Coarse-graining in micromagnetic simulations of dynamic hysteresis loops

Abstract

We use micromagnetic simulations based on the stochastic Landau–Lifshitz–Gilbert equation to calculate dynamic magnetic hysteresis loops at finite temperature that are invariant with simulation cell size. As a test case, we simulate a magnetite nanorod, the building block of magnetic nanoparticles that have been employed in preclinical studies of hyperthermia. With the goal to effectively simulate loops for large iron-oxide-based systems at relatively slow sweep rates on the order of 1 Oe ns−1 or less, we modify and employ a previously derived renormalization group approach for coarse-graining (Grinstein and Koch 2003 Phys. Rev. Lett. 20 207201). The scaling algorithm is shown to produce nearly identical loops over several decades in the model cell volume. We also demonstrate sweep-rate scaling involving the Gilbert damping parameter that allows orders of magnitude speed-up of the loop calculations.