Datta-Das Spin Transistor: Rashba Precession

Channel & Gate

Rashba coefficient α 15.0 meV·nm

Channel length L 200 nm

Effective mass m*/m₀ 0.050

Injection speed 1.0×

Drain Analyzer

Spin & Current Readout

Precession at drain θ(L)

0.0°

π-rotation length L_π

– nm

Drain current I / I₀0%

Spin precession rate dθ/dx = 2m*α/ħ²

–

How it works

The Rashba effect gives electrons confined to a 2D layer (a 2DEG) with structural-inversion asymmetry — e.g. a gated semiconductor heterostructure — a momentum-dependent spin splitting from the Hamiltonian

H_R = (α/ħ)(k_x σ_y − k_y σ_x)

For an electron injected along +x with momentum k_x = k, this acts as an in-plane effective magnetic field along y that the spin precesses about while the electron crosses the channel. Over a distance x the precession angle is

θ(x) = 2 m* α x / ħ²

This is the Datta–Das spin field-effect transistor (1990): a ferromagnetic source injects spin polarized along the transport axis; the gate voltage tunes α (via the confinement electric field) and hence the precession; a ferromagnetic drain acts as a spin analyzer whose transmitted current depends on the angle between the precessed spin and the drain's magnetization,

I(θ_L) ∝ 1 + cosθ_L   (parallel analyzer)
I(θ_L) ∝ 1 − cosθ_L   (antiparallel analyzer)

α slider — the gate-tunable Rashba coefficient; larger α precesses the spin faster per nanometre of travel.
L slider — channel length; a longer channel accumulates more total precession before the drain.
m* slider — effective mass of the semiconductor's conduction band (real materials range roughly 0.02–0.1 m₀ for III-V compounds like InGaAs).
Parallel / Antiparallel — flips the drain contact's magnetization, inverting which precession angle passes the most current, exactly as it toggles the device between "on" and "off" states.

The corkscrew ribbon in the scene is a geometric plot of the spin vector's own (Sᵧ, S_z) components against position x — it visualizes precession in spin-space, not a literal spatial trajectory: electrons travel in a straight line down the channel while only their spin direction winds.

Electron spin projection Channel / transport axis

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