# Origin of the Magnetization Anisotropy of Superparamagnetic Beads

## TL;DR

The paper explains why superparamagnetic beads used in magnetic tweezers experiments have a weak magnetic anisotropy, which affects the accuracy of measurements.

## Contribution

The study reveals that bead anisotropy arises from the finite sum of randomly oriented nanoparticle anisotropies.

## Key findings

- Bead anisotropy is an inherent property due to randomly oriented magnetic domains.
- Brownian fluctuations of beads occur up to ~100 Hz and affect biomolecule dynamics.
- Simulations show that a single anisotropy axis forms from ensembles of nanoparticles.

## Abstract

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.

Superparamagnetic beads are widely employed to study the mechanics of biomolecules with magnetic tweezers. It is shown that the residual anisotropy of the beads is due to averaging over a finite number of randomly oriented nanoparticles contained in the beads. Pinning of the anisotropic beads in the field causes low and high‐frequency noise in magnetic tweezers measurements, and ways to overcome this resolution limit are discussed.