Theory of magnon hydrodynamics in collinear antiferromagnets

TL;DR

This work develops a two‑fluid magnon hydrodynamics framework for electrically insulating collinear antiferromagnets, deriving diffusion and Navier–Stokes equations for two chiral magnon branches with opposite spin $\pm\hbar$. It shows that interband magnon–magnon interactions induce drag between $\alpha$ and $\beta$ magnons, while intraband scattering yields viscous effects, placing the system in a hydrodynamic transport regime when momentum‑conserving processes dominate. The theory is applied to nonlocal transverse and longitudinal NM|AF|NM geometries, predicting signatures such as negative nonlocal currents, vortex-like flow, and Poiseuille magnon transport, indicative of collective spin transport. These findings position antiferromagnetic insulators as promising platforms for observing magnon fluid dynamics and exploring viscous spin transport phenomena with potential for low-dissipation spintronic devices.

Abstract

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.

Figures (5)

• Figure 1: Schematic description for the fluid-like dynamics of magnon currents in a collinear AF. Magnonic bands are splitted because of an applied Zeeman field. Due to interconversion of chiral antiferromagnetic magnons, and viscous effects, linear momentum is transferred among the pair of chiral $\alpha-$ and $\beta-$magnon subsystem. Under an external driving, e.g., induced by a spin Hall effect (SHE), a magnon spin current ${\boldsymbol{j}}_{\alpha}$ is accompanied by the dragged magnon spin current ${\boldsymbol{j}}_{\beta}$.
• Figure 2: Schematic setups for the (a) nonlocal transverse magnon transport and (b) longitudinal magnon transport through the NM-AF-NM heterostructure. The Néel ground state is along ${\boldsymbol{z}}$ direction, as displayed at panel (b). The identical left and right metallic leads are separated at distance $d$. Boundary conditions imposed at the interface with the metallic leads considers a difference between the magnon chemical potentials and a spin accumulation, induced by the SHE Jungwirth2016Baltz2018rmp.
• Figure 3: (a) Nonlocal magnon spin current ratio $j_{\text{out}}/j_{\text{in}}$ as a function of the injector–detector separation, calculated in zero magnetic field for different magnon spin-diffusion lengths. The sample width is $W=0.1{\cal D}$ and the inelastic spin-conserving parameter is $g=2\times 10^{13}$ S/m$^{2}$. The inset shows the magnon current ratio for $g=0$. Each curve is plotted for different values of the slip length in the range $l_b\in[0.051\mu\text{m},0.15\mu\text{m}]$, from top to bottom. (b) Visualization of magnon current streamlines, with both incoming $j_{\text{in}}$ and outgoing $j_{\text{out}}$ spin currents, for the system with the following parameters: $l_b=0.1\mu\text{m}$$\sigma^0_{\alpha}=10^{5}$ S/m, $\ell=0.1\mu$m, $g=g_s=10^{13}$ S/m$^{2}$, ${\cal D}=0.3\mu$m, $\tau^{-1}_{\alpha\alpha}=0.125$ Hz, $\tau^{-1}_{\alpha\beta}=0.25$ Hz. The magnon chemical potential is depicted as the background of the image.
• Figure 4: Magnon spin current ratio $j_{\text{out}}/j_{\text{in}}$ in the nonlocal setup as a function of distance in the presence of magnetic field for (a) $\alpha-$ and (b) $\beta-$magnons for different magnon spin-diffusion lengths. The yellow area denote regions where $\alpha$-magnons (panel (a)) and $\beta$-magnons (panel (b)) exhibit a negative spin current ratio, indicative of the viscous regime. The curves at panel (a) and (b) are plotted for different values of the slip length in the range $l_b\in[0.018\mu\text{m},0.067\mu\text{m}]$, from top to bottom, and ${\cal D}_{\alpha}={\cal D}_{\beta}=0.1\mu$m.
• Figure 5: Current streamlines in the longitudinal setup, demonstrating the characteristic parabolic profile of Poiseuille flow, shown at panel (b). The white streamlines illustrate the velocity profile, with their concavity (shown on panel (a) at different positions) providing insight into to flow dynamics. In regions with high velocity gradients, the streamlines exhibit inward curvature. In contrast, regions with lower velocity gradients show outward concavity, indicating flow expansion as the fluid moves away from the boundaries. The set of parameters used are, $l_b=0.2\mu$m $\sigma_{\alpha 0}=10^{5}$ S/m, $\ell=0.2\mu$m, $G_{\alpha}=G_{\beta}=10^{13}$ S/m$^{2}$, ${\cal D}=0.3\mu$m, $\tau^{-1}_{\alpha\alpha}=0.125$ Hz, and $\tau^{-1}_{\alpha\beta}=0.25$ Hz. The magnon chemical potential is depicted as the background of the image.