Multiscale modelling of magnetostatic effects on magnetic nanoparticles with application to hyperthermia

TL;DR

This paper develops a multiscale micromagnetic simulation method incorporating magnetostatic effects to study magnetic nanoparticles used in hyperthermia, revealing effective parameters and interaction approximations at clinically relevant scales.

Contribution

It introduces an extended renormalization group-based coarse-graining method that accurately models magnetostatic interactions in magnetic nanoparticles for hyperthermia applications.

Findings

Effective uniaxial anisotropy and saturation magnetization differ from bulk materials.

Dipole approximation suffices for NP interactions beyond 1.5 times the diameter.

Optimal time step scales linearly with micromagnetic cell volume.

Abstract

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.