  We extend a renormalization group-based course-graining method for
micromagnetic simulations to include properly scaled magnetostatic
interactions. We apply the method in simulations of dynamic hysteresis loops at
clinically relevant sweep rates and at 310 K of iron oxide nanoparticles (NPs)
of the kind that have been used in preclinical studies of magnetic
hyperthermia. The coarse-graining method, along with a time scaling involving
sweep rate and Gilbert damping parameter, allow us to span length scales from
the unit cell to NPs approximately 50 nm in diameter with reasonable simulation
times. For both NPs and the nanorods composing them, we report effective
uniaxial anisotropy strengths and saturation magnetizations, which differ from
those of the bulk materials magnetite and maghemite of which they are made, on
account of the combined non-trivial effects of temperature, inter-rod exchange,
magnetostatic interactions and the degree of orientational order within the
nanorod composites. The effective parameters allow treating the NPs as single
macrospins, and we find for the test case of calculating loops for two aligned
NPs that using the dipole approximation is sufficient for distances beyond 1.5
times the NP diameter. We also present a study on relating integration time
step to micromagnetic cell size, finding that the optimal time step size scales
approximately linearly with cell volume.
