Spin-valve small-field sensitivity ($dR/dB=(dR/d\theta )(d\theta /dB)$)

A spin valve detects a small field by rotating a free layer relative to a pinned magnetic reference. The chain rule separates transport angular response from the magnetic rotational susceptibility. An angular response proportional to $1-\cos \theta$ has zero slope at perfect parallel and antiparallel alignment but a nonzero slope near perpendicular alignment. The smallest detectable field also depends on electronic and magnetic noise, thermal stability, hysteresis and the chosen bias current; a large magnetoresistance ratio alone does not determine sensitivity.