On-chip measurements of Brownian relaxation vs. concentration of 40 nm magnetic beads

We present on-chip Brownian relaxation measurements on a logarithmic dilution series of 40 nm beads dispersed in water with bead concentrations between 16 μg/ml and 4000 μg/ml. The measurements are performed using a planar Hall effect bridge sensor at frequencies up to 1 MHz. No external fields are needed as the beads are magnetized by the field generated by the applied sensor bias current. We show that the Brownian relaxation frequency can be extracted from fitting the Cole-Cole model to measurements for bead concentrations of 64 μg/ml or higher and that the measured dynamic magnetic response is proportional to the bead concentration. For bead concentrations higher than or equal to 500 μg/ml, we extract a hydrodynamic diameter of 47(1) nm for the beads, which is close to the nominal bead size of 40 nm. Furthermore, we study the signal vs. bead concentration at a fixed frequency close to the Brownian relaxation peak and find that the signal from bead suspensions with concentrations down to 16 μg/ml can be resolved.