  Vertical packaging of multiple Giant Magnetoresistance (multi-GMR) stacks is
a very interesting noise reduction strategy for local magnetic sensor
measurements, which has not been reported experimentally so far. Here, we have
fabricated multi-GMR sensors (up to 12 repetitions) keeping good GMR ratio,
linearity and low roughness. From magnetotransport measurements, two different
resistance responses have been observed with a crossover around 5 GMR
repetitions: step-like (N<5) and linear (N>5) behavior, respectively. With the
help of micromagnetic simulations, we have analyzed in detail the two main
magnetic mechanisms: the Neel coupling distribution induced by the roughness
propagation and the additive dipolar coupling between the N free layers.
Furthermore we have correlated the dipolar coupling mechanism, controlled by
the number of GMRs (N) and lateral dimensions (width), to the sensor
performance (sensitivity, noise and detectivity) in good agreement with
analytical theory. The noise roughly decreases in multi-GMRs as 1/\sqrt{N} in
both regimes (low frequency 1/f and thermal noise). The sensitivity is even
stronger reduced, scaling as 1/N, in the strong dipolar regime (narrow devices)
while converges to a constant value in the weak dipolar regime (wide devices).
Very interestingly, they are more robust against undesirable RTN noise than
single GMRs at high voltages and the linearity can be extended towards much
larger magnetic field range without dealing with the size and the reduction of
GMR ratio. Finally, we have identified the optimal conditions for which
multi-GMRs exhibit lower magnetic field detectivity than single GMRs: wide
devices operating in the thermal regime where much higher voltage can be
applied without generating remarkable magnetic noise.
