Direct Determination of Magnetic Properties from Energy Landscapes around Trapped Magnetic Beads

Abstract

Many recent Lab-on-Chip systems make use of micrometer sized polystyrene beads containing superparamagnetic iron oxide nanoparticles. For applications in the field of micromagnetic manipulation precise knowledge of magnetic properties is important. While the ensemble-averaged properties have been widely studied, the measurement of single magnetic beads is yet a challenge. In previous works, we have demonstrated that superparamagnetic micro beads can be reliably trapped in a microfabricated 100 μm diameter current-carrying micro ring combined with a superimposed homogeneous field pointing perpendicular to the ring plane. Long-term observations of Brownian motion of the trapped beads over time scales of minutes to hours allow the determination of individual bead magnetic moments. The contribution made in this study is based on two magnetic beads simultaneously trapped in the same micro ring structure which are coupled via magnetic dipole–dipole interactions. From the dynamics of two coupled beads undergoing Brownian motion in the trap potential, we extract information about the trap interaction stiffness and the average magnetic dipole moment of the beads from just one single experiment. We show that the interaction force of superparamagnetic beads trapped in the center of a current conducting ring can be approximated by a first-order analytical series expansion. It can be simulated numerically as well as calculated analytically by a series of Legendre polynomials. We find that the restricted movement of two beads allows for a quick and accurate measurement of the average magnetic moment of the pair of beads compared to experiments with single beads.