Origin of the Magnetization Anisotropy of Superparamagnetic Beads

Superparamagnetic beads are used in single-molecule magnetic tweezers experiments to investigate the mechanics and dynamics of biomolecules. The beads exhibit a weak anisotropy, such that they align with the applied magnetic field. This allows to rotate the beads and thus to twist of attached biomolecules. To quantitatively understand the origin of the magnetization anisotropy, we use high-speed magnetic tweezers experiments, numerical simulations, as well as fluxgate magnetorelaxometry measurements. We find that Brownian orientation fluctuations of the beads occur up to cut-off frequencies of ∼100 Hz being only weakly dependent on the applied field, which superimpose the dynamics of attached biomolecules. When simulating the equilibrium magnetization of single beads as ensembles of ∼10⁵ anisotropic and randomly oriented superparamagnetic nanoparticles, a single anisotropy axis is formed, which matches the magnitude of the experimental results. The time scale of the magnetization relaxation spans several orders of magnitude. Overall, our data reveal that the magnetic beads contain randomly oriented magnetic domains with a rather wide size distribution in which the bead anisotropy is the finite residual of the sum of the nanoparticle anisotropies. It is thus an inherent property of magnetic beads and needs to be considered in high-resolution measurements of magnetic tweezers.