  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.
