Size Dependence of Nanoparticle Magnetization

The magnetization of noninteracting metallic nanoparticles is investigated by comparing the particle-size and temperature dependences of the magnetization for several mechanisms. The nanoparticle magnetization deviates from that of the underlying bulk materials due to zero-temperature and thermal effects, and on a mean-field level, the corresponding surface-core interaction is described by a Landau-Ginzburg approach. A major factor is the reduced atomic coordination at the surface, which has often, but not always, opposite effects on the zero-temperature magnetization and Curie temperatures. The coordination effect is particularly pronounced for very weak itinerant ferromagnets and for strongly exchange-enhanced Pauli paramagnets. With regard to external magnetic fields, the nanoparticle magnetization involves several “superparamagnetic” phenomena, namely, Néel relaxation, Brownian relaxation, and Langevin macrospin paramagnetism.