Fe₃O₄ nanoparticles are one of the most promising candidates for biomedical applications such as magnetic hyperthermia and theranostics due to their bio-compatibility, structural stability and good magnetic properties. However, much is unknown about the nanoscale origins of the observed magnetic properties of particles due to the dominance of surface and finite size effects. Here we have developed an atomistic spin model of elongated magnetite nanocrystals to specifically address the role of faceting and elongation on the magnetic shape anisotropy. We find that for faceted particles simple analytical formulae overestimate the magnetic shape anisotropy and that the underlying cubic anisotropy makes a significant contribution to the energy barrier for moderately elongated particles. Our results enable a better estimation of the effective magnetic anisotropy of highly crystalline magnetite nanoparticles and is a step towards quantitative prediction of the heating effects of magnetic nanoparticles.

铁₃ O ₄纳米颗粒由于其生物相容性，结构稳定性和良好的磁性能而成为生物医学应用如磁热疗和治疗学最有希望的候选者之一。然而，由于表面和有限尺寸效应的支配性，关于所观察到的颗粒的磁性的纳米尺度起源还不清楚。在这里，我们已经开发了细长磁铁矿纳米晶体的原子自旋模型，以专门解决刻面和延伸对磁性形状各向异性的作用。我们发现，对于刻面颗粒，简单的分析公式会高估磁形状各向异性，而基本的立方各向异性则对中等伸长颗粒的能垒产生了重大影响。