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

The giant magnetoresistance mechanism is spin-dependent conduction through the two ferromagnets. Exchange splitting gives majority and minority $d$ bands different density of states values at the Fermi energy. Scattering into those bands, together with interface scattering, produces different resistances for the two spin channels. The relevant quantity is the spin-dependent transport/scattering rate, not simply a count of all available states.

For parallel layer magnetizations, one global spin channel encounters relatively weak scattering in both Co and NiFe, providing a low-resistance path. For antiparallel magnetizations, each global spin channel encounters one more strongly scattering ferromagnet, so both paths are comparatively resistive. The channels conduct in parallel while each crosses the layers in series. This is current-perpendicular-to-plane magnetoresistance, because the current crosses the interfaces.^[ref]

In the simplest two-current resistor model, with equal magnetic layers having channel resistances $a,b$ and spacer resistance $r$ per channel,Real Co/NiFe layers need not have equal parameters, but the same-sign spin asymmetries normally give $R_{AP}>R_P$. Their different magnetic coercivities allow the two configurations to be selected separately.

Assume NiFe is the softer layer, with $0<H_{c,\mathrm{NiFe}}<H_{c,\mathrm{Co}}$, 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:

On decreasing $H$ from positive saturation, the high-resistance window instead lies between $-H_{c,\mathrm{Co}}$ and $-H_{c,\mathrm{NiFe}}$. Thus the two sweep directions give displaced rectangular high-resistance windows, not a single reversible resistance peak centered on zero.

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.

Specify the magnetoresistance ratio as $(R_{AP}-R_P)/R_P$. Increasing a continuous Cu spacer adds spin-independent series resistance. Even when $d$ remains below the spin diffusion length, this dilutes the ratio; spin information need not be destroyed to reduce the percentage signal. In the illustrative two-current resistor model,which decreases as $d$ increases. The absolute difference also decreases in this model. At a fixed bias current, the measured voltage contrast is $\Delta V=I(R_{AP}-R_P)$.

For $d$ comparable to or greater than the spin diffusion length, additional spin relaxation further suppresses the contrast. At the other extreme an ultrathin or discontinuous Cu layer can introduce direct magnetic coupling or pinholes, preventing a fully antiparallel state. Thickness-dependent interlayer coupling can therefore make the very-thin-spacer trend nonmonotonic; a universal exponential law does not follow from the supplied assumptions.

Roughness can produce a distribution of local switching fields and nonuniform reversal. The abrupt edges in the ideal pseudo spin valve loops then become rounded or sloping, the antiparallel plateau becomes less flat, and overlapping layer-reversal distributions can narrow or partly eliminate the clear high-resistance window. The middle panel of the original diagram illustrates only this broadening mechanism.

Correlated roughness on the two interfaces can also introduce orange-peel coupling, a magnetostatic coupling that favors parallel alignment. Such coupling shifts switching fields and can suppress independent reversal. Sufficiently severe roughness or pinholes can have a similar qualitative effect by directly coupling the ferromagnets.

Changes in amplitude require care. Some spin-dependent interface scattering contributes to giant magnetoresistance, so a small increase in roughness is not guaranteed to lower the signal monotonically. Intermixing, spin-flip scattering and an incompletely antiparallel state generally reduce useful contrast. The detailed width, displacement and height of $R(H)$ therefore depend on how the interfaces become rough, rather than on a single roughness number.

Two practical approaches retaining Co and NiFe are:

Increasing magnetic-layer thickness toward the useful spin-dependent-scattering scale can be another optimization, but growth beyond the relevant spin diffusion scale eventually gives diminishing returns. Merely increasing the bias current increases the readout voltage and possible heating; it does not, by itself, increase the intrinsic giant magnetoresistance ratio.