Theoretical study of in-plane response of magnetic field sensor to magnetic beads magnetized by the sensor self-field

Abstract

We present a theoretical study of the spatially averaged in-plane magnetic field on square and rectangular magnetic field sensors from a single magnetic bead, a monolayer of magnetic beads, and a half-space filled with magnetic beads being magnetized by the magnetic self-field due to the applied bias current through the sensor. The analysis of the single bead response shows that beads always contribute positively to the average magnetic field as opposed to the case for an applied homogeneous magnetic field where the sign of the signal depends on the bead position. General expressions and analytical approximations are derived for the sensor response to beads as function of the bead distribution, the bias current, the geometry and size of the sensor, and the bead characteristics. Consequences for the sensor design are exemplified and it is described how the contribution from the self-field experimentally can be separated from that due to static magnetic fields.

Planar Hall effect bridge sensors with NiFe/Cu/IrMn stack optimized for self-field magnetic bead detection

“…For the sensor with the highest bead signal at fixed amplitude of the bias current (t FM ¼ 10 nm, t Cu ¼ 0.75 nm), we estimated a limit of detection (taken as the field where the signal equals three times the standard deviation of the baseline signal) of B b ¼ 0.5 nT corresponding to a bead concentration of 13 lg/ml. As the sensor is mainly sensitive to magnetic beads close to the sensor, we can use the results of Hansen et al 19 to estimate that most of the signal is due to beads in a volume over the four sensor branches of V % 2lp(1.3w) 2 ¼ 1.1 nl. Combining this with the mass density of the magnetic beads of 3200 kg/m 3 specified by the manufacturer, we estimate that the signal from a bead concentration of 13 lg/ml is generated by approximately 1.6 Â 10 4 beads in suspension.…”

“…The magnetized beads generate a dipole magnetic field that allows their detection with no need for other external magnetic fields. The magnetic field from the beads (B b ) is proportional to the sensor bias current 7,15,18,19 and can be written as…”

“…17 (2) As opposed to magnetic beads magnetized by a homogeneous external magnetic field, the signal from a magnetic bead has the same sign irrespective of the position of the magnetic bead relative to the sensor, and therefore, signal cancelation effects are avoided. 19,20 The magnetic bead signal obtained using the self-field detection approach is proportional to the square of the sensor bias current, 19 and therefore, it is desirable to use a high bias current.…”

On-chip measurement of the Brownian relaxation frequency of magnetic beads using magnetic tunneling junctions

“…Moreover, assuming a linear bead response, the average fields from the magnetic beads on the sensor are ␣ H dc and ␤ I CL , where is the effective bead susceptibility and ␣ and ␤ are factors that depend on the sensor geometry and the bead size and distribution. 10,11 Hence, we have…”

Planar Hall effect bridge geometries optimized for magnetic bead detection

“…This contribution depends on the sensor stack and width and its magnitude can be written as c 0 I bar . 20 A second contribution is from magnetic beads being magnetized by the sensor self-field. These give rise to a magnetic field of magnitude c 1 vI bar , where c 1 is a positive constant depending on the distribution and amount of magnetic beads as well as the sensor geometry, which relates the current times the magnetic bead susceptibility to the average magnetic field experienced by the sensor due to the magnetic beads.…”