Elementary excitations of ferromagnetic metal nanoparticles

We present a theory of the elementary spin excitations in transition-metal ferromagnet nanoparticles which achieves a unified and consistent quantum description of both collective and quasiparticle physics. The theory starts by recognizing the essential role played by spin-orbit interactions in determining the energies of ferromagnetic resonances in the collective excitation spectrum and the strength of their coupling to low-energy particle-hole excitations. We argue that a crossover between Landau-damped ferromagnetic resonance and pure-state collective magnetic excitations occurs as the number of atoms in typical transition-metal ferromagnet nanoparticles drops below approximately 10(4), about where the single-particle level spacing, delta, becomes larger than rootalphaE(res), where E-res is the ferromagnetic resonance frequency and alpha is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semirealistic model Hamiltonians, which we solve numerically for nanoparticles containing several hundred atoms. For small nanoparticles, we find one isolated ferromagnetic resonance collective mode below the lowest particle-hole excitation energy, at E(res)approximate to0.1 meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As delta approaches rootalphaE(res), the ferromagnetic collective excitation is more likely to couple strongly with discrete particle-hole excitations. In this regime the distinction between the two types of excitations blurs. We discuss the significance of this picture for the interpretation of recent single-electron tunneling experiments.