Frequency-dependent aggregate structures and dynamic behaviour of magnetic cubic particles in a rotating magnetic field

We investigated dimensionality-dependent aggregate formation and structural transitions of magnetic cubic particles in a rotating magnetic field using three-dimensional Brownian dynamics simulations. Unlike quasi-two-dimensional models, the particle centres were free to move in all directions, allowing out-of-plane face-to-face contacts. As the magnetic particle–particle interaction increased, the system changed from dispersed particles to disordered aggregates and finally to compact three-dimensional aggregates with ordered face-to-face packing. For strongly interacting particles, increasing the magnetic field strength destabilised the compact aggregates and induced a transition through disordered three-dimensional networks to wall-like planar aggregates extending mainly in the field-rotation plane. Although no geometrical confinement was imposed, these wall-like aggregates exhibited quasi-two-dimensional-like internal ordering, indicating that such ordering can emerge dynamically in a fully three-dimensional system. Cluster-size distributions and gyration-tensor-based shape parameters quantitatively supported these structural changes. We also examined the frequency-dependent stability and reorganisation of a preassembled compact aggregate. At high frequency, the compact structure was retained, whereas at intermediate frequencies it collapsed and reorganised into planar aggregates. At low frequency, an elongated aggregate rotated with a small phase delay relative to the field. These findings show that field strength and frequency can control aggregate morphology and magnetic response.