[Paper Review] Spin hydrodynamic generation in graphene

Mamoru Matsuo, D. A. Bandurin+3 more|arXiv (Cornell University)|May 4, 2020

Electrohydrodynamics and Fluid Dynamics1 references4 citations

TL;DR

This paper proposes a novel mechanism for generating spin currents in graphene via viscous electron hydrodynamics, where spin-vorticity coupling in electron flows produces transverse spin accumulation. The key result shows spin Hall angles exceeding 0.1 across a wide temperature range, with measurable spin accumulation (~3×10⁻² μeV) detectable by modern magnetometry techniques.

ABSTRACT

Graphene hosts an ultra-clean electronic system with electron-electron collisions being the dominant source of scattering above liquid nitrogen temperatures. In this regime, the motion of the electron fluid resembles the flow of classical liquids and gases with high viscosity. Here we show that such a viscous electron flow can cause the generation of a spin current perpendicular to the direction of flow. Combining the Navier-Stokes equations and the spin diffusion equation in the presence of the spin-vorticity coupling, we derive an expression for the spin accumulation emerging purely as a result of the viscous electron flow. We explore Poiseuille flow and Jeffery-Hamel flow and show that the spin Hall angle may exceed 0.1 over a wide range of temperatures and can be controlled by carrier density, temperature, and the geometry of sample boundaries. Our theory points to new functionality of graphene as a spin current source.

Motivation & Objective

• To explore spin current generation in graphene beyond conventional spin injection or spin-orbit coupling.
• To address the limited methods for generating spin-polarized currents in ultra-clean graphene devices.
• To bridge electron hydrodynamics and spintronics by leveraging viscous electron flows in graphene.
• To predict experimentally accessible spin accumulation and spin Hall angles in hydrodynamic flow configurations.
• To demonstrate control of spin current via carrier density, temperature, and sample geometry.

Proposed method

• Modeling electron flow in graphene using the Navier-Stokes equations for viscous electron fluids.
• Incorporating spin-vorticity coupling into the spin diffusion equation to describe spin current generation.
• Analyzing Poiseuille flow and Jeffery-Hamel flow geometries to study spin accumulation patterns.
• Deriving the spin Hall angle as a function of viscosity, spin relaxation length, and flow geometry.
• Using numerical solutions of the spin diffusion equation to estimate spin accumulation magnitude in different flow regimes.
• Normalizing spin accumulation to a reference scale δμ^SHD ≈ 0.1 meV for quantitative comparison and experimental feasibility assessment.

Experimental results

Research questions

• RQ1 Can viscous electron flow in graphene generate a transverse spin current via spin-vorticity coupling?
• RQ2 What is the magnitude and tunability of the spin Hall angle in hydrodynamic electron flows in graphene?
• RQ3 How does the geometry of the sample (e.g., convergent vs. divergent flow) affect spin accumulation?
• RQ4 Can the predicted spin accumulation be experimentally detected with current techniques?
• RQ5 How do temperature, carrier density, and viscosity influence the efficiency of spin current generation?

Key findings

• The spin Hall angle exceeds 0.1 over a wide temperature range, comparable to values in materials with strong spin-orbit coupling.
• Spin accumulation reaches up to approximately 3×10⁻² μeV (or 1 Oe) at sample boundaries in Jeffery-Hamel flow, within the sensitivity of scanning NV-magnetometry.
• The spin accumulation is tunable via carrier density, temperature, and sample geometry, particularly the angle between edges.
• In Jeffery-Hamel flow, the radial spin current is small due to the sample size being comparable to the spin relaxation length.
• For Re = 100, the flow may become unstable, leading to complex spin accumulation patterns that differ from laminar flow.
• The predicted spin current generation is experimentally accessible using scanning photovoltage microscopy or two-dimensional sensing techniques.