Magnetic nanoparticle hyperthermia is an attractive emerging cancer treatment, but the acting microscopic energy deposition mechanisms are not well understood and optimization suffers. We describe several approximate forms for the characteristic time of N{e}el rotations with varying properties and external influences. We then present stochastic simulations that show agreement between the approximate expressions and the micromagnetic model. The simulations show nonlinear imaginary responses and associated relaxational hysteresis due to the field and frequency dependencies of the magnetization. This suggests efficient heating is possible by matching fields to particles instead of resorting to maximizing the power of the applied magnetic fields.
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