Model and experiment of detecting multiple magnetic nanoparticles as biomolecular labels by spin valve sensors

We present an analytical model for detection of multiple magnetic nanoparticles (NP) as biomolecular labels by spin valve (SV) sensors, aiming to establish the relationship between the SV sensor signal and the number of magnetic labels. The model is based on the assumptions of equivalent average field of magnetic NPs and the coherent magnetization rotation of SVs free layer. Using the model, we have calculated the sensor signals of multiple NPs uniformly or randomly distributed over a SV sensor at various aspect ratios of the NP array. Satisfactory signal linearity at low particle number or high aspect ratio has been found. The model also reveals that the SV sensors could be made insensitive to the random configuration of NPs and only sensitive to the number of NPs. This feature is desired for quantitative bio-detection. To check the validity of the model, we performed experiments on a monolayer of 16-nm Fe₃O₄ NPs coated on 0.3-μm-wide SV sensors. We found that the measured signals could be well described by the analytical model.