Theoretical study of in-plane response of magnetic field sensor to magnetic beads in an in-plane homogeneous field

Abstract

We present a systematic theoretical study of the average in-plane magnetic field on square and rectangular magnetic field sensors from a single magnetic bead and a monolayer of magnetic beads magnetized by an in-plane externally applied homogeneous magnetic field. General theoretical expressions are derived such that the sensor response and its dependence on the sensor size, spacer layer thickness, bead diameter, and bead susceptibility can easily be evaluated. The average magnetic field from a single bead close to the sensor shows a strong dependence on the position of the bead and a change of sign when the bead passes the edge of the sensor in the direction of the applied field. Analytical approximations are derived for the average field from a homogeneous monolayer of beads for beads much smaller than the sensor dimension and for a bead size chosen to minimize the position sensitivity of the sensor response. We discuss implications for the sensor design and give general guidelines for optimum choices of sensor dimension, spacer layer thickness, and bead diameter, as well as simple expressions for the average magnetic field from the beads. The usage of the general guidelines is exemplified in the design considerations for a sensor, which is fully covered by 100 beads and has a spacer layer thickness of 100 nm.