Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 2 / c

If removal restores the original random-domain magnetic state, the magnetostrictive strain and induced voltage return toward their original values. Elastic strain transfer then relaxes the stress on the central layer.

A ferromagnetic nickel layer can retain remanent magnetization and an altered domain population, so removing the external field does not guarantee removal of all magnetostriction. The electrical time response also depends on leakage and the input impedance of the voltmeter: an open-circuit strain-induced voltage can decay through a finite resistance even while some strain remains. The final observed voltage is therefore history- and circuit-dependent.

Reversing a saturating longitudinal field gives approximately the same strain and the same voltage polarity relative to the original unmagnetized reference. In the isotropic orientational model,It is unchanged under $\mathbf{m}\to -\mathbf{m}$. Both positive and negative longitudinal saturation therefore contract the negative-magnetostriction nickel in the same axial direction. The resulting stress on the piezoelectric layer has the same sign.

During field reversal there can be a hysteretic transient as domains reorganize, and finite circuit leakage can alter the measured waveform. Those effects do not turn the saturated strain law into a response odd in the field.

Assume that the transverse field is large enough to saturate through the thickness despite demagnetizing effects, and retain the thin-layer plane-stress and open-circuit assumptions from part(a). The two imposed in-plane strains now becomeTheir sum is $-\Lambda$, whereas it was $\Lambda /2$ for longitudinal saturation. The in-plane stress sum, and hence the induced open-circuit voltage, is multiplied by $-2$:Thus the magnitude is about $24\mathrm{mV}$ with the opposite polarity, under this model. The larger demagnetizing field for an out-of-plane direction means the same external field magnitude might not produce the same degree of saturation. Changes in thickness constraint or strain transfer would also modify the estimate.