Nonlocal Spin Transport as a Probe of Viscous Magnon Fluids

Magnons in ferromagnets behave as a viscous fluid over a length scale, the momentum-relaxation length, below which momentum-conserving scattering processes dominate. We show theoretically that in this hydrodynamic regime viscous effects lead to a sign change in the magnon chemical potential, which can be detected as a sign change in the nonlocal resistance measured in spin transport experiments. This sign change is observable when the injector-detector distance becomes comparable to the momentum-relaxation length. Taking into account momentum- and spin-relaxation processes, we consider the quasiconservation laws for momentum and spin in a magnon fluid. The resulting equations are solved for nonlocal spin transport devices in which spin is injected and detected via metallic leads. Because of the finite viscosity we also find a backflow of magnons close to the injector lead. Our work shows that nonlocal magnon spin transport devices are an attractive platform to develop and study magnon-fluid dynamics.

Figure 1

Schematics of a nonlocal transport device for the detection of viscous magnon flow. Two metallic leads of width $w_l$ (depicted in green) are placed on top of a ferromagnetic insulator and are separated by a distance $d$. The ferromagnetic insulator has dimensions $W\times L$ in the $\widehat{\mathit{x}}\text{−}\widehat{\mathit{y}}$ plane, while the system is translational invariant along $\widehat{\mathit{z}}$. The left lead hosts a spin accumulation (${\mu }_s>0$) and injects spin into the ferromagnetic insulator. The right lead is modeled as a spin sink (${\mu }_s=0$) and acts as spin detector. Because of viscous effects, the current has nonzero vorticity close to the injector, which leads to local changes in the direction of the magnon current (${\mathit{j}}_m$) and to sign changes in the magnon chemical potential (${\mu }_m$). The streamlines of the magnon current are depicted with black arrows, while the color code indicates the behavior of the normalized variations of the magnon chemical potential around its spatial average, i.e., $[{\mu }_m-⟨{\mu }_m⟩]/{\mu }_m^{\max }$. The main panel shows the result for a viscous magnon fluid ($D_{\nu }\sim W$) while the inset shows the result for the diffusive regime ($D_{\nu }\to 0$). The change of sign of the spin current injected into the detector provides evidence for the existence of a viscous magnon fluid.

Figure 2

(a) Nonlocal signal as a function of injector-detector distance $d$ for a sample of width $W=5D_{\nu }$ considering different values of the magnon spin diffusion length. (b) Profile of the normalized magnon chemical potential ${\overline{\mu }}_m={\mu }_m/{\mu }_m^{\max }$ along the $\widehat{\mathit{x}}$ direction at different distances from the upper boundary (see Fig. 1). We consider $d=1.6D_{\nu }$ and ${\ell }_m/D_{\nu }=1$. The dashed lines depict the central position of the injector (left) and detector (right).