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.