= Spin-valve small-field sensitivity
{title2=$dR/dB=(dR/d\theta)(d\theta/dB)$}
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.
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