Anisotropic Magnetoresistance (AMR) Sensor

Applied Field

Field angle θ_H 30°

Field strength 55%

Strip

Material

Sense current 40 mA

Live Readout

Resistance R(θ)

— Ω

ΔR / R

—

M–I angle θ

—

Joule power

—

How it works

In a ferromagnetic metal, spin-orbit coupling makes an electron's scattering cross-section off d-band states depend on the angle θ between the local magnetization M and the current direction I, not just their magnitudes. That gives an angle-dependent sheet resistance:

R(θ) = R⊥ + (R∥ − R⊥)·cos²θ

θ = angle between magnetization M and current I
R∥ = resistance when M ∥ I   (θ = 0°)
R⊥ = resistance when M ⊥ I   (θ = 90°)
ΔR/R = (R∥ − R⊥) / R⊥   — the AMR ratio, a few % for 3d ferromagnets

The magnetization does not track the external field instantly — shape anisotropy along the strip pins it, so M relaxes toward the field direction at a rate set by the field strength:

dφ_M/dt = (φ_H − φ_M) / τ(H)      τ(H) shrinks as field strength grows

At low field strength the magnetization lags visibly behind a rotating field — exactly the nonlinearity that real AMR sensors fight with a "barber-pole" bias structure. This effect is the working principle of early hard-disk read heads (before GMR/TMR replaced them), automotive wheel-speed and steering-angle sensors, and electronic compasses.

Magnetization M Applied field H Current I (electrons)

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