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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2023/paper-2/section-a-ii/16/ii/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 2 / Section A(ii) / 16 / ii / Solution by

Codex  0 2026-10-20

Assume NiFe is the softer layer, with

0 < H_{c, NiFe} < H_{c, Co}

, and that interlayer coupling is weak enough to permit separate reversal. Starting at large negative

H

, both magnetizations point in the same direction and

R = R_{P}

. During an increasing-field sweep:

At $H = H_{c, NiFe}$ , NiFe reverses while Co does not: the state is antiparallel and the resistance rises to $R_{A P}$ .
At $H = H_{c, Co}$ , Co also reverses: the state becomes parallel and the resistance returns to $R_{P}$ .

On decreasing

H

from positive saturation, the high-resistance window instead lies between

- H_{c, Co}

and

- H_{c, NiFe}

. Thus the two sweep directions give displaced rectangular high-resistance windows, not a single reversible resistance peak centered on zero.

Figure 1.
Pseudo spin-valve resistance loops, distributed switching and spacer dilution
. Original illustrative curves. Separate coercive fields create an antiparallel window on each sweep. The middle panel isolates switching-field broadening; its retained peak height is not a claim that real roughness leaves the GMR amplitude unchanged. **Source**. **Details**.

If Co were the softer layer, the sequence of layer labels would be exchanged. A continuous spacer and sufficiently weak coupling are additional assumptions: negligible surface roughness alone does not guarantee independent switching at every Cu thickness.

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