STT-MRAM Spin-Transfer Torque Switching

Write Current

Current density J 0.00 mA

Free-Layer Material

Damping α 0.10

Anisotropy field H_k 1.50

Thermal noise T 0.15

Junction State

m·p (mz)

1.00

Resistance

5.0 kΩ

Bit state

PARALLEL — 0

Critical I_c

0.25 mA

Switches

How it works

The free layer of a magnetic tunnel junction (MTJ) is modelled as one macrospin m(t) obeying the Landau-Lifshitz-Gilbert-Slonczewski equation — the same equation used to design real STT-MRAM cells:

dm/dt = -γ/(1+α²)[ m×H_eff + α m×(m×H_eff) ]
        -γβ/(1+α²)[ m×(m×p) - α m×p ]

H_eff = H_k (m·ẑ) ẑ      (uniaxial anisotropy)
β = k·J                   (Slonczewski spin-torque, ∝ current J)
p = ẑ                     (fixed reference layer, pinned)

The first line is ordinary precession + Gilbert damping around the anisotropy field. The second line is the Slonczewski spin-transfer torque: electrons crossing the tunnel barrier arrive spin-polarized along p, and transferring that spin angular momentum to the free layer acts exactly like an extra damping term — except its sign flips with the current direction, so it can fight the natural damping instead of reinforcing it.

Linearising near m = ẑ shows the parallel state loses stability once the spin torque exceeds the damping restoring rate: β_c = α H_k — the critical switching current. Push J past that threshold (either sign) and the macrospin spirals away from one pole and relaxes into the other, flipping the junction between low-resistance parallel (0) and high-resistance antiparallel (1) states — a magnetic 1-bit memory cell written purely with current, no external field, exactly as in real STT-MRAM.

Current J — the write current; its sign selects which state it favours, its magnitude must clear I_c to switch.
Damping α and anisotropy H_k — material parameters that set I_c = αH_k/k directly.
Thermal noise — a small stochastic field that seeds the symmetry-breaking real devices get from finite temperature (exactly at the poles the torques vanish identically, so some perturbation is physically required to switch).
Resistance — computed from the tunnel magnetoresistance (Julliere) formula R(θ) = R_P(1 + TMR·(1−cosθ)/2), the actual readout mechanism of an MTJ bit.

Time here is scaled up from the real nanosecond precession/switching timescale so the dynamics are visible to the eye — the physics (equation, threshold, resistance readout) is the real macrospin model used in spintronics device design.

Free layer m Fixed layer p Electron flow

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