Magnetic Tunnel Junction — Spin-Dependent Tunneling Magnetoresistance (2D)

Free-Layer Magnetization

Angle θ vs fixed layer 30°

Junction Parameters

Spin polarization P 42%

Barrier (MgO) thickness d 1.20 nm

Live Readout

Junction resistance R

—

TMR ratio

—

Alignment state

—

How it works

A magnetic tunnel junction (MTJ) is two ferromagnetic electrodes separated by a nanometre-thin insulating barrier (here, MgO). Electrons cross the barrier purely by quantum tunneling — there is no classical path through an insulator. What makes an MTJ useful is that the tunneling rate depends on the relative orientation of the two layers' magnetizations.

Barrier decay (WKB):   G₀(d) ∝ exp(−2κd),   κ = √(2mφ)/ħ
Angle-dependent conductance (Slonczewski):
                       G(θ) = G₀·[1 + P² cos θ]
Julliere's TMR formula (θ = 0 vs θ = 180°):
                       TMR = (R_AP − R_P) / R_P = 2P² / (1 − P²)

θ = 0° (parallel) — majority-spin electrons from one electrode tunnel straight into matching majority-spin empty states on the other side: high conductance, low resistance.
θ = 180° (antiparallel) — a majority-spin electron on one side must land in a minority-spin state on the other: conductance drops, resistance rises. That resistance swing is the TMR effect used to read bits in MRAM and hard-drive heads.
Spin polarization P — how strongly each electrode favors one spin channel. Higher P (e.g. CoFeB electrodes) means a bigger swing between the parallel and antiparallel states.
Barrier thickness d — resistance grows exponentially with d (the WKB tunneling factor), exactly like the transmission coefficient of any quantum tunneling barrier; thicker barriers tunnel far less current for the same voltage.
The moving dots in the scene are a two-current (Mott) visualization: each carries a spin channel, and its crossing speed scales with that channel's conductance at the current angle — slower, sparser flow means higher measured resistance.

Real-world relevance: this exact physics (MgO-based MTJs) is what reads and writes every bit in modern MRAM chips and the read heads of hard-disk drives.

Majority-spin electron Minority-spin electron