Understanding the self-propulsion behavior of active particles and predicting their trajectories is crucial for achieving desired paths by using external stimuli, such as chemical and thermal gradients, electric and magnetic fields, etc. This phenomenon plays a vital role in various fields, such as drug delivery, cargo transportation, and environmental remediation. In this regard, anisotropic magnetic microswimmers (platinum-coated core-shell cube particles) with different intrinsic magnetic strengths have been employed to study the self-propulsion trajectories under a geomagnetic field, using hydrogen peroxide as a fuel medium. Interestingly, these particles exhibit three different types of self-propulsion trajectories based on their intrinsic magnetic strength: random, meandering, and straight tracks, each with a distinct mean-squared displacement. The experimental and simulation studies revealed that the self-propulsion trajectories are determined by the interplay between rotational diffusivity ($D_R$) and characteristic magnetic frequency (${\omega }_c$) of the particle under the geomagnetic field. Where $D_R$ attempts to randomize the direction of the self-propelled particle, while the ${\omega }_c$ aligns the particles in the geomagnetic field direction by constraining the particle angle. This is further confirmed by using another shape of magnetic microswimmer (platinum-coated core-shell spherocylindrical particles), which show similar trajectory behavior for different ${\omega }_c$ values, confirming that the intrinsic magnetic strength of the particle defines the type of trajectories in the Earth's magnetic field. These distinct trajectories of magnetic active particles were characterized by the ratio of rotational diffusion time (${\tau }_R=D_R^{-1}$) and magnetic constraint time (${\tau }_M={\omega }_c^{-1}$), irrespective of particle shape. Where a particle with ${\tau }_R/{\tau }_M \ll 1$ shows a random trajectory, while a particle having ${\tau }_R/{\tau }_M \gg 1$ shows a straight trajectory, and for ${\tau }_R/{\tau }_M \approx 1$, the particle shows meandering-like trajectories. Finally, we have demonstrated the practical applicability of the core-shell magnetic particles by creating complex patterns with controlled fluctuations by using an external magnetic field.

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• Living matter & active matter
• Self-propelled janus particles
• Janus particles
• Magnetic colloids
• Self-propelled particles
• Langevin equation
• Magnetization measurements
• Optical microscopy
• Scanning transmission electron microscopy
• Transmission electron microscopy