Multiple Giant-Magnetoresistance Sensors Controlled by Additive Dipolar Coupling

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 fabricate multi-GMR sensors (up to 12 repetitions) that maintain a good GMR ratio, linearity, and low roughness. From magnetotransport measurements, two different resistance responses are observed with a crossover at around five GMR repetitions: steplike (N 5) and linear (N \ensuremath{\ge} 5) behavior, respectively. With the help of micromagnetic simulations, we analyze, in detail, the two main magnetic mechanisms: the N\'eel coupling distribution induced by the roughness propagation and the additive dipolar coupling between the N free layers. Furthermore, we correlate the dipolar coupling mechanism, which is controlled by the number of GMRs (N) and lateral dimensions (width), to the sensor performance (sensitivity, noise, and detectivity); this is 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 more strongly reduced, scaling as ${N}^{\ensuremath{-}1}$, in the strong dipolar regime (narrow devices), while converging to a constant value in the weak dipolar regime (wide devices). Interestingly, they are more robust against undesirable random telegraphic noise than single GMRs at high voltages, and the linearity can be extended towards a much larger magnetic field range, without dealing with the size and reduction of the GMR ratio. Finally, we identify the optimal conditions for which multi-GMRs exhibit lower magnetic field detectivity than that of single GMRs: wide devices operating in the thermal regime, where much higher voltage can be applied without generating remarkable magnetic noise. These results open the path towards spintronics sensors connected and coupled in three dimensions with reduced noise, compact footprint, and mainly tuned by the dipolar coupling.