  The Arrhenius law predicts the transition time between equilibrium states in
physical systems due to thermal activation, with broad applications in material
science, magnetic hyperthermia and paleomagnetism where it is used to estimate
the transition time and thermal stability of assemblies of magnetic
nanoparticles. Magnetite is a material of great importance in paleomagnetic
studies and magnetic hyperthermia but existing estimates of the attempt
frequency $f_0$ vary by several orders of magnitude in the range $10^7-10^{13}$
Hz, leading to significant uncertainty in their relaxation rate. Here we
present a dynamical method enabling full parameterization of the
Arrhenius-N\'eel law using atomistic spin dynamics. We determine the
temperature and volume dependence of the attempt frequency of magnetite
nanoparticles with cubic anisotropy and find a value of $f_0 = 0.562 \pm 0.059$
GHz at room temperature. For particles with enhanced anisotropy we find a
significant increase in the attempt frequency and a strong temperature
dependence suggesting an important role of anisotropy. The method is applicable
to a wide range of dynamical systems where different states can be clearly
identified and enables robust estimates of domain state stabilities, with
particular importance in the rapidly developing field of micromagnetic analysis
of paleomagnetic recordings where samples can be numerically reconstructed to
provide a better understanding of geomagnetic recording fidelity over
geological time scales.
