Electron-Magnon Coupling and Nonlinear Tunneling Transport in Magnetic Nanoparticles

Abstract

We present a theory of single-electron tunneling transport through a ferromagnetic nanoparticle in which particle-hole excitations are coupled to spin collective modes. The model employed to describe the interaction between quasiparticles and collective excitations captures the salient features of a recent microscopic study. Our analysis of nonlinear quantum transport in the regime of weak coupling to the external electrodes is based on a rate-equation formalism for the nonequilibrium occupation probability of the nanoparticle many-body states. For strong electron-boson coupling, we find that the tunneling conductance as a function of bias voltage is characterized by a large and dense set of resonances. Their magnetic field dependence in the large-field regime is linear, with slopes of the same sign. Both features are in agreement with recent tunneling experiments.Metallic nanoparticles are among the best physical realizations of the concept of Fermi liquid introduced by Landau more than fifty years ago. Their discrete lowenergy spectra can be put in a one-to-one correspondence with those of corresponding noninteracting electron systems. Single-electron tunneling spectroscopy [1] in normal-metal nanograins provides a vivid example of Landau's enormous simplification of interacting Fermi systems. Most of the interesting phenomena studied in these experiments can indeed be understood in terms of the quantum mechanics of confined noninteracting quasiparticles. If the grain is made of a ferromagnetic transition-metal material, however, the discrete resonant spectrum seen in tunneling experiments [2,3] is far more complex than the one predicted in an independent particle picture, and indicates that the quasiparticle states are coupled to the collective magnetic moment of the grain. Since ferromagnetic transition metals, in addition to Landau's particle-hole (p-h) excitations, support low-energy collective spin excitations, it is reasonable to assume that tunneling transport through ferromagnetic nanoparticles involves some kind of spin excitations that are the finitesystem analogue of the familiar spin-waves or magnons of bulk ferromagnets. So far attempts of including spin collective modes in tunneling transport based on a simple toy model [4,5,6] have explained only in part the rich phenomena seen in experiment.In this paper we present a theoretical study of singleelectron tunneling transport through a ferromagnetic metal nanoparticle based on a model that captures the salient features of its elementary excitations -p-h and spin collective -as derived from a recent microscopic study [7]. A few remarkable features seen in experiment emerge in a very transparent and direct way from our treatment of the electron-magnon coupling. We find that when a low-energy p-h excitation is strongly coupled to one of the spin collective modes, the tunneling differential conductance versus bias voltage displays an enhanced density of resonances with spacings smaller than the independent-electron energy mean-level spacing δ. The depe...

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