Analytical solution demonstrates nonlinear rotation effects in spherical magnetic particles, highlighting implications for imaging and hyperthermia.
Abstract The application of a weak rotating magnetic field to magnetic particles, that show only Brownian dynamics and are suspended in a liquid leads to a nonlinear rotation if the magnetic field is not strong enough to overcome the rotational friction at the applied frequency. In this paper, the analytical solution to the equation of motion is derived for the case of negligible angular momentum and no random thermal interactions. The former is an accurate approximation in all typical applications such as magnetic particle imaging or magnetic particle based hyperthermia. Having a closed solution for the theoretical edge case, where random thermal interactions go to zero, can be used as a verification tool for more generalized particle simulations and it can also be used as a basis for constructing approximations for more general cases.
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Kampf et al. (2025) studied this question.
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