Two Currents in One Wire: How Giant Magnetoresistance Let the Hard-Disk Bit Keep Shrinking — Epoche C1
A recorded bit on a hard disk is a small patch of magnetised film, and a read head detects it only through the stray field leaking above the disk surface — a field that falls roughly in proportion to the patch's area as bits shrink. By the late 1980s that arithmetic was closing in on the sensors then available, and the usual account of what happened next describes incremental refinement: smaller heads, purer films, tighter flying height. That account misplaces the cause. The sensors that carried disk storage through the 1990s changed the physical mechanism they exploited, moving from effects available to the electron's charge to one available only to its spin. This essay works out why the charge-based ceiling is where it is, derives the spin-based effect from a resistor network anyone can check, and then explains what had to be added before a laboratory effect requiring two tesla could respond to the hundredth of a tesla a bit provides. The ceiling on charge-only sensing Take first the effect any metal shows. A magnetic field bends an electron's path between collisions, and in the Drude picture the fractional change in resistance is of order $(\omega_c\tau)^2$, the square of the fraction of a cyclotron orbit completed before the next collision randomises the motion. Here $\omega_c = eB/m$ is the cyclotron angular frequency and $\tau$ the mean free time. The square appears because the field enters the equation of motion through a cross product that is odd in $B$, while the resistance is a scalar even in $B$ for a simple metal, so the leading correction is quadratic. The numbers decide the question. A bit supplies roughly $100\,\mathrm{G}$, that is $10^{-2}\,\mathrm{T}$, at the sensor. Then $$\omega_c = \frac{(1.60\times10^{-19}\,\mathrm{C})(10^{-2}\,\mathrm{T})}{9.11\times10^{-31}\,\mathrm{kg}} = 1.76\times10^{9}\ \mathrm{rad\,s^{-1}},$$ and copper at room temperature has $\tau \approx 2\times10^{-14}\,\mathrm{s}$, so $\omega_c\tau \approx 3.5\times10^{-5}$ and $(\omega_c\tau)^2 \approx 1.2\times10^{-9}$. A signal of one part in a billion is not a signal. The reason is visible in the product: $\tau$ is fixed by the metal's purity and temperature and cannot be raised by orders of magnitude in a working device, while $\omega_c$ is fixed by the field the bit can supply, which is precisely the quantity that shrinking bits reduces. Ferromagnets do better. Their resistivity depends slightly on the angle between the current direction and the magnetisation, an effect called anisotropic magnetoresistance; McGuire and Potter (1975) surveyed it across the 3d alloys and found room-temperature ratios of a few per cent in the best permalloy compositions, which is what the read heads introduced around 1991 exploited. But the mechanism is spin–orbit coupling, the relativistic term linking an electron's spin to its orbital motion, whose strength in a 3d metal is a small fraction of the bandwidth. Two per cent is therefore not an engineering limit but close to the physical one, and a sensor built on it cannot be improved by another order of magnitude. Effect Physical origin Size at 300 K in a field of about 100 G Ordinary magnetoresistance Lorentz bending of orbits, $(\omega_c\tau)^2$ $\sim 10^{-9}$ Anisotropic magnetoresistance Spin–orbit coupling about 2 per cent Giant magnetoresistance Spin-dependent scattering in multilayers tens of per cent Mott's two currents The mechanism that broke the ceiling had been described in principle half a century earlier. Mott (1936) argued that in a ferromagnet the current is carried by two nearly independent populations: electrons whose spin — their intrinsic angular momentum, which along any chosen axis takes one of two values — is parallel to the local magnetisation, and those whose spin is antiparallel. The two populations are independent because processes that flip a spin are rare compared with processes that merely deflect one: flipping requires either the weak spin–orbit interaction or the absorption of a magnon, a quantised spin wave, whose population falls away as the temperature drops. Below the temperature at which magnons are plentiful, the two populations act as two resistors in parallel, sharing the same wire and not exchanging carriers. They have different resistivities, and Fermi's golden rule says why. The rate at which an electron scatters out of its state is proportional to the number of final states available at the same energy, that is to the density of states at the Fermi energy $E_F$, the level separating occupied from empty states. In a ferromagnet the exchange interaction rigidly shifts the 3d bands of the two spin orientations apart — by roughly $2\,\mathrm{eV}$ in iron — so the two spin orientations meet quite different densities of available final states at $E_F$. In layered structures the asymmetry is sharpest at the interfaces, where the mismatch between the bands of the two metals is itself spin-dependent: in a cobalt–copper stack the copper band matches the majority-spin band of cobalt closely and the minority-spin band poorly, so one spin passes almost unimpeded while the other is strongly reflected. Write $\rho_\uparrow$ for the resistivity seen by electrons whose spin is parallel to the local magnetisation and $\rho_\downarrow$ for the antiparallel case, and let $\alpha = \rho_\downarrow/\rho_\uparrow$ measure the asymmetry. The stack as a spin resistor network Baibich and co-workers (1988) grew superlattices of iron layers $30\,\text{Å}$ thick separated by chromium spacers $9\,\text{Å}$ thick, sixty periods deep. Two features of that recipe do the work. First, the spacer thickness sets the sign of the magnetic coupling between successive iron layers: Parkin, More and Roche (1990) showed that this interlayer exchange coupling oscillates between favouring parallel and antiparallel alignment as the spacer grows, with a period of roughly a nanometre, so $9\,\text{Å}$ of chromium is not an arbitrary choice but a thickness at which neighbour