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The Arrhenius law predicts the transition time between equilibrium states inphysical systems due to thermal activation, with broad applications in materialscience, magnetic hyperthermia and paleomagnetism where it is used to estimatethe transition time and thermal stability of assemblies of magneticnanoparticles. Magnetite is a material of great importance in paleomagneticstudies and magnetic hyperthermia but existing estimates of the attemptfrequency $f_0$ vary by several orders of magnitude in the range $10^7-10^{13}$Hz, leading to significant uncertainty in their relaxation rate. Here wepresent a dynamical method enabling full parameterization of theArrhenius-N\'eel law using atomistic spin dynamics. We determine thetemperature and volume dependence of the attempt frequency of magnetitenanoparticles 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 asignificant increase in the attempt frequency and a strong temperaturedependence suggesting an important role of anisotropy. The method is applicableto a wide range of dynamical systems where different states can be clearlyidentified and enables robust estimates of domain state stabilities, withparticular importance in the rapidly developing field of micromagnetic analysisof paleomagnetic recordings where samples can be numerically reconstructed toprovide a better understanding of geomagnetic recording fidelity overgeological time scales.

Atomistic calculation of the f0 attempt frequency in Fe3O4 magnetite nanoparticles