A real spin-valve read head is a trilayer: an antiferromagnet exchange-pins one ferromagnetic layer's magnetization rigidly in place, a thin non-magnetic Cu spacer decouples it from a second, magnetically "free" ferromagnetic layer that rotates freely with an external field.
Electrons carry spin up or down and split into two independent conduction channels (the two-current / Mott model). Each channel's resistance is a series sum over the layers it crosses, weighted by how misaligned that layer's magnetization is from the channel's own spin axis:
mismatch(θ) = (1 − cosθ) / 2
R_channel = R_lead + Σ_layers [ R0 + A·mismatch(θ_layer) ]
R_total = (R_up · R_down) / (R_up + R_down)
When the free layer sits parallel to the pinned layer, one spin channel is aligned with both layers everywhere along its path (low resistance) and short-circuits the other — R_total is low. When it flips antiparallel, every channel is mismatched with one layer or the other, and R_total is high. The GMR ratio slider sets ΔR/R_P by solving A in closed form from the two-current algebra above, so the readout matches the dialled-in percentage exactly.
The free layer does not track the field continuously — it flips discretely once |H| exceeds the coercive field H_c (set by spacer thickness, since a thinner spacer means stronger interlayer coupling and a harder switch), and it remembers which way it last flipped. That memory is exactly what produces the rectangular hysteresis loop on the R–H plot: sweeping the field up and down traces two different branches, offset from zero by the exchange-bias field H_ex.