Spin Valve: GMR/TMR Hysteresis and the Two-Current Model
An interactive spin valve. In the metallic case the two-current model treats spin-up and spin-down electrons as independent parallel channels, giving a parallel-state resistance $R_P = 2 R_{\uparrow} R_{\downarrow}/(R_{\uparrow} + R_{\downarrow})$ and an antiparallel-state resistance $R_{AP} = (R_{\uparrow} + R_{\downarrow})/2$, so $R_P \le R_{AP}$ always (the arithmetic-harmonic mean inequality) and $\mathrm{GMR} = (R_{AP} - R_P)/R_P = (R_{\uparrow} - R_{\downarrow})^2/(4 R_{\uparrow} R_{\downarrow}) = \beta^2/(1 - \beta^2)$ with channel asymmetry $\beta$. In the tunnel-junction case the Julliere model gives $\mathrm{TMR} = 2 P_1 P_2/(1 - P_1 P_2)$ with electrode spin polarisations $P_1, P_2$. A soft free layer switches at $\pm H_{c,\mathrm{free}}$ while an exchange-biased pinned layer stays fixed, so sweeping the applied field traces a hysteretic $R(H)$ loop that toggles between the low-resistance parallel state and the high-resistance antiparallel state. Sweeping the applied field through the two coercive fields toggles the stack between the low-resistance parallel and high-resistance antiparallel states, tracing the hysteretic $R(H)$ loop that giant magnetoresistance (GMR) read heads exploit.
WHAT TO TRY
- Sweep the applied field H around the hysteresis loop: the free layer flips at its coercive field while the pinned layer stays put, switching the stack between parallel (low R) and antiparallel (high R). That resistance jump is the read signal of a hard drive head.
- Raise the spin polarization P: the magnetoresistance ratio climbs steeply, since the two-current model gives MR proportional to P squared over (1 - P squared). Higher polarization means a bigger signal.
- Switch from GMR to TMR: the metallic spacer becomes a tunnel barrier and the Julliere model takes over, giving the much larger tunnelling magnetoresistance used in modern MRAM.