Monte Carlo simulations are used to investigate the effect of surface anisotropy on the spin configurations and hysteresis loops of ferromagnetic nanoparticles. Spherical particles of radius $\rho a$ are composed of $N$ atoms located on a simple cubic lattice with interatomic spacing $a$. The particles have $2⩽\rho ⩽13$. A classical Heisenberg model is assumed, with surface and bulk anisotropy. When surface anisotropy is positive there are two types of ground states separated by a large energy barrier: a “throttled” configuration with reduced magnetization for intermediate values of surface anisotropy and a “hedgehog” configuration with zero magnetization in the strong surface anisotropy limit. Beyond a threshold, surface anisotropy of either sign induces ⟨111⟩ easy axes for the net magnetization. Easy-axis hysteresis loops are then square, with a continuous approach to saturation, and the effective anisotropy is deduced either from the switching field or from the initial slope of the perpendicular magnetization curve. The hedgehog state shows a stepwise magnetization curve involving $\rho$ discrete configurations, and it passes to a throttled configuration before saturating. The hysteresis loop has the unusual feature that it involves a state in the first quadrant, which lies on the reversible initial magnetization curve; it is possible to recover the zero-field cooled state after saturation. A survey of the exchange and anisotropy parameters for a range of ferromagnetic materials indicates that the effects of surface anisotropy on the spin configuration should be most evident in nanoparticles of ferromagnetic actinide compounds such as US, and rare-earth metals and alloys with Curie points below room temperature; the effects in nanoparticles of $3d$ ferromagnets and their alloys are usually insignificant, with the possible exception of FePt.

• Received 7 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.104431