Spin Hall Effect (2D Top-Down View): Charge-to-Spin Current Conversion

Mode

DIRECT SHE — charge → spin

Heavy-Metal Layer

Material

Charge current density J_c 1.0

Film width W 5.0 nm

Live Readouts

Spin Hall angle θ_SH

+0.08

Transverse spin current J_s

0.08

Edge spin accumulation μ_s

0.00

How it works

Spin–orbit coupling scatters electrons of opposite spin sideways in opposite directions, even with no applied magnetic field. Drive an unpolarized charge current J_c through a heavy metal and the two spin species pile up on opposite edges — a pure transverse spin current with no net charge flow:

Direct SHE:   Js = θ_SH (ħ/2e) (σ̂ × Jc)
Inverse SHE:  Jc = θ_SH (2e/ħ) (Js × σ̂)

θ_SH is the spin Hall angle — the conversion efficiency, set by spin–orbit scattering strength:

Pt — θ_SH ≈ +0.08, λ_sf ≈ 1.4 nm (workhorse spin-current source/detector).
β-W — θ_SH ≈ −0.30, λ_sf ≈ 2.1 nm (largest known angle, opposite sign to Pt).
β-Ta — θ_SH ≈ −0.15, λ_sf ≈ 2.7 nm.
Cu — θ_SH ≈ +0.003, λ_sf ≈ 500 nm (light element, negligible spin–orbit coupling — kept as a control).

Direct mode — this is a top-down view of the film: the flow axis runs left-right, the transverse axis runs top-bottom. Red (spin-up) and blue (spin-down) carriers drift rightward under J_c and are skewed toward opposite edges at a rate set by θ_SH; the edge bands glow as spin accumulates, decaying at the spin-relaxation rate once carriers stop arriving. This is how a Pt or W layer injects spin current into an adjacent ferromagnet in spin–orbit-torque MRAM.

Inverse mode (ISHE) — a pure spin current is pumped in from the top edge (as it would be by a precessing ferromagnet via spin pumping); the same skew scattering deflects it into a net transverse charge current along the flow axis, read out as a voltage — the standard way spin currents are electrically detected in the lab.

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Spin-up carrier Spin-down carrier Charge accumulation (inverse mode)

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