecies scattering between antiferromagnetic magnons with opposite spin angular momentum induces drag-like effects that strongly modify spin current propagation. We derive expressions for magnon conductivity and introduce an accessibility parameter quantifying intra-band momentum transfer. Our results establish antiferromagnetic insulators as a promising platform for observing magnon-fluid dynamics and exploring collective spin transport phenomena.