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The measuring electric current crosses the layer planes. This geometry motivates the serial-layer paths in the two-current resistor model. A quantitative material calculation can also require interface electrical resistances, spin relaxation and spin accumulation; the circuit below intentionally isolates a smaller set of assumptions.

Giant magnetoresistance connects the relative magnetizations of adjacent magnetic layers to their electrical transport. In a suitable magnetic-metal/nonmagnetic-metal stack, aligning the layers can leave one spin channel with an easy conducting path through both magnetic layers; opposite alignments make each channel encounter a more resistive layer. Albert Fert's account traces the spin-dependent-conduction idea to Nevill Mott and distinguishes the later device geometries.^[ref]

The beauty is that a magnetic arrangement becomes an electrical readout. Preparing reproducible layers, establishing their magnetizations, and measuring electrical resistance are separate parts of that inference. The Fe-Cr giant magnetoresistance experiments show how those parts were joined; the two-current resistor model isolates a simple transport mechanism under stated assumptions.

Sweep the in-plane magnetic field approximately along the wires' easy axes. At large negative field, both magnetizations are parallel. If the wires reverse at different positive coercive fields, an antiparallel interval separates this state from the final parallel positive-field state. In the usual positive giant magnetoresistance case, the antiparallel interval has higher resistance; the reverse sweep gives a mirrored interval and a hysteresis loop.

An ideal angular model isSpin-dependent injection and scattering favor transmission through similarly aligned electrodes. The two-current resistor model represents this using unequal majority- and minority-spin resistances. Both layers can reverse, hence pseudo spin valve, rather than an absolutely pinned reference layer.

The different thicknesses can produce different switching properties, but thickness alone does not identify which electrode reverses first. Measure their coercive fields. The local resistance also contains Cu, contact and Py anisotropic magnetoresistance contributions. Rotation scans and individual-wire controls distinguish them. Py/Cu experiments showed that local contact-related signals can exceed the spin-valve contribution, motivating nonlocal detection.^[ref]

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.

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.

Exchange-split bands in a ferromagnet generally give a different spin-resolved density of states for each spin branch, $D_{\uparrow }(E_F)$ and $D_{\downarrow }(E_F)$. If spin is approximately conserved across a multilayer, its two spin channels conduct in parallel. A spin valve combines a comparatively fixed reference-layer magnetization with a soft free layer that rotates in a small applied field. Its readout depends on the relative angle, not simply the absolute spin population. Biasing the layers near a perpendicular alignment gives a useful linear response instead of operating at the flat parallel/antiparallel extrema.

In giant magnetoresistance, a metallic spacer separates ferromagnetic layers. Spin-dependent bulk and interface scattering make their channel resistances unequal. The density of available final $d$ states influences scattering of more mobile states; however, a large total density of states does not by itself guarantee a large conductivity. The scattering-weighted spin-channel asymmetry also involves velocity and scattering matrix elements. In the elementary identical-layer two-current resistor model, let each magnetic layer have resistances $a,b$ in the two spin channels and neglect spacer resistance. Parallel moments give channels $2a$ and $2b$, while antiparallel moments give $a+b$ in each channel. ThereforeOne favorable spin channel traverses both aligned layers efficiently; reversal removes that common easy path. A conducting spacer adds resistance, and spin mixing weakens the separate-channel approximation. The channel asymmetry is material/interface dependent, so positive magnetoresistance is not a theorem for every pair of different ferromagnets.^[ref]

In tunnelling magnetoresistance, the spacer is an ultrathin insulator and current flows across a magnetic tunnel junction. In the simple spin-conserving density-of-states tunnelling magnetoresistance model, assume spin-independent matrix elements and low voltage. Available initial and final states giveWriting $P_i=(D_{i\uparrow }-D_{i\downarrow })/(D_{i\uparrow }+D_{i\downarrow })$ and $G_0=C{D}_1{D}_2/2$, these become $G_P=G_0(1+P_1{P}_2)$ and $G_{AP}=G_0(1-P_1{P}_2)$. ThusThe effective tunnelling polarization can depend on the barrier and orbital symmetry, not just a bulk density-of-states sketch. Crystalline MgO junctions exploit symmetry-selective transmission, so the elementary product model is not a quantitative universal formula for them.^[ref]

Both devices convert a free-layer rotation into an electrical change. A useful approximate GMR interpolation is $R(\theta )=R_P+\Delta R(1-\cos \theta )/2$; the elementary tunnelling model instead gives $G(\theta )=G_0(1+P_1{P}_2\cos \theta )$. The spin-valve small-field sensitivity is a chain rule,magnetic anisotropy, biasing and pinning set the rotation susceptibility. Conducting-spacer GMR usually offers low resistance and supports current-in-plane or current-perpendicular geometries. TMR uses perpendicular tunnelling, often offers a larger fractional signal and a larger resistance-area product, but demands uniform, stable barriers and has bias dependence and breakdown limits. Neither is automatically the better small-field sensor: heating, Johnson and low-frequency noise, domain switching, hysteresis and stability set the detectable field. Reverse sweep direction, vary current and temperature, and independently test reference-layer pinning to distinguish a reproducible magnetic signal from drift or heating.