Rolling at right angles: the dynamics of superparamagnetic active rollers

Quincke rotation occurs when a dielectric particle in a conducting fluid rotates spontaneously in response to an external DC electric field E. Above a threshold value E_c, surface friction drives rolling in the plane orthogonal to E at a constant speed set by the field. Typical Quincke systems showcase individual random walks, with collective motion arising at sufficient densities. We introduce an additional degree of freedom using superparamagnetic colloids, & observe markedly different dynamics. With no magnetic field B, rollers execute tight circular trajectories or even orbits. These are more unstable at higher E fields, as periods of circular motion may be interspersed with short “walks”. Introducing a homogeneous in-plane B alongside E linearises the circular motion, as the rollers' induced magnetic moment aligns with B, fixing the Quincke rotation axis to stabilise rolling perpendicular to the magnetic field lines, consistent with other work. However, as we increase the applied B field beyond 200G, we see the emergence of an anomalous secondary mode of active rollers travelling parallel to the magnetic field lines. We have used a model of anisotropic magnetic susceptibility to successfully reproduce these quasi-stable trajectories in numerical simulations, showing the magnetic dipole moment tumbling in the plane orthogonal to the rolling surface. By continued exploration of the phase space to expand our model, we aim to capture the full range of dynamics & better elucidate the stabilising mechanism.