Magnetic Torque of Microfabricated Elements and Magnetotactic Bacteria

We present a thorough theoretical analysis of the magnetic torque on microfabricated elements with dimensions in the range of 100 to 500 {\mu}m and magneto-somes of magnetotactic bacteria of a few {\mu}m length. We derive simple equations for field dependent torque and magnetic shape anisotropy that can be readily used to replace the crude approximations commonly used. We illustrate and verify the theory on microfabricated elements and magnetotactic bacteria, by field depedent torque magnetometry and by observing their rotation in water under application of a rotating magnetic field. The maximum rotation frequency of the largest microfabricated elements agrees within error boundaries with theory. For smaller, and especially thinner, elements the measured frequencies are a factor of three to four too low. We suspect this is caused by incomplete saturation of the magnetisation in the elements, which is not incorporated in our model. The maximum rotation frequency of magnetotactic bacteria agrees with our model within error margins, which are however quite big due to the large spread in bacteria morphology. The model presented provides a solid basis for the analysis of experiments with magnetic objects in liquid, which is for instance the case in the field of medical microrobotics.