Elementary Excitations of Ferromagnetic Metal Nanoparticles

Abstract

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 $10^4$, approximately where the single-particle level spacing, $\delta$, becomes larger than, $\sqrt{\alpha }{E}_{\mathrm{res}}$, where $E_{\mathrm{res}}$ is the ferromagnetic resonance frequency and $\alpha$ is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semi-realistic 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 $E_{\mathrm{res}}\approx 0.1$ meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As $\delta$ approaches $\sqrt{\alpha }{E}_{\mathrm{res}}$, 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.

19 pages, 13 figures

References in corpus (9)

• Spectroscopy of discrete energy levels in ultrasmall metallic grains
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• Magnetic Anisotropy Variations and Non-Equilibrium Tunneling in a Cobalt Nanoparticle
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• A Model for Ferromagnetic Nanograins with Discrete Electronic States
• Magnetization orientation dependence of the quasiparticle spectrum and hysteresis in ferromagnetic metal nanoparticles
• Nonequilibrium excitations in Ferromagnetic Nanoparticles
• Chern Numbers for Spin Models of Transition Metal Nanomagnets
• Microscopic relaxation mechanisms and linear magnetization dynamics

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• Anisotropy in Ferromagnetic Nanoparticles: Level-to-Level Fluctuations of a Collective Effect
• Strong spin-orbit induced Gilbert damping and g-shift in iron-platinum nanoparticles
• The Interplay of Charge and Spin in Quantum Dots: The Ising Case
• Detecting and Switching Magnetization of Stoner Nanograin in Non-local Spin Valve
• Mesoscopic bound on anisotropy in itinerant ferromagnets
• Landau-Zener quantum tunneling in disordered nanomagnets
• Spin Waves and Switching: The Dynamics of Exchange - Biased Co Core - CoO Shell Nanoparticles