Spin Valve

Intuition

A spin valve is the simplest magnetic resistor you can build out of two ferromagnets. Stack two magnetic layers with a thin non-magnetic conductor between them and the device’s electrical resistance becomes a function of the relative orientation of their magnetizations — low when the two layers are parallel, high when they are antiparallel. The reason is that the conduction electrons themselves carry spin, and each ferromagnetic layer acts as a spin filter: it lets through electrons aligned with its magnetization much more easily than the opposite spin. Two filters in series transmit a lot of current when their preferences agree and very little when they disagree — exactly like crossing two polarizers in optics. This effect is giant magnetoresistance (GMR), and it underlies nearly every magnetic sensor and read head built since the 1990s.

Formal Definition

A spin valve is a multilayer of the form

$${\text{FM}}_1|\text{NM}|{\text{FM}}_2,$$

with two ferromagnetic layers (${\text{FM}}_1$, ${\text{FM}}_2$) separated by a thin non-magnetic metallic spacer ($\text{NM}$, e.g. Cu, Cr). The magnetizations of the two FM layers, ${\vec{m}}_1$ and ${\vec{m}}_2$, make an angle $\theta$. The device’s two-terminal resistance $R(\theta )$ interpolates between the parallel and antiparallel values:

$$R(\theta )=R_P+(R_{AP}-R_P)\frac{1-\cos \theta }{2},R_P<R_{AP}.$$

The GMR ratio

$$\mathrm{GMR}\equiv \frac{R_{AP}-R_P}{R_P}$$

quantifies the contrast, typically a few percent to tens of percent in metallic stacks at room temperature.

Key Results

1. Why the resistance depends on alignment — spin-dependent scattering

In a ferromagnetic metal, the conduction electrons of majority spin (parallel to the local magnetization) and minority spin (antiparallel) see different densities of states at the Fermi level. They scatter differently — typically the minority channel resists more. Sorting the current by spin gives two resistances in parallel, one per spin species: the Mott two-current model.

• Parallel configuration (${\vec{m}}_1\parallel {\vec{m}}_2$): the spin-up channel is “majority” in both layers and travels easily; the spin-down channel is “minority” in both. The low-resistance spin-up channel short-circuits the high-resistance one, and the total resistance is low.
• Antiparallel configuration (${\vec{m}}_1\parallel -{\vec{m}}_2$): every electron is “majority” in one layer and “minority” in the other. Neither spin channel finds an easy path, both channels are similarly resistive, and the parallel combination is higher than in the parallel case.

This is the microscopic content of the Mott two-current model — the explanation Fert and Grünberg gave for the GMR they each discovered in 1988 (Nobel Prize in Physics, 2007).

2. Pedagogical toy model

A useful intuition pump (not literal physics, but the right spirit): treat each layer as a probabilistic filter that transmits an aligned spin with high probability and an opposite spin with low probability. Take 50% spin-up, 50% spin-down at the input, and per-layer transmission probabilities $\sim 90\%$ (aligned) and $\sim 10\%$ (opposite):

Electron spin	Parallel ($\uparrow \uparrow$)	Antiparallel ($\uparrow \downarrow$)
Up	$0.9\times 0.9\approx 81\%$ pass	$0.9\times 0.1\approx 9\%$ pass
Down	$0.1\times 0.1\approx 1\%$ pass	$0.1\times 0.9\approx 9\%$ pass
Total	$\sim 41\%$	$\sim 9\%$

The parallel stack transmits much more current than the antiparallel stack — i.e. has lower resistance. The same conclusion the two-current model gives, in cartoon form.

The crucial subtlety: scattering is not counted layer by layer for each electron classically. Each spin species is a quantum channel whose transmission depends on both layers — what matters is the joint probability for a spin channel to make it through the stack.

3. The atoms don’t change — only the spin direction does

Applying a small external field flips the magnetization of the free layer relative to the pinned (reference) layer. The magnetic atoms themselves stay locked in the lattice; only their collective spin orientation rotates. So the device’s resistance is electrically reconfigurable by a magnetic field — the foundation of every modern hard-disk read head.

Summary

Property	Parallel ($\theta =0$)	Antiparallel ($\theta =\pi$)
Resistance	$R_P$ (low)	$R_{AP}$ (high)
Spin-up channel	majority everywhere — easy path	majority/minority — blocked once
Spin-down channel	minority everywhere — hard	minority/majority — blocked once
Net effect	one short-circuit channel	no short-circuit channel

A spin valve is therefore a magnetically tunable resistor. Replace the metallic spacer with a thin insulating barrier (e.g. MgO) and the same geometry becomes a magnetic tunnel junction, where tunneling magnetoresistance (TMR) replaces GMR with much larger ratios.

Connections

• magnetic-atom — bound vs conduction electrons, the prerequisite for spintronics
• magnetization — what defines the “majority” direction in each layer
• spin-polarized-current — the current that emerges from a ferromagnetic filter (stub)
• spin-transfer-torque — when the spin-polarized current acts back on $\vec{m}$ (stub)
• magnetic-tunnel-junction — the tunneling cousin of the spin valve (stub)

References

• M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988) — discovery of GMR.
• G. Binasch et al., Phys. Rev. B 39, 4828 (1989) — independent GMR discovery.
• N. F. Mott, Adv. Phys. 13, 325 (1964) — two-current model.
• A. Fert, Rev. Mod. Phys. 80, 1517 (2008) — Nobel lecture, spintronics overview.