Physical bounds on velocities in soft magnetic microswimmers

Magnetic microswimmers are being studied for their biomedical applications and manipulation and sensing abilities in microscales. We study rigid magnetic microswimmers propelled rotationally using a rotating magnetic field as a commonly examined class of these microswimmers. Based on current understanding of paramagnetic and hard ferromagnetic swimmers, it is commonly thought that higher velocities can generally be achieved by increasing the magnetic field magnitude. Here we investigate, instead, soft magnetic microswimmers, and show analytically that there is a maximum limit for velocity depending on the material's property and geometry. We also perform numerical simulations demonstrating this effect for two examples: first, a helical microswimmer with an ellipsoidal head, which has a relatively simple magnetization model, and second, a helical microswimmer with a thin square plate head, which is similar to several experimental realizations of magnetic microswimmers.