Patterns of active dipolar particles in external magnetic fields

TL;DR

This study addresses how an external magnetic field shapes collective states in active dipolar particles. Using 2D Brownian dynamics simulations of self-propelled dipoles with a homogeneous field along x, the authors map state diagrams across density, field strength, dipole moment, and activity, classifying states with three order parameters. They find field-free states dominated by chains and networks evolve under strong fields into oriented chains and ferrofluid-like columnar bands, with dipolar interactions suppressing motility-induced phase separation. The work links active matter behavior to ferrofluid-like ordering and shows that field orientation can robustly control pattern formation, with implications for remote manipulation of microrobots and smart materials.

Abstract

Active particles with a (magnetic) dipole moment are of interest for steering self-propelled motion, but also result in novel collective effects due to their dipole-dipole interaction. Here systems of active dipolar particles are studied with Brownian dynamics simulations to systematically characterize the different patterns they form, specifically in the presence of an external (magnetic) field. The combination of three types of order - clustering, orientational alignment and chain formation - is used to classify the patterns observed in these systems. In the presence of an external field, oriented chains and bands are found to be dominant. These structures show some similarities with columnar cluster seen in (passive) ferrofluids and display columnar spacing and number of lanes per cluster that both decrease with increasing field strength.

Figures (12)

• Figure 1: Schematic illustrating single active particle with orientation $\hat{\bm{e}}$ in external homogeneous magnetic field $B\hat{\bm{e}}_x$ (blue). Particle has magnetic strength $\mu$ and self-propulsion speed $v_0$ (back).
• Figure 2: Snapshots showing examples for states introduced in \ref{['tab:orderParamCombi']} for systems at low density ($\Phi=0.13$), without an external field. Snapshots were taken at time $t=20$. The following states are shown: a. disordered gas ($\mu=0$, $v_0=23$), b. oriented gas ($\mu=2.6$, $v_0=500$), c. gas of chains ($\mu=1.6$, $v_0=23$), d. oriented chains ($\mu=1.6$, $v_0=500$), e. network of chains ($\mu=2.6$, $v_0=23$), f. bands ($\mu=4$, $v_0=100$). The color wheel (top left) indicates the orientation of the particles.
• Figure 3: Diagram of states in the absence of an external field for three densities $\Phi=$0.13;0.23;0.57 (left to right). The states result from order parameter criteria combinations according to \ref{['tab:orderParamCombi']}. The red box in the right diagram ($\Phi=0.57$) highlights cluster formation that corresponds to MIPS for apolar ($\mu=0$) active particles.
• Figure 4: Collection of snapshots of the system at low density ($\Phi =0.13$) for intermediate self-propulsion speed $v_0=23$ for different magnetic field strengths $B$ (rows) and values for magnetic interaction strengths $\mu$ (columns). External magnetic field points from left to right. All snapshots have been taken at time $t=20$.
• Figure 5: Three order parameters: fraction of largest cluster (top), polarization (center) and polymerization (bottom) against self-propulsion speed $v_0$ for four magnetic moments $\mu$ (colors). Solid color and solid lines show data for strong external magnetic field $B=14$, transparent colors and dashed lines show data with weak magnetic field strength $B=0.1$. System density was set to $\Phi=0.13$. Cut-off for cluster formation set at $\delta_c=1.28$.