Energy contributions in magnetite nanoparticles: computation of magnetic phase diagram, theory, and simulation

In this study, we present a theoretical analysis of magnetization processes by considering energy contributions in magnetite fine particles. The focus is on the K _S-driven magnetic phase transition taking place between the low surface-anisotropy ferrimagnetic state and the hedgehog configuration obtained in the high surface-anisotropy limit. Analytical expressions of energy terms (exchange, magnetocrystalline anisotropy, surface-anisotropy) are presented and their magnitudes are computed for different particle sizes. Monte Carlo simulations were also carried out for comparison purposes. A core–shell model is implemented for simulating magnetite nanoparticles between 2 and 10 nm in diameter. Our simulation framework is based on a three-dimensional classical Heisenberg-like Hamiltonian with nearest magnetic neighbors interactions. It includes exchange coupling, cubic magnetocrystalline anisotropy for core ions, and single-ion site surface-anisotropy for those atoms belonging to the shell. The magnetic phase diagram and comparisons between analytical and numerical results are presented and discussed.